Computation of the number of params in the model CNN_UNIV_5.
\\n\\n
IntechOpen Book Series will also publish a program of research-driven Thematic Edited Volumes that focus on specific areas and allow for a more in-depth overview of a particular subject.
\\n\\nIntechOpen Book Series will be launching regularly to offer our authors and editors exciting opportunities to publish their research Open Access. We will begin by relaunching some of our existing Book Series in this innovative book format, and will expand in 2022 into rapidly growing research fields that are driving and advancing society.
\\n\\nLaunching 2021
\\n\\nArtificial Intelligence, ISSN 2633-1403
\\n\\nVeterinary Medicine and Science, ISSN 2632-0517
\\n\\nBiochemistry, ISSN 2632-0983
\\n\\nBiomedical Engineering, ISSN 2631-5343
\\n\\nInfectious Diseases, ISSN 2631-6188
\\n\\nPhysiology (Coming Soon)
\\n\\nDentistry (Coming Soon)
\\n\\nWe invite you to explore our IntechOpen Book Series, find the right publishing program for you and reach your desired audience in record time.
\\n\\nNote: Edited in October 2021
\\n"}]',published:!0,mainMedia:{caption:"",originalUrl:"/media/original/132"}},components:[{type:"htmlEditorComponent",content:'With the desire to make book publishing more relevant for the digital age and offer innovative Open Access publishing options, we are thrilled to announce the launch of our new publishing format: IntechOpen Book Series.
\n\nDesigned to cover fast-moving research fields in rapidly expanding areas, our Book Series feature a Topic structure allowing us to present the most relevant sub-disciplines. Book Series are headed by Series Editors, and a team of Topic Editors supported by international Editorial Board members. Topics are always open for submissions, with an Annual Volume published each calendar year.
\n\nAfter a robust peer-review process, accepted works are published quickly, thanks to Online First, ensuring research is made available to the scientific community without delay.
\n\nOur innovative Book Series format brings you:
\n\nIntechOpen Book Series will also publish a program of research-driven Thematic Edited Volumes that focus on specific areas and allow for a more in-depth overview of a particular subject.
\n\nIntechOpen Book Series will be launching regularly to offer our authors and editors exciting opportunities to publish their research Open Access. We will begin by relaunching some of our existing Book Series in this innovative book format, and will expand in 2022 into rapidly growing research fields that are driving and advancing society.
\n\nLaunching 2021
\n\nArtificial Intelligence, ISSN 2633-1403
\n\nVeterinary Medicine and Science, ISSN 2632-0517
\n\nBiochemistry, ISSN 2632-0983
\n\nBiomedical Engineering, ISSN 2631-5343
\n\nInfectious Diseases, ISSN 2631-6188
\n\nPhysiology (Coming Soon)
\n\nDentistry (Coming Soon)
\n\nWe invite you to explore our IntechOpen Book Series, find the right publishing program for you and reach your desired audience in record time.
