Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\n
We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\n
Throughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\n
We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
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\r\n\tGlycosylation is an important and very precisely regulated biological event of protein processing within the cellular environment. This mega event plays a crucial role in ascertaining protein structure, function, fate, and ligand-receptor association. The glycosylation process also has a significant role in several human diseases. The present book will provide deep insights into non-enzymatic glycosylation events in the cells and how biomacromolecules like proteins, lipids, and nucleic acids get affected by this event.
\r\n
\r\n\tThis book also puts light on the various categories of glycosylation like N-linked, O-linked, C-linked, and phosphoserine glycosylation events that are involved in disease biology and its pathogenesis. The frontier part of this book gives newer treatment approaches by targeting glycosylation to treat human diseases like diabetes and its associated micro-vascular and macro-vascular complication, cancer, viral hepatitis B, Gaucher disease, etc. This book will provide a complete package of glycosylation fundamentals for the healthcare system, clinicians, and researchers.
",isbn:"978-1-83969-135-5",printIsbn:"978-1-83969-134-8",pdfIsbn:"978-1-83969-136-2",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"f1f82214d3d5460d3b52c4d8e87e3858",bookSignature:"Dr. Alok Raghav and Dr. Jamal Ahmad",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10219.jpg",keywords:"N Linked, O Linked, C Linked, Nucleic Acids, Proteins, Lipids, Diabetes Mellitus, Diabetic Retinopathy, Diabetic Nephropathy, Cancer, Hepatitis B, Gaucher Disease",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 23rd 2020",dateEndSecondStepPublish:"December 21st 2020",dateEndThirdStepPublish:"February 19th 2021",dateEndFourthStepPublish:"May 10th 2021",dateEndFifthStepPublish:"July 9th 2021",remainingDaysToSecondStep:"a month",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Alok Raghav is a motivational, visionary independent researcher with a meticulous understanding of glycosylation, holding editorial positions in reputed International journals, and an honorary fellow of the Indian Association of Nanoscience and Nanotechnology. His research focuses on designing new targets against glycosylation using a nanotechnology approach to treat human diseases.",coeditorOneBiosketch:"Dr. Jamal Ahmad is an expert endocrinologist equipped with knowledge and experience of diabetes and its understanding. He is a former Dean Faculty of Medicine and a recipient of the RSSDI award, and a Lifetime Achievement Award by Diabetes India 2019. He has made a significant contribution toward determining the role of protein glycation in diabetes and its associated complications.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"334465",title:"Dr.",name:"Alok",middleName:null,surname:"Raghav",slug:"alok-raghav",fullName:"Alok Raghav",profilePictureURL:"https://mts.intechopen.com/storage/users/334465/images/system/334465.jpg",biography:"Alok Raghav is an Research Scientist at Multidisciplinary Research Unit, Ganesh Shankar Vidyarthi Medical College, Kanpur, India. He has completed his PhD and postdoctorate research on albumin protein glycation in diabetes and its associated complications and has extensive research experience in the field of medical science and healthcare. His research focuses on the designing new targets against glycosylation using nanotechnology approach. to treat human diseases. He has published more than 40 research papers in International peer reviewed journals and has presented his work at various reputed national and International conferences. He is also recipient of prestigious Endocrine Society Award, USA and honorary fellow of Indian Association of Nanoscience and Nanotechnology. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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1. Introduction
New processing routes for metal-matrix functionally graded materials (FGMs) and structures through combinations of powder metallurgy and casting are described in this chapter. FGMs are well known as a relatively new class of inhomogeneous composite materials having property gradient. The property gradient in the FGMs is caused by a position-dependent chemical composition, microstructure, or atomic order [1]. These FGMs are generally fabricated based on powder metallurgy, melt-processing technique, chemical vapor deposition, physical vapor deposition and so on.
Figure 1.
A schematic illustration showing a typical fabrication process of FGMs by the powder metallurgy method through spark plasma sintering (SPS).
Figure 1 shows a schematic illustration of a typical fabrication process of FGMs by the powder metallurgy method through spark plasma sintering (SPS). At first, mixed powders with various ratios of materials A and B are prepared. Predesigned mixed powders are stacked inside a die for the SPS as shown in Figure 1. The case of six-graded composition layers is shown in Figure 1. The number of graded layers can be freely chosen. Then, FGMs with stepwise graded structure can be obtained by sintering these powders with an SPS machine. Ti–ZrO2 FGMs with stepwise graded structure were fabricated by this method in our previous study [2]. A continuous graded structure can also be obtained by this method with a green body having continuous graded composition. For example, Ti–ZrO2 FGMs were fabricated by this method in our previous studies [3, 4].
The melt-processing technique is also an effective way to fabricate continuous graded structure. In terms of melt-processing techniques to fabricate metal-based FGMs, various kinds of centrifugal method were developed: centrifugal casting [5–7], centrifugal solid-particle method [8, 9], centrifugal in situ method [10, 11], and so on. The centrifugal casting is a processing method that uses centrifugal force caused by rotation of a mold. By the centrifugal force in the rotating mold including molten metal and solid particles, compositional gradient due to the difference of the material densities between the molten metal and the solid particles is generated. By controlling these phenomena, FGMs can be fabricated. Basically, both the centrifugal solid-particle method and the centrifugal in-situ method are based on the centrifugal casting. The centrifugal solid-particle method can be conducted at a temperature of liquid–solid coexistence in alloy systems, such as Al–Ti [8, 9]. On the other hand, the centrifugal in-situ method can be made at a temperature of liquid phase in alloy systems, such as Al–Ni [10] and Al–Cu [11]. By using these processing techniques, various kinds of FGMs having specific graded distributions of reinforcement can be made.
As new melt processing techniques, centrifugal mixed-powder method [12–15] and centrifugal sintered-casting method [16, 17] have been recently developed. These two melt processing techniques are introduced in this chapter. Applications of metal-matrix FGMs processed by the centrifugal sintered-casting are also described. Fabricated metal-matrix FGMs can be used as grinding wheel and applied to carbon fiber-reinforced plastic (CFRP) machining [17].
2. Materials processing
2.1. Centrifugal mixed-powder method
Many attempts to fabricate FGMs have been done by the centrifugal casting [5–7]. Generally, the finer dispersed particle size becomes, the more difficult to disperse them into molten matrix. The equation for velocity of a solid particle in a viscous liquid can be written as:
dxdt=|ρp−ρm|GgDp218ηE1
where ρp is density of particles, ρm density of molten matrix, g gravitational acceleration, Dp particle diameter, and η viscosity of melt [7]. Since the velocity of a solid particle in a viscous liquid is dependent on the square of the particle diameter Dp, it is quite difficult to control graded distributions of dispersion nanoparticles in FGMs in the case of the conventional centrifugal casting. As a new processing technique for metal-matrix FGMs, the centrifugal mixed-powder method is proposed by Watanabe et al. [12] for overcoming these problems. The centrifugal mixed-powder method could give us fine particle-dispersed FGMs by using a combination of high centrifugal force and mixed powder. This new method is a developed technique of the centrifugal casting by setting predesigned mixed powder in a mold in advance [12].
Figure 2.
A schematic illustration showing the process of the centrifugal mixed-powder method [12].
Figure 2 shows the experimental procedure of the centrifugal mixed-powder method. At first, a predesigned mixed powder is prepared. This mixed powder consists of metal-matrix particles and dispersion particles. Basically, the melting point of dispersion particles should be higher than that of metal-matrix particles to form FGMs. Particles such as ceramics, metals, and alloys that have higher melting points compared with metal matrix can be chosen as dispersion particles for metal-matrix FGMs. The mixed powder including metal-matrix particles and dispersion particles is inserted into a spinning mold as shown in Figure 2(a). After that, a metal-matrix ingot is melted in a crucible. This molten metal matrix is poured into the spinning mold as shown in Figure 2(b). The poured molten metal matrix penetrates into the space between the particles due to the applied centrifugal force as shown in Figure 2(c). The heat from the poured molten matrix melts the metal-matrix particles as shown in Figure 2(d). Finally, ring- or disc-shaped FGMs or structures having dispersion particles distributed in the outer part of the cast sample can be obtained as shown in Figure 2(e). FGMs, such as Cu/SiC [12], Al/TiO2 [12], and Al/Al3Ti/Ti [15], were obtained with this processing method in our previous studies.
Figure 3.
A typical appearance of vacuum centrifugal casting machine.
The centrifugal mixed-powder method can also be performed by using centrifugal casting machines which are commercially available. Figure 3 shows a typical appearance of vacuum centrifugal casting machine supplied by Yasui & Co, Japan. This centrifugal casting machine has a heating coil, a straight arm, a crucible, a mold, and a balancer inside the casting chamber [18]. By setting predesigned mixed powder in the mold in advance, FGMs can be obtained. By using this processing method, Cu/diamond [13], Al alloy/diamond [14], and the other FGMs were fabricated in our previous studies. Detailed processing method and microstructural characterization of fabricated Cu/diamond FGMs are shown below.
Figure 4.
A cross-sectional drawing of a mold for centrifugal casting.
A cross-sectional drawing of a mold for centrifugal casting is shown in Figure 4. The mold has a cylindrical casting pattern with 40 mm width and 22.8 mm diameter. A cylindrical core with 15 mm width and 12 mm diameter is also attached in the mold as shown in Figure 4. Since fabricated FGMs can be applied to grinding wheel for mechanical machining as described in Section 3, these pattern and core are required. Dendritic-shaped Cu particles in the mean particle diameter of approximately 22 μm and 100/120 mesh diamond particles (149 μm in JIS B 4130) were used. Both the particles were mixed in a mortar. The volume fraction of diamond to Cu was chosen as 25 vol.%. The mixed powder was inserted into the mold as shown in Figure 4. Then, molten Cu was cast into the spinning mold by applying centrifugal force with the vacuum centrifugal casting machine in vacuum at 1473 K and 1573 K. The mold was spun for 99 s. The calculated applied G number (ratio of centrifugal force to gravity) at the top of mold along the direction of centrifugal force was about 36 G.
Figure 5.
Cu/diamond FGMs fabricated by the centrifugal mixed-powder method. Casting temperatures were 1473 K (a) and 1573 K (b) [13].
Figure 5 shows Cu/diamond FGMs cast at 1473 K (Fig. 5a) and 1573 K (Fig. 5b) [13]. As these samples were fabricated for an application as grinding wheel, these cast samples have hollows for attaching pulley. It was observed that consolidated mixed-powder area kept leaning to the right side of the cast sample, that is, the position of maximum centrifugal force as shown in Figure 5. Since density of diamond (3.52 Mg/m3) was smaller than that of molten Cu (8.00 Mg/m3), a little amount of diamond particles were distributed around surface at sprue side due to the molten metal flow. A graded structure should be made by this difference of density between diamond and Cu.
Figure 6.
A backscattered electron compositional image showing a cross section of the Cu-based diamond graded cast sample obtained by the centrifugal mixed-powder method [13].
Cross-sectional observations were carried out with scanning electron microscope (SEM) to investigate diamond dispersion behavior after casting at 1473 K. Figure 6 shows a backscattered electron compositional image showing a cross section of the Cu-based diamond graded cast sample fabricated without pulley hollow [13]. Diamond particles were distinguished from Cu matrix as black colored area in the sample. It should be noted that the distribution of diamond particles in the inner part of the cast sample also biased to the top side (right side) as shown in Figure 6. It was also confirmed that obvious traces or boundaries of Cu particles were not observed although voids were seen around some diamond particles. Therefore, Cu particles in the predesigned mixed powder were fully melted and fused each other due to heat transfer from the poured molten Cu.
Figure 7.
The number of diamond particles as a function of distance from the top of Cu/diamond cast sample [13].
Figure 8.
The particle diameter as a function of distance from the top of Cu/diamond cast sample [13].
The number of diamond particles and the mean diameter of diamond particles at each divided area along the direction of centrifugal force were measured. The results are shown in Figures 7 and 8, respectively. These data were taken from the cross-sectional image of the cast sample as shown in Figure 6. In Figure 7, the number of diamond particles was drastically decreased at around 3 mm from the top, where the mixed powder was inserted before the centrifugal casting. The result indicates that the mixed powder was compressed and immobilized by pressure of molten metal due to centrifugal force. Whereas diamond particles were sufficiently immobilized by Cu particles between diamond particles, graded distribution of diamond particles was successfully obtained. Within the diamond particles densely dispersed region between 0 and 3 mm from the top of the Cu/diamond cast sample, the number of diamond particles increased with approaching to the top of the Cu/diamond cast sample. Thus, the Cu/diamond FGMs were successfully fabricated by the centrifugal mixed-powder method. On the other hand, the particle diameter distribution between 0 and 3 mm is almost homogeneous as shown in Figure 8. The mean diameters of diamond particles in this range are 80–100 μm. In the distance from the top, between 3 and 5 mm, particle diameter distribution is also homogeneous. However, the mean diameters of diamond particles in this range are 30–40 μm. These results may suggest that collision of Cu molten metal with the mixed powder at surface of the powder area washed away part of the diamond particles, and molten Cu flow sent it to the surface at the sprue side. This phenomenon is not appropriate for production of FGMs. To overcome this problem, a modified processing method is described in the next section.
2.2. Centrifugal sintered-casting method
As the latest processing method for metal-matrix FGMs developed by our research group, centrifugal sintered-casting method is shown in this section. The centrifugal sintered-casting method is a modified processing technique of the centrifugal mixed-powder method. In the centrifugal sintered-casting method, FGMs are processed by the combination of centrifugal sintering and centrifugal casting [16, 17]. As described in Section 2.1, the centrifugal mixed-powder method enables us to fabricate metal-matrix FGMs. Especially, the centrifugal mixed-powder method is an effective way to fabricate metal-matrix FGMs reinforced with nanoparticles [12]. However, predesigned powder mixtures tended to flow away during the centrifugal casting in the case of some combinations of powders in the centrifugal mixed-powder method. As an attempt to overcome this problem, the centrifugal sintered-casting method is developed through the combination of centrifugal sintering and centrifugal casting.
Figure 9.
A schematic illustration showing the process of the centrifugal sintered-casting method [17].