\n\nNote: Edited in October 2021
\n'}],latestNews:[{slug:"intechopen-supports-asapbio-s-new-initiative-publish-your-reviews-20220729",title:"IntechOpen Supports ASAPbio’s New Initiative Publish Your Reviews"},{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"}]},book:{item:{type:"book",id:"8385",leadTitle:null,fullTitle:"Nanocrystalline Materials",title:"Nanocrystalline Materials",subtitle:null,reviewType:"peer-reviewed",abstract:'The term "nanocrystalline materials" relates to the sizes of structural elements. The range of application of these materials is huge, such as more efficient catalysts, films, magnetic materials, protective coatings, and biological and biomaterials. Many compounds and elements, if made on the nanoscale, behave quite differently from how they would have in their conventional state. The overall purpose of this book, "Nanocrystalline Materials", is to provide present selected advanced topics on nanocrystals, allowing the book to be a good resource for scholars and students of material science, nanotechnology, and physical chemistry.',isbn:"978-1-78985-594-4",printIsbn:"978-1-78985-593-7",pdfIsbn:"978-1-83880-274-5",doi:"10.5772/intechopen.78515",price:119,priceEur:129,priceUsd:155,slug:"nanocrystalline-materials",numberOfPages:130,isOpenForSubmission:!1,isInWos:null,isInBkci:!1,hash:"cf72d957868565da82cc4ad919e6c4d7",bookSignature:"Behrooz Movahedi",publishedDate:"February 5th 2020",coverURL:"https://cdn.intechopen.com/books/images_new/8385.jpg",numberOfDownloads:5674,numberOfWosCitations:3,numberOfCrossrefCitations:16,numberOfCrossrefCitationsByBook:0,numberOfDimensionsCitations:41,numberOfDimensionsCitationsByBook:0,hasAltmetrics:0,numberOfTotalCitations:60,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 6th 2019",dateEndSecondStepPublish:"March 27th 2019",dateEndThirdStepPublish:"May 26th 2019",dateEndFourthStepPublish:"August 14th 2019",dateEndFifthStepPublish:"October 13th 2019",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6,7",editedByType:"Edited by",kuFlag:!1,featuredMarkup:null,editors:[{id:"150371",title:"Prof.",name:"Behrooz",middleName:null,surname:"Movahedi",slug:"behrooz-movahedi",fullName:"Behrooz Movahedi",profilePictureURL:"https://mts.intechopen.com/storage/users/150371/images/system/150371.jpg",biography:"Dr. Behrooz Movahedi obtained his Ph.D degree in Materials Engineering at Isfahan University of Technology (IUT) in Iran in 2010. During this period, while on a sabbatical leave he visited the School of Materials Science and Engineering in Nanyang Technological University (NTU) in Singapore. After that he joined the Department of Nanotechnology Engineering in the University of Isfahan (UI) as an Associate Professor. Recently, he is the head of the Nanotechnology Engineering Department in Faculty of Advanced Sciences and Technologies. Dr. Behrooz Movahedi has over 10 years of experience in the nanotechnology, amorphous materials, optical ceramics and advanced thermal spray coatings for environmental and industrial applications. He was invited as a reviewer in some potential ISI journals such as Materials & Design, Journal of Alloys and Compounds, Surface and coatings Technology, Applied Surface Science, Materials Science & Engineering B, Ceramics International, Journal of Materials Engineering and Performance.",institutionString:"University of Isfahan",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"1",institution:null}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"208",title:"Material Science",slug:"nanotechnology-and-nanomaterials-material-science"}],chapters:[{id:"70447",title:"Introductory Chapter: Nanocrystalline Materials",doi:"10.5772/intechopen.90255",slug:"introductory-chapter-nanocrystalline-materials",totalDownloads:749,totalCrossrefCites:1,totalDimensionsCites:1,hasAltmetrics:0,abstract:null,signatures:"Behrooz Movahedi",downloadPdfUrl:"/chapter/pdf-download/70447",previewPdfUrl:"/chapter/pdf-preview/70447",authors:[{id:"92198",title:"Dr.",name:"Behrooz",surname:"Movahedi",slug:"behrooz-movahedi",fullName:"Behrooz Movahedi"}],corrections:null},{id:"67576",title:"Silicon Nanocrystals and Amorphous Nanoclusters in SiOx and SiNx: Atomic, Electronic Structure, and Memristor