Figure 9 shows a schematic illustration of the process of the centrifugal sintered-casting method [17]. In the centrifugal sintered-casting method, a ring-shaped metal-matrix preform with dispersed particles is produced by the centrifugal sintering at first. Predesigned mixed powder of dispersion particles and metal-matrix particles is inserted into a spinning mold as shown in Figure 9(a). Basically, the melting point of dispersion particles should be higher than that of metal-matrix particles to form FGMs in this method as well. Subsequently, the mixed powder is sintered under centrifugal force by heating coils to fabricate a preform as shown in Figure 9(b). Then, molten metal matrix is poured into the fabricated preform by the centrifugal casting to obtain metal-matrix FGMs as shown in Figure 9(c). The molten metal matrix penetrates into the space between the particles by the applied centrifugal force as shown in Figure 9(d). At the same time, the metal matrix particles are melted by the heat from the molten metal matrix. Finally, ring- or disc-shaped FGMs with dispersed particles distributed in the outer part of the samples can be obtained as shown in Figure 9(e).
In our previous studies, Al–Si and Cu were selected as metal matrix to fabricate Al–Si alloy/diamond and Cu/diamond FGMs, respectively [16, 17]. Al–Si alloy particles and Cu particles were uniformly mixed with diamond particles, respectively. The volume fraction of diamond particles in mixed powder was chosen as 10 vol.%. The predesigned mixed powder was set in the cylindrical mold having a rotational axis of 20 mm diameter and 30 mm length, respectively. The mixed powders were sintered in the spinning cylindrical mold under the centrifugal force of about 280 G at 843 K in argon atmosphere for Al–Si alloy/diamond particles [16] and 1100 G at 1273 K in vacuum for Cu/diamond particles [17], respectively. Then, the centrifugal casting was performed under the centrifugal force of about 78 G at 1373 K with pouring molten Al in the case of Al–Si alloy/diamond preform [16]. In the same way, molten Cu was poured into the Cu/diamond preform in the mold under the centrifugal force of about 34 G at 1393 K [17].
Figure 10.
Macrographs of Al–Si alloy based (a) and Cu-based (b) FGMs with dispersed diamond particles fabricated by the centrifugal sintered-casting method and SEM images showing the microstructures of the outer part of the cast samples [16, 17].
Figure 10 shows macrographs of Al–Si alloy and Cu-based FGMs with dispersed diamond particles fabricated by the centrifugal sintered-casting method. SEM images showing the microstructures of the outer part of the Al–Si alloy and Cu-based FGMs are also shown in Figure 10. It should be noted that the diamond particles were distributed at only outer part of the cast samples as shown in Figure 10. The centrifugal sintered-casting method is an effective way to fabricate metal-matrix FGMs.
3. Applications of FGMs processed by the centrifugal sintered-casting
In this section, applications of metal-matrix FGMs processed by the centrifugal sintered-casting method are introduced. As described in Section 2.2, Al–Si alloy/diamond and Cu/diamond FGMs were fabricated by the centrifugal sintered-casting method. Diamond plays important role as abrasive in the field of mechanical machining. Recently, CFRP is widely used as main structural parts for aircraft due to its high strength, stiffness, and lightweight [19]. However, some issues about occurring defects, such as fiber pullout, delamination, burrs, and splintering, have become problems in machining CFRP by common drills. These technical issues have led numerous researchers to seek solutions for precision machining of CFRP [20–23]. The key issue of precision machining of CFRP has been obtaining good hole quality in the aircraft industry. In addition, tool change is frequently required in drilling CFRP in many practical situations. Therefore, the improvement of tool life for machining CFRP is important subject since high-priced diamond grains have been widely used as abrasive.
Figure 11.
A schematic illustration of the gyro-driving grinding wheel system [24].
A novel CFRP machining equipment, that is, gyro-driving grinding wheel system for machining CFRP was recently developed [24–26]. The gyro-driving grinding wheel system was developed for overcoming problems related to defect issues during mechanical machining. Figure 11 shows a schematic illustration of the gyro-driving grinding wheel system [24]. In the gyro-driving grinding wheel system, a grinding wheel is used instead of drill bits for drilling CFRP. The equipped grinding wheels required toughness as a desirable mechanical property as the grinding wheel was subjected to the torsion force in the gyro-driving grinding wheel system. In the previous studies [17, 24], holes with good quality in CFRP plates have been obtained without defects by this machining system equipped with our fabricated metal-matrix FGMs.
CFRP drilling tests were performed with the gyro-driving grinding wheel system equipped with fabricated Cu/diamond FGMs as a grinding wheel. Cu was selected as metal matrix for its mechanical properties and high thermal conductivity. Diamond particles were used as abrasive in Cu matrix for machining CFRP. CFRP drilling tests were carried out with feed rate of 5 mm/min, peripheral wheel speed of 7000 rpm, spindle speed of 2800 rpm, and dry machining. Bidirectional CFRP composite laminates having thickness of 5 mm were used as workpiece material. Photographs of a hole having diameter of 20 mm drilled by the gyro-driving grinding wheel system equipped with fabricated Cu/diamond FGMs as a grinding wheel (Fig. 12a) and the one having diameter of 10 mm drilled by a conventional drill bit (Fig. 12b) in CFRP plates are shown in Figure 12. Delamination and burrs were seen in the drilled CFRP plate in the case of the conventional drill bit. It should be noted that precision drilling of CFRP plate without burring and delamination were achieved by the gyro-driving grinding wheel system equipped with fabricated Cu/diamond FGMs as grinding wheel. In this way, FGMs fabricated by the centrifugal sintered-casting method have been attempted to apply for the practical use.
Figure 12.
Drilled hole having diameter of 20 mm made by the gyro-driving grinding wheel system equipped with fabricated Cu/diamond FGMs as a grinding wheel (a) and the one having diameter of 10 mm made by a conventional drill bit (b) in CFRP plates [17].
As the other possibilities for application of FGMs, materials for heat sink can be considered as candidate. Nowadays, thermal management materials such as heat sink for microelectronics and semiconductors have been investigated, extensively [27–30]. The materials currently used for heat sinks are Al and Cu due to their high thermal conductivity in metals and alloys. The thermal conductivities of Al and Cu are about 250 and 400 W m−1 K−1, respectively. On the other hand, diamond is well known as the material having the highest thermal conductivity in materials. To enhance the thermal conductivity of heat sink materials, Al/diamond and Cu/diamond composites are promising materials. Our Al alloy/diamond and Cu/diamond FGMs fabricated by the centrifugal sintered-casting method might work as well in this field.
4. Summary
Two kinds of new processing routes for metal-matrix FGMs through combinations of powder metallurgy and casting were developed: the centrifugal mixed-powder method and the centrifugal sintered-casting method. Metal-matrix FGMs were obtained by these two methods. These processing methods enable us to overcome existing problems in the conventional fabrication process of FGMs. Fabricated FGMs were also applied to machining CFRP as an attempt for the practical use. Continued studies for fabrication processes of FGMs and the gyro-driving grinding wheel system are still required to put them into practical use in the future. Further investigations should open up a new field of and a market for FGMs.