Effects",doi:"10.5772/intechopen.86508",slug:"silicon-nanocrystals-and-amorphous-nanoclusters-in-sio-sub-x-sub-and-sin-sub-x-sub-atomic-electronic",totalDownloads:914,totalCrossrefCites:1,totalDimensionsCites:1,hasAltmetrics:0,abstract:"Semiconductor nanocrystals in dielectric films are interesting from fundamental aspect, because quantum-size effects in them appear even at room temperature, so such objects can be called as “quantum dots”. Silicon nanocrystals and amorphous silicon nanoclusters in substoichiometric SiOx and SiNx films are traps for electrons and holes that apply in nonvolatile memory devices. In this chapter the formation of silicon nanocrystals and silicon amorphous nanoclusters in SiOx and SiNx films was studied using structural and optical methods. The phonon confinement model was refined to obtain sizes of silicon nanocrystals from analysis of Raman scattering data. Structural models that lead to nanoscale potential fluctuation in amorphous SiOx and SiNx are considered. A new structural model which is intermediate between random mixture and random bonding models is proposed. Memristor effects in SiOx films are discussed.",signatures:"Vladimir Volodin, Vladimir Gritsenko, Andrei Gismatulin and Albert Chin",downloadPdfUrl:"/chapter/pdf-download/67576",previewPdfUrl:"/chapter/pdf-preview/67576",authors:[{id:"295149",title:"Prof.",name:"Vladimir",surname:"Volodin",slug:"vladimir-volodin",fullName:"Vladimir Volodin"},{id:"299276",title:"Prof.",name:"Vladimir",surname:"Gritsenko",slug:"vladimir-gritsenko",fullName:"Vladimir Gritsenko"},{id:"317682",title:"Dr.",name:"Andrei",surname:"Gismatulin",slug:"andrei-gismatulin",fullName:"Andrei Gismatulin"},{id:"317683",title:"Dr.",name:"Albert",surname:"Chin",slug:"albert-chin",fullName:"Albert Chin"}],corrections:null},{id:"68155",title:"Ferrite-Based Nanoparticles Synthesized from Natural Iron Sand as the Fe3+ Ion Source",doi:"10.5772/intechopen.88027",slug:"ferrite-based-nanoparticles-synthesized-from-natural-iron-sand-as-the-fe-sup-3-sup-ion-source",totalDownloads:1136,totalCrossrefCites:0,totalDimensionsCites:2,hasAltmetrics:0,abstract:"Ferrite-based nanoparticles, namely, bismuth ferrite (BiFeO3) and calcium ferrite (CaFe4O7), have been synthesized via sol-gel and chemically dissolved method, respectively, employing hematite (α-Fe2O3) as the Fe3+ ion source. Firstly, α-Fe2O3 nanoparticles were prepared from natural iron sand containing mostly magnetite (Fe3O4) phase through coprecipitation technique continued by sintering process at 800°C for 2 h. Higher BiFeO3 phase content was achieved after Bi-Fe gel being annealed at 650°C for 1 h in air atmosphere. Furthermore, major phase of CaFe4O7 was formed with molar ratio of Fe3+/Ca2+ = 6 and sintering temperature of 800°C for 3 h. Interestingly, the powders with dominant CaFe4O7 phase, known as calcium biferrite, exhibit higher ferromagnetism at room temperature. The magnetic properties of the calcium biferrite are comparable to those of barium hexaferrite which can be applied for radar-absorbing material. Meanwhile, BiFeO3 powders also show weak room temperature ferromagnetism. It has also demonstrated that Ni doping in the bismuth ferrite (BiFe1−xNixO3 with x = 0.1) nanoparticles results in enhancement of the magnetic properties. Moreover, a ferroelectric hysteresis loop and a trend of frequency dependence of the dielectric constant have been observed, which were enhanced by Pb doping (Bi1−yPbyFeO3 with y = 0.1). These results suggest a multiferroic behavior in the BiFeO3 nanoparticles.",signatures:"Malik Anjelh Baqiya, Retno Asih, Muhammad Ghufron, Mastuki, Dwi Yuli Retnowati, Triwikantoro and Darminto",downloadPdfUrl:"/chapter/pdf-download/68155",previewPdfUrl:"/chapter/pdf-preview/68155",authors:[{id:"192041",title:"Prof.",name:"D",surname:"Darminto",slug:"d-darminto",fullName:"D Darminto"},{id:"192812",title:"Dr.",name:"Malik",surname:"Baqiya",slug:"malik-baqiya",fullName:"Malik Baqiya"},{id:"195349",title:"Dr.",name:"T.",surname:"Triwikantoro",slug:"t.