Acknowledgments
The authors would like to acknowledge financial supports by the Regional Innovation Cluster Program (Global Type) “Tokai Region Nanotechnology Manufacturing Cluster” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. The authors would like to thank Mr. Hideaki Tsuge, Industrial Research Institute of Gifu Prefecture, for use of the gyro-driving grinding wheel system and his valuable inputs. The authors are grateful to Ms. Motoko Yamada, Nagoya Institute of Technology, for her assistance in parts of experiments.
\n',keywords:"Functionally graded materials (FGMs), Metal-matrix composite, Powder metallurgy, Centrifugal sintering, Centrifugal casting",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/50078.pdf",chapterXML:"https://mts.intechopen.com/source/xml/50078.xml",downloadPdfUrl:"/chapter/pdf-download/50078",previewPdfUrl:"/chapter/pdf-preview/50078",totalDownloads:1801,totalViews:415,totalCrossrefCites:1,totalDimensionsCites:6,hasAltmetrics:0,dateSubmitted:"May 22nd 2015",dateReviewed:"February 4th 2016",datePrePublished:null,datePublished:"March 31st 2016",dateFinished:null,readingETA:"0",abstract:"New processing routes for metal-matrix functionally graded materials (FGMs) and structures through combinations of powder metallurgy and casting are described in this chapter. Centrifugal mixed-powder method is introduced as a processing method for metal-matrix FGMs at first. The centrifugal mixed-powder method is a developed technique of centrifugal casting by setting predesigned mixed powder in a spinning mold in advance. As an example of processed FGMs by this method in our previous studies, Cu-based FGMs with dispersed diamond particles are shown. Graded structures in the Cu-based FGMs are investigated through scanning electron microscope (SEM) observations of microstructures. As the latest processing method for metal-matrix FGMs developed by our research group, centrifugal sintered-casting method is shown. The centrifugal sintered-casting method is a modified processing technique of the centrifugal mixed-powder method. In the centrifugal sintered-casting method, FGMs are processed by the combination of centrifugal sintering and centrifugal casting. Al–Si alloy and Cu-based FGMs with dispersed diamond particles are introduced as examples. Applications of metal-matrix FGMs processed by the centrifugal sintered-casting method are also described. Fabricated metal-matrix FGMs can be used as grinding wheel and applied to carbon fiber-reinforced plastic (CFRP) machining.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/50078",risUrl:"/chapter/ris/50078",book:{slug:"advances-in-functionally-graded-materials-and-structures"},signatures:"Takahiro Kunimine, Hisashi Sato, Eri Miura-Fujiwara and Yoshimi\nWatanabe",authors:[{id:"41301",title:"Prof.",name:"Yoshimi",middleName:null,surname:"Watanabe",fullName:"Yoshimi Watanabe",slug:"yoshimi-watanabe",email:"yoshimi@nitech.ac.jp",position:null,institution:null},{id:"88513",title:"Prof.",name:"Hisashi",middleName:null,surname:"Sato",fullName:"Hisashi Sato",slug:"hisashi-sato",email:"sato.hisashi@nitech.ac.jp",position:null,institution:{name:"Nagoya Institute of Technology",institutionURL:null,country:{name:"Japan"}}},{id:"176971",title:"Dr.",name:"Takahiro",middleName:null,surname:"Kunimine",fullName:"Takahiro Kunimine",slug:"takahiro-kunimine",email:"kuniminet9@gmail.com",position:null,institution:{name:"Kyoto University",institutionURL:null,country:{name:"Japan"}}},{id:"178446",title:"Prof.",name:"Eri",middleName:null,surname:"Miura-Fujiwara",fullName:"Eri Miura-Fujiwara",slug:"eri-miura-fujiwara",email:"emiura@eng.u-hyogo.ac.jp",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Materials processing",level:"1"},{id:"sec_2_2",title:"2.1. Centrifugal mixed-powder method",level:"2"},{id:"sec_3_2",title:"2.2. Centrifugal sintered-casting method",level:"2"},{id:"sec_5",title:"3. Applications of FGMs processed by the centrifugal sintered-casting",level:"1"},{id:"sec_6",title:"4. Summary",level:"1"},{id:"sec_7",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Kieback B, Neubrand A, Riedel H. Processing techniques for functionally graded materials. Materials Science and Engineering A. 2003;362:81–105. DOI:10.1016/S0921-5093(03)00578-1.'},{id:"B2",body:'Tsukamoto H, Kunimine T, Yamada M, Sato H, Watanabe Y. Microstructure and mechanical properties of Ti-ZrO2 composites fabricated by spark plasma sintering. Key Engineering Materials. 2012;520:269–275. DOI:10.4028/www.scientific.net/KEM.520.269.'},{id:"B3",body:'Watanabe Y, Miura-Fujiwara E, Sato H. 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1. Introduction
The rapid development of technology has led to the registration of many processes in an electronic environment, the storage of these records, and the accessibility of these records when requested. With the evolving technology such as cloud computing, big data, the accumulation of a large amount of data stored in databases, and the process of parsing and screening useful information made data mining necessary.
It is possible to examine the data which are kept in databases and reach to huge amounts of size every second, in two parts according to their changes in time: static and temporal. Data is called the static data when its feature values do not change with time, if the feature comprise values change with time then it is called the temporal or time-series data.
Today, with the increase in processor speed and the development of storage technologies, real-world applications can easily record changing data over time.
Time-series analysis is a trend study subject because of its prevalence in various fields ranging from science, engineering, bioinformatics, finance, and government to health-care applications [1, 2, 3]. Data analysts are looking for the answers of such questions: Why does the data change this way? Are there any patterns? Which series show similar patterns? etc. Subsequence matching, indexing, anomaly detection, motif discovery, and clustering of the data are the answers of some questions [4]. Clustering, which is one of the most important concepts of data mining, defines its structure by separating unlabeled data sets into homogeneous groups. Many general-purpose clustering algorithms are used for the clustering of time-series data, either by directly or by evolving. Algorithm selection depends entirely on the purpose of the application and on the properties of the data such as sales data, exchange rates in finance, gene expression data, image data for face recognition, etc.
In the age of informatics, the analysis of multidimensional data that has emerged as part of the digital transformation in every field has gained considerable importance. These data can be from data received at different times from one or more sensors, stock data, or call records to a call center. This type of data, that is, observing the movement of a variable over time, where the results of the observation are distributed according to time, is called time-series data. Time-series analysis is used for many purposes such as future forecasts, anomaly detection, subsequence matching, clustering, motif discovery, indexing, etc. Within the scope of this study, the methods developed for the time-series data clustering which are important for every field of digital life in three main sections. In the first section, the proposed methods for the preparation of multidimensional data for clustering (dimension reduction) in the literature are categorized. In the second section, the similarity criteria to be used when deciding on the objects to be assigned to the related cluster are classified. In the third section, clustering algorithms of time-series data are examined under five main headings according to the method used. In the last part of the study, the use of time-series clustering in bioinformatics which is one of the favorite areas is included.
2. Time-series clustering approaches
There are many different categorizations of time-series clustering approaches. Such as, time-series clustering approaches can be examined in three main sections according to the characteristics of the data used whether they process directly on raw data, indirectly with features extracted from the raw data, or indirectly with models built from the raw data [5]. Another category is according to the clustering method: shape-based, feature-based, and model-based [6]. But whatever the categorization is, for any time-series clustering approach, the main points to be considered are: how to measure the similarity between time series; how to compress the series or reduce dimension and what algorithm to use for cluster. Therefore, this chapter examines time-series clustering approaches according to three main building blocks: data representation methods, distance measurements, and clustering algorithms (Figure 1).
Figure 1.
Time-series clustering.
2.1 Data representation
Data representation is one of the main challenging issues for time-series clustering. Because, time-series data are much larger than memory size [7, 8] that increases the need for high processor power and time for the clustering process increases exponentially. In addition, the time-series data are multidimensional, which is a difficulty for many clustering algorithms to handle, and it slows down the calculation of the similarity measurement. Consequently, it is very important for time-series data to represent the data without slowing down the algorithm execution time and without a significant data loss. Therefore, some requirements can be listed for any data representation methods [9]:
Significantly reduce the data size/dimensionality,
Maintain the local and global shape characteristics of the time series,
Acceptable computational cost,
Reasonable level of reconstruction from the reduced representation,
Insensitivity to noise or implicit noise handling.
Dimension reduction is one of the most frequently used methods in the literature [7, 10, 11, 12] for the data representation.
Definition:
The representation of a time series T with length n is a model T̅ with reduced dimensions, so that T approximates T [13]. Dimension reduction or feature extraction is a very useful method for reducing the number of variables/attributes or units in multivariate statistical analyzes so that the number of attributes can be reduced to a number that “can handle.”
Due to the noisy and high-dimensional features of many time-series data, data representations have been studied and generally examined in four main sections: data adaptive, nondata adaptive, model-based, and data dictated [6].
Data adaptive methods that have changing parameters according to processing time-series data. Methods in this category try to minimize global reconstruction error by using unequal length segments. Although it is difficult to compare several time series, this method approximates each series better. Some of the popular data adaptive representation methods are: Symbolic Aggregate Approximation (SAX) [14], Adaptive Piecewise Constant Approximation (APCA) [15], Piecewise Linear Approximation (PLA) [16], Singular Value Decomposition (SVD) [17, 18], and Symbolic Natural Language (NLG) [19].
Non-data adaptive methods are use fix-size parameters for the representing time-series data. Following methods are shown among non-data adaptive representation methods: Discrete Fourier Transform (DFT) [18], Discrete Wavelet Transform (DWT) [20, 21, 22], Discrete Cosine Transformation (DCT) [17], Perceptually Important Point (PIP) [23], Piecewise Aggregate Approximation (PAA) [24], Chebyshev Polynomials (CHEB) [25], Random Mapping [26], and Indexable Piecewise Linear Approximation (IPLA) [27].
Model-based methods assume that observed time series was produced by an underlying model. The real issue here is to find the parameters that produce this model. Two time series produced by the same set of parameters using the underlying model are considered similar. Some of the model-based methods can be listed as: Auto-regressive Moving Average (ARMA) [28, 29], Time-Series Bitmaps [30], and Hidden Markov Model (HMM) [31, 32, 33].
Data dictated methods automatically determine the dimension reduction rate but in the three methods mentioned above, the dimension reduction rates are automatically determined by the user. The most common example of data dictated method is clipped data [34, 35, 36].
Many representation methods for time-series data are proposed and each of them offering different trade-offs between the aforementioned requirements. The correct selection of the representation method plays a major role in the effectiveness and usability of the application to be performed.
2.2 Similarity/distance measure
In particular, the similarity measure is the most essential ingredient of time-series clustering.
The similarity or distance for the time-series clustering is approximately calculated, not based on the exact match as in traditional clustering methods. It requires to use distance function to compare two time series. In other words, the similarity of the time series is not calculated, it is estimated. If the estimated distance is large, the similarity between the time series is less and vice versa.
Definition:
Similarity between two “n” sized time series T = {t1,t2,….tn} and U = {u1,u2,….un} is the length of the path connecting pair of points [11]. This distance is the measure of similarity. D (T, U) is a function that takes two times series (T, U) as input and calculates their distance “d”.
Metrics to be used in clustering must cope with the problems caused by common features of time-series data such as noise, temporal drift, longitudinal scaling, offset translation, linear drift, discontinuities, and amplitude scaling. Various methods have been developed for similarity measure, and the method to choose is problem specific. These methods can be grouped under three main headings: similarity in time, similarity in shape, and similarity in change.
2.2.1 Similarity in time
The similarity between the series is that they are highly time dependent. Such a measure is costly for the raw time series, so a preprocessing or transformation is required beforehand [34, 36].
2.2.2 Similarity in shape
Clustering algorithms that use similarity in shape measure, assigns time series containing similar patterns to the same cluster. Independently of the time, it does not care how many times the pattern exists [37, 38].
2.2.3 Similarity in change
The result of using this metric is time-series clusters that have the similar autocorrelation structure. Besides, it is not a suitable metric for short time series [29, 39, 40].
2.3 Clustering algorithms
The process of separating groups according to similarities of data is called “clustering.” There are two basic principles: the similarity within the cluster is the highest and the similarity between the clusters is the least. Clustering is done on the basis of the characteristics of the data and using multivariate statistical methods. When dividing data into clusters, the similarities/distances of the data to each other are measured according to the specification of the data (discrete, continuous, nominal, ordinal, etc.)
Han and Kamber [41] classify the general-purpose clustering algorithms which are actually designed for static data in five main sections: partition-based, hierarchical-based, density-based, grid-based, and model-based. Besides these, a wide variety of algorithms has been developed for time-series data. However, some of these algorithms (ignore minor differences) intend to directly use the methods developed for static data without changing the algorithm by transforming it into a static data form from temporal data. Some approaches apply a preprocessing step on the data to be clustered before using the clustering algorithm. This preprocessing step converts the raw-time-series data into feature vectors using dimension reduction techniques, or converts them into parameters of a specified model [42].
Definition:
Given a dataset on n time series T = {t1, t2,…., tn}, time-series clustering is the process of partitioning of T into C = {C1,C2,….,Ck} according to certain similarity criterion. Ci is called “cluster” where,
T=⋃i=1kCiandCi⋂Cj=∅fori≠jE1
In this section, previously developed clustering algorithms will be categorized. Some of these algorithms work directly with raw time-series data, while others use the data presentation techniques that are previously mentioned.
Clustering algorithms are generally classified as: partitioning, hierarchical, graph-based, model-based, and density-based clustering.
2.3.1 Partitioning clustering
The K-means [43] algorithm is a typical partition-based clustering algorithm such that the data are divided into a number of predefined sets by optimizing the predefined criteria. The most important advantage is its simplicity and speed. So it can be applied to large data sets. However, the algorithm may not produce the same result in each run and cannot handle the outlier. Self-organizing map [44] is stronger than the noisy data clustering from K-means. The user is prompted to enter the cluster number and grid sets. It is difficult to determine the number of clusters for time-series data. Other examples of partition-based clustering are CLARANS [45] and K-medoids [46]. In addition, the partitioning approach is suitable for low-dimensional, well-separated data. However, time-series data are multidimensional and often contain intersections, embedded clusters.
In essence, these algorithms act as n-dimensional vectors to time-series data and applies distance or correlation functions to determine the amount of similarity between two series. Euclidean distance, Manhattan distance, and Pearson correlation coefficient are the most commonly used functions.
2.3.2 Hierarchical clustering
Contrary to the partitioning approach, which aims segmenting data that do not intersect, the hierarchical approach produces a hierarchical series of nested clusters that can be represented graphically (dendrogram, tree-like diagram). The branches of the dendrogram show the similarity between the clusters as well as the knowledge of the shaping of the clusters. Determined number of clusters can be obtained by cutting the dendrogram at a certain level.
Hierarchical clustering methods [47, 48, 49] are based on the separating clusters into subgroups that are processed step by step as a whole, or the stepwise integration of individual clusters into a cluster [50]. Hierarchical clustering methods are divided into two methods: agglomerative clustering methods and divisive hierarchical clustering methods according to the creation of the dendrogram.
In agglomerative hierarchical clustering methods, each observation is initially treated as an independent cluster, and then repeatedly, until each individual observation obtains a single set of all observations, thereby forming a cluster with the closest observation.
In the divisive hierarchical clustering methods, initially all observations are evaluated as a single cluster and then repeatedly separated in such a way that each observation is separated from the farthest observation to form a new cluster. This process continues until all the observations create a single cluster.
Hierarchical clustering not only forms a group of similar series but also provides a graphical representation of the data. Graphical presentation allows the user to have an overall view of the data and an idea of data distribution. However, a small change in the data set leads to large changes in the hierarchical dendrogram. Another drawback is high computational complexity.
2.3.3 Density-based clustering
The density-based clustering approach is based on the concepts of density and attraction of objects. The idea is to create clusters of dense multi-dimensional areas where objects attract each other. In the core of dense areas, objects are very close together and crowded. The objects in the walls of the clusters were scattered less frequently than the core. In other words, density-based clustering determines dense areas of object space. The clusters are dense areas which are separated by rare dense areas. DBSCAN [51] and OPTICS [52] algorithms are the most known of density-based clustering examples.
The density-based approach is robust for noisy environments. The method also deals with outliers when defining embedded clusters. However, density-based clustering techniques cause difficulties due to high computational complexity and input parameter dependency when the dimensional index structure is not used.
2.3.4 Model-based clustering
The model-based approach [53, 54, 55] uses a statistical infrastructure to model the cluster structure of the time-series data. It is assumed that the underlying probability distributions of the data come from the final mixture. Model-based algorithms usually try to estimate the likelihood of the model parameters by applying some statistical techniques such as Expectation Maximization (EM). The EM algorithm iterates between an “E-step,” which computes a matrix z such that zik is an estimate of the conditional probability that observation i belongs to group k given the current parameter estimates, and an “M-step,” which computes maximum likelihood parameter estimates given z. Each data object is assigned to a cluster with the highest probability until the EM algorithm converges, so as to maximize likelihood for the entirety of the grant.
The most important advantage of the model-based approach is to estimate the probability that i. observation belongs to k. cluster. In some cases, the time series is likely to belong to more than one cluster. For such time-series data, the probability-giving function of the approach is the reason for preference. In this approach, it is assumed that the data set has a certain distribution but this assumption is not always correct.
2.3.5 Grid-based clustering
In this approach, grids made up of square cells are used to examine the data space. It is independent of the number of objects in the database due to the used grid structure. The most typical example is STING [56], which uses various levels of quadrilateral cells at different levels of resolution. It precalculates and records statistical information about the properties of each cell. The query process usually begins with a high-level hierarchical structure. For each cell at the current level, the confidence interval, which reflects the cell’s query relation, is computed. Unrelated cells are exempt from the next steps. The query process continues for the corresponding cells in the lower level until reaching the lowest layer.
After analyzing the data set and obtaining the clustering solution, there is no guarantee of the significance and reliability of the results. The data will be clustered even if there is no natural grouping. Therefore, whether the clustering solution obtained is different from the random solution should be determined by applying some tests. Some methods developed to test the quality of clustering solutions are classified into two types: external index and internal index.
The external index is the most commonly used clustering evaluation method also known as external validation, external criterion. The ground truth is the goal clusters, usually created by experts. This index measures how well the target clusters and the resulting clusters overlap. Entropy, Adjusted Rand Index (ARI), F-measure, Jaccard Score, Fowlkes and Mallows Index (FM), and Cluster Similarity Measure (CSM) are the most known external indexes.
The internal indexes evaluate clustering results using the features of data sets and meta-data without any external information. These are often used in cases where the correct solutions are not known. Sum of squared error is one of the most used internal methods which the distance to the nearest cluster determines the error. So clusters with similar time series are expected to give lower error values. Distance between two clusters (CD) index, root-mean-square standard deviation (RMSSTD), Silhouette index, R-squared index, Hubert-Levin index, semi-partial R-squared (SPR) index, weighted inter-intra index, homogeneity index, and separation index are the common internal indexes.
2.3.6 Clustering algorithm example: FunFEM
The funFEM algorithm [55, 57] allows to cluster time series or, more generally, functional data. FunFem is based on a discriminative functional mixture model (DFM) which allows the clustering of the curves (data) in a functional subspace. If the observed curves are {x1,x2…xn}, FunFem aims cluster into K homogenous groups. It assumes that there exists an unobserved random variable Z = {z1,z2…zn} ∈01k, if x belongs to group k, Zk is defined as 1 otherwise 0. The clustering task goal is to predict the value zi = (zi1,… zik) of Z for each observed curve xi, for i = 1…n. The FunFem algorithm alternates, over the three steps of Fisher EM algorithm [57] (“F-step,” “E-Step” and “M-step”) to decide group memberships of Z = {z1,z2…zn}. In other words, from 12 defined discriminative functional mixture (DFM) models, Fisher-EM decides which data fit the best. The Fisher-EM algorithm alternates between three steps:
an E step in which posterior probabilities that observations belong to the K groups are computed,
an F step that estimates the orientation matrix U of the discriminative latent space conditionally to the posterior probabilities,
an M step in which parameters of the mixture model are estimated in the latent subspace by maximizing the conditional expectation of the complete likelihood.
Fisher-EM algorithm updates the parameters repeatedly until the Aitken criterion is provided. Aitken criterion estimates the asymptotic maximum of the log-likelihood in order to detect in advance the algorithm converge [57]. In model-based clustering, a model is defined by its number of component/cluster K and its parameterization. In model selection task, several models are reviewed while selecting the most appropriate model for the considered data.
FunFEM allows to choose between AIC (Akaike Information Criterion) [58], BIC (Bayesian information criteria) [59], and ICL (Integrated Completed Likelihood) [60] when deciding the number of clusters. The penalty terms are: γM2logn in the BIC criterion, γM in the AIC criterion, and ∑i=1n∑k=1Ktiklogtik in the ICL criterion. Here, M indicates the number of parameters in the model, n is the number of observations, K is the number of clusters, and tik is the probability of ith observation belonging to kth cluster.
FunFem is implemented in R programming languages and serves as a function [61]. The algorithm is applied on a time series gene expression data in the following section. Input of the algorithm is gene expression data which is given in Table 1. The table shows the gene expression values measured as a result of the microarray experiment. The measurement was performed at six different times for each gene. The data were taken from the GEO database (GSE2241) [62]. FunFEM method is decided, and the best model is DkBk with K = 4 (bic = −152654.5) for input data. As a result, method assigned each gene to the appropriate cluster which is determined by the algorithm. Table 2 demonstrates the gene symbol and cluster number. As a result, method assigned each gene to the appropriate cluster which is determined by the algorithm (Table 2).
Gene Symbol
TP1
TP2
TP3
TP4
TP5
TP6
AADAC
18.4
29.7
30
79.7
86.7
163.2
AAK1
253.2
141.8
49.2
118.7
145.2
126.7
AAMP
490
340.9
109.1
198.4
210.5
212
AANAT
5.6
1.4
3.7
3.1
1.6
4.9
AARS
1770
793.6
226.5
1008.9
713.3
1253.7
AASDHPPT
940.1
570.5
167.2
268.6
683
263.5
AASS
10.9
1.9
1.5
4.1
19.7
25.5
AATF
543.4
520.1
114.5
305.7
354.2
384.9
AATK
124.5
74.5
17
25.6
64.6
13.6
.
.
.
.
.
.
.
.
.
.
.
.
.
.
ZP2
4.1
1.4
0.8
1.4
1.4
3
ZPBP
23.4
13.7
7
7.8
22.3
26.9
ZW10
517.1
374.5
72.6
240.8
345.7
333.1
ZWINT
1245.4
983.4
495.3
597.4
1074.3
620.7
ZYX
721.6
554.9
135.5
631.5
330.9
706.8
ZZEF1
90.5
49.3
18.6
66.7
10.4
52.2
ZZZ3
457.3
317.1
93
243.2
657.5
443
Table 1.
Input data of the FunFEM algorithm.
Gene symbol
Cluster number
AADAC
2
AAK1
3
AAMP
3
AANAT
1
AARS
4
AASDHPPT
3
AASS
1
AATF
3
AATK
2
.
.
.
.
ZP2
1
ZPBP
1
ZW10
3
ZWINT
4
ZYX
4
ZZEF1
2
ZZZ3
3
Table 2.
Output data of the FunFEM algorithm.
3. Clustering approaches for gene expression data clustering
The approach to be taken depends on the application area and the characteristics of the data. For this reason, as a case study, the clustering of gene expression data, which is a special area of clustering of time-series data, will be examined in this section. Microarray is the technology which measures the expression levels of large numbers of genes simultaneously. DNA microarray technology overcomes traditional approaches in the identification of gene copies in a genome, in the identification of nucleotide polymorphisms and mutations, and in the discovery and development of new drugs. It is used as a diagnostic tool for diseases. DNA microarrays are widely used to classify gene expression changes in cancer cells.
The gene expression time series (gene profile) is a set of data generated by measuring expression levels at different cases/times in a single sample. Gene expression time series have two main characteristics, short and unevenly sampled. In The Stanford Microarray database, more than 80% of the time-series experiments contains less than 9 time points [63]. Observations below 50 are considered to be quite short for statistical analysis. Gene expression time-series data are separated from other time-series data by this characteristics (business, finance, etc.). In addition to these characteristics, three basic similarity requirements can be identified for the gene expression time series: scaling and shifting, unevenly distributed sampling points, and shape (internal structure) [64]. Scaling and shifting problems arise due to two reasons: (i) the expression of genes with a common sequence is similar, but in this case, the genes need not have the same level of expression at the same time. (ii) Microarray technology, which is often corrected by normalization. The scaling and shifting factor in the expression level may hide similar expressions and should not be taken into account when measuring the similarity between the two expression profiles. Sampling interval length is informative and cannot be ignored in similarity comparisons. In microarray experiments, the density change characterizes the shape of the expression profile rather than the density of the gene expression. The internal structure can be represented by deterministic function, symbols describing the series, or statistical models.
There are many popular clustering techniques for gene expression data. The common goal of all is to explain the different functional roles of the genes that play a key biological process. Genes expressed in a similar way may have a similar functional role in the process [65].
In addition to all these approaches, it is possible to examine the cluster of gene expression data in three different classes as gene-based clustering, sample-based clustering, and subspace clustering (Figure 2) [66]. In gene-based clustering, genes are treated as objects, instances (time-point/patient-intact) as features. Sample-based clustering is exactly the opposite: samples are treated as objects, genes as features. The distinction between these two clustering approaches is based on the basic characterization of the clustering process used for gene expression data. Some clustering algorithms, such as K-means and hierarchical approach, can be used to cluster both genes and fragments of samples. In the molecular biology, “any function in the cell is carried out with the participation of a small subset of genes, and the cellular function only occurs on a small sample subset.” With this idea, genes and samples are handled symmetrically in subspace clustering; gene or sample, object or features.
Figure 2.
Gene expression data clustering approaches.
In gene-based clustering, the aim is to group the co-expressed genes together. However, due to the complex nature of microarray experiments, gene expression data often contain high amounts of noise, characterizing features such as gene expression data often linked to each other (clusters often have a high intersection ratio), and some problems arising from constraints from the biological domain.
Also, among biologists who will use microarray data, the relationship between genes or clusters that are usually related to each other within the cluster, rather than the clusters of genes, is a more favorite subject. That is, it is also important for the algorithm to make graphical presentations not just clusters. K-means, self-organizing maps (SOM), hierarchical clustering, graph-theoretic approach, model-based clustering, and density-based approach (DHC) are the examples of gene-based clustering algorithms.
The goal of the sample-based approach is to find the phenotype structure or the sub-structure of the sample. The phenotypes of the samples studied [67] can only be distinguished by small gene subsets whose expression levels are highly correlated with cluster discrimination. These genes are called informative genes. Other genes in the expression matrix have no role in the decomposition of the samples and are considered noise in the database. Traditional clustering algorithms, such as K-means, SOM, and hierarchical clustering, can be applied directly to clustering samples taking all genes as features. The ratio of the promoter genes to the nonrelated genes (noise ratio) is usually 1:10. This also hinders the reliability of the clustering algorithm. These methods are used to identify the informative genes. Selection of the informative genes is examined in two different categories as supervised and unsupervised. The supervised approach is used in cases where phenotype information such as “patient” and “healthy” is added. In this example, the classifier containing only the informative genes is constructed using this information. The supervised approach is often used by biologists to identify informative genes. In the unsupervised approach, no label specifying the phenotype of the samples is placed. The lack of labeling and therefore the fact that the informative genes do not guide clustering makes the unsupervised approach more complicated. There are two problems that need to be addressed in the unsupervised approach: (i) the high number of genes versus the limited number of samples and (ii) the vast majority of collected genes are irrelevant. Two strategies can be mentioned for these problems in the unsupervised approach: unsupervised gene selection and clustering. In unsupervised gene selection, gene selection and sample clustering are treated as two separate processes. First, the gene size is reduced, and then classical clustering algorithms are applied. Since there is no training set, the choice of gene is based solely on statistical models that analyze the variance of gene expression data. Associated clustering dynamically supports the combination of repetitive clustering and gene selection processes by the use of the relationship between genes and samples. After many repetitions, the sample fragments converge to the real sample structure and the selected genes are likely candidates for the informative gene cluster.
When subspace clustering is applied to gene expression vectors, it is treated as a “block” consisting of clusters of genes and subclasses of experimental conditions. The expression pattern of the genes in the same block is consistent under the condition in that block. Different greedy heuristic approaches have been adapted to approximate optimal solution.
Subspace clustering was first described by Agrawal et al. in 1998 on general data mining [68]. In subspace clustering, two subspace sets may share the same objects and properties, while some objects may not belong to any subspace set. Subspace clustering methods usually define a model to determine the target block and then search in the gen-sample space. Some examples of subspatial cluster methods proposed for gene expression are biclustering [69], coupled two way clustering (CTWC) [70], and plaid model [71].
According to different clustering criteria, data can be clustered such as the co-expressing gene groups, the samples belonging to the same phenotype or genes from the same biological process. However, even if the same criteria are used in different clustering algorithms, the data can be clustered in different forms. For this reason, it is necessary to select more suitable algorithm for data distribution.
4. Conclusions
Clustering for time-series data is used as an effective method for data analysis of many areas from social media usage and financial data to bioinformatics. There are various methods introduced for time-series data. Which approach is chosen is specific to the application. The application is determined by the needs such as time, speed, reliability, storage, and so on. When determining the approach to clustering, three basic issues need to be decided: data representation, similarity measure, and clustering algorithm.
The data representation involves transforming the multi-dimensional and noisy structure of the time-series data into a less dimensional that best expresses the whole data. The most commonly used method for this purpose is dimension reduction or feature extraction.
It is challenging to measure the similarity of two time series. The chapter has been examined similarity measures in three sections as similarity in shape, similarity in time, and similarity in change.
For the time-series clustering algorithms, it is not wrong to say that the evolution of conventional clustering algorithms. Therefore, the classification of traditional clustering algorithms (developed for static data) has been included. It is classified as partitioning, hierarchical, model-based, grid-based, and density-based. Partition algorithms initially require prototypes. The accuracy of the algorithm depends on the defined prototype and updated method. However, they are successful in finding similar series and clustering time series with equal length. The fact that the number of clusters is not given as the initial parameter is a prominent and well-known feature of hierarchical algorithms. At the same time, works on time series that are not of equal length causes it to be one step ahead of other algorithms. However, hierarchical algorithms are not suitable for large data sets due to the complexity of the calculation and the scalability problem. Model-based algorithms suffer from problems such as initialization of parameters based on user predictions and slow processing time for large databases. Density-based algorithms are not generally preferred over time-series data due to their high working complexity. Each approach has pros and cons compared to each other, and the choice of algorithm for time-series clustering varies completely according to the characteristics of the data and the needs of the application. Therefore, in the last chapter, a study on the clustering of gene expression data, which is a specific field of application, has been mentioned.
In time-series data clustering, there is a need for algorithms that execute fast, accurate, and with less memory on large data sets that can meet today’s needs.
\n',keywords:"time-series data, data mining, data representation, similarity measure, clustering algorithms, gene expression data clustering",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/65772.pdf",chapterXML:"https://mts.intechopen.com/source/xml/65772.xml",downloadPdfUrl:"/chapter/pdf-download/65772",previewPdfUrl:"/chapter/pdf-preview/65772",totalDownloads:887,totalViews:0,totalCrossrefCites:1,dateSubmitted:"June 12th 2018",dateReviewed:"January 17th 2019",datePrePublished:"February 3rd 2020",datePublished:"January 20th 2021",dateFinished:"February 21st 2019",readingETA:"0",abstract:"The process of separating groups according to similarities of data is called “clustering.” There are two basic principles: (i) the similarity is the highest within a cluster and (ii) similarity between the clusters is the least. Time-series data are unlabeled data obtained from different periods of a process or from more than one process. These data can be gathered from many different areas that include engineering, science, business, finance, health care, government, and so on. Given the unlabeled time-series data, it usually results in the grouping of the series with similar characteristics. Time-series clustering methods are examined in three main sections: data representation, similarity measure, and clustering algorithm. The scope of this chapter includes the taxonomy of time-series data clustering and the clustering of gene expression data as a case study.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/65772",risUrl:"/chapter/ris/65772",signatures:"Esma Ergüner Özkoç",book:{id:"9961",title:"Data Mining",subtitle:"Methods, Applications and Systems",fullTitle:"Data Mining - Methods, Applications and Systems",slug:"data-mining-methods-applications-and-systems",publishedDate:"January 20th 2021",bookSignature:"Derya Birant",coverURL:"https://cdn.intechopen.com/books/images_new/9961.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"15609",title:"Dr.",name:"Derya",middleName:null,surname:"Birant",slug:"derya-birant",fullName:"Derya Birant"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"262719",title:"Dr.",name:"Esma",middleName:null,surname:"Ergüner Özkoç",fullName:"Esma Ergüner Özkoç",slug:"esma-erguner-ozkoc",email:"eeozkoc@baskent.edu.tr",position:null,institution:{name:"Başkent University",institutionURL:null,country:{name:"Turkey"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Time-series clustering approaches",level:"1"},{id:"sec_2_2",title:"2.1 Data representation",level:"2"},{id:"sec_2_3",title:"Definition:",level:"3"},{id:"sec_4_2",title:"2.2 Similarity/distance measure",level:"2"},{id:"sec_4_3",title:"Definition:",level:"3"},{id:"sec_5_3",title:"2.2.1 Similarity in time",level:"3"},{id:"sec_6_3",title:"2.2.2 Similarity in shape",level:"3"},{id:"sec_7_3",title:"2.2.3 Similarity in change",level:"3"},{id:"sec_9_2",title:"2.3 Clustering algorithms",level:"2"},{id:"sec_9_3",title:"Definition:",level:"3"},{id:"sec_10_3",title:"2.3.1 Partitioning clustering",level:"3"},{id:"sec_11_3",title:"2.3.2 Hierarchical clustering",level:"3"},{id:"sec_12_3",title:"2.3.3 Density-based clustering",level:"3"},{id:"sec_13_3",title:"2.3.4 Model-based clustering",level:"3"},{id:"sec_14_3",title:"2.3.5 Grid-based clustering",level:"3"},{id:"sec_15_3",title:"Table 1.",level:"3"},{id:"sec_18",title:"3. 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IEEE Transactions on Knowledge and Data Engineering. 2004;16(11):1370-1386'},{id:"B67",body:'Golub TR, Slonim DK, Tamayo P, Huard C, Gaasenbeek M, Mesirov JP, et al. Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring. Science. 1999;286(5439):531-537'},{id:"B68",body:'Agrawal R, Gehrke J, Gunopulos D, Raghavan P. Automatic Subspace Clustering of High Dimensional Data for Data Mining Applications. ACM; 1998;27(2):94-105'},{id:"B69",body:'Cheng Y, Church GM. Biclustering of expression data. In: ISMB; 2000, Vol. 8, No. 2000. pp. 93-103'},{id:"B70",body:'Getz G, Levine E, Domany E. Coupled two-way clustering analysis of gene microarray data. Proceedings of the National Academy of Sciences. 2000;97(22):12079-12084'},{id:"B71",body:'Lazzeroni L, Owen A. Plaid models for gene expression data. 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