-triwikantoro",fullName:"T. Triwikantoro"},{id:"299625",title:"Dr.",name:"Retno",surname:"Asih",slug:"retno-asih",fullName:"Retno Asih"},{id:"299626",title:"Mr.",name:"Muhammad",surname:"Gufron",slug:"muhammad-gufron",fullName:"Muhammad Gufron"},{id:"299627",title:"Ms.",name:"Dwi Yuli",surname:"Retnowati",slug:"dwi-yuli-retnowati",fullName:"Dwi Yuli Retnowati"},{id:"306331",title:"MSc.",name:"M",surname:"Mastuki",slug:"m-mastuki",fullName:"M Mastuki"}],corrections:null},{id:"67838",title:"Surface Plasmons in Oxide Semiconductor Nanoparticles: Effect of Size and Carrier Density",doi:"10.5772/intechopen.86999",slug:"surface-plasmons-in-oxide-semiconductor-nanoparticles-effect-of-size-and-carrier-density",totalDownloads:836,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,abstract:"Oxide semiconductors have received much attention for potential use in optoelectronic applications such as transparent electrodes, transistors, and emitting devices. Recently, new functionalities of oxide semiconductors have been discovered such as localized surface plasmon resonances (LSPRs), which show high-efficiency plasmon excitations in the infrared (IR) range using different structures such as nanorods, nanoparticles (NPs), and nanodots. In this chapter, we introduce optical properties of carrier- and size-dependent LSPRs in oxide semiconductor NPs based on In2O3: Sn (ITO). In particular, systematic examinations of carrier- and size-dependent LSPRs reveal the damping mechanisms on LSPR excitations of ITO NPs, which play an important role in determining excitation efficiency of LSPRs. Additionally, the control of carrier and size in the ITO NPs contribute toward improving solar-thermal shielding in the IR range. The high IR reflectance of assembled films of ITO NPs is due to three-dimensional plasmon coupling between the NPs, which is related to electron carriers and particle size of ITO NPs. This chapter provides new information concerning structural design when fabricating thermal-shielding materials based on LSPRs in oxide semiconductor NPs.",signatures:"Hiroaki Matsui",downloadPdfUrl:"/chapter/pdf-download/67838",previewPdfUrl:"/chapter/pdf-preview/67838",authors:[{id:"7227",title:"Dr.",name:"Hiroaki",surname:"Matsui",slug:"hiroaki-matsui",fullName:"Hiroaki Matsui"}],corrections:null},{id:"68946",title:"A Facile Method for Formulation of Atenolol Nanocrystal Drug with Enhanced Bioavailability",doi:"10.5772/intechopen.88191",slug:"a-facile-method-for-formulation-of-atenolol-nanocrystal-drug-with-enhanced-bioavailability",totalDownloads:733,totalCrossrefCites:1,totalDimensionsCites:2,hasAltmetrics:0,abstract:"Atenolol is a commonly used antihypertensive drug of class III BCS category. The objective of the present study is to enhance the permeability of atenolol by using a suitable technique which is economical and devoid of using any organic solvents. The nanocrystal technology by high pressure homogenization was chosen for this purpose, which is less expensive and simple method. In this technique, no organic solvent was used. The study was further aimed to characterize prepared nanocrystals in solid state by Fourier-transform infrared spectroscopy (FTIR), powder X-ray diffraction (PXRD) patterns, particle size, zeta potential, % yield, and drug permeation study through isolated goat’s intestine. An in vivo study was carried out to determine the pharmacokinetic property in comparison to pure drug powder using rats as experimental animals. The formulation design was optimized by a 3(2) factorial design. In these designs, two factors, namely surfactant amount (X1) and speed of homogenizer (X2), were evaluated on three dependent variables, namely particle size (Y1), zeta potential (Y2), and production yield (Y3).",signatures:"Luis Castañeda",downloadPdfUrl:"/chapter/pdf-download/68946",previewPdfUrl:"/chapter/pdf-preview/68946",authors:[{id:"294990",title:"Prof.",name:"Luis",surname:"Castañeda",slug:"luis-castaneda",fullName:"Luis Castañeda"}],corrections:null},{id:"68817",title:"Production, Processes and Modification of Nanocrystalline Cellulose from Agro-Waste: A Review",doi:"10.5772/intechopen.87001",slug:"production-processes-and-modification-of-nanocrystalline-cellulose-from-agro-waste-a-review",totalDownloads:1306,totalCrossrefCites:13,totalDimensionsCites:35,hasAltmetrics:1,abstract:"Nanocrystalline cellulose is a renewable nanomaterial that has gained huge attention for its use in various applications from advanced biomedical material to food packaging material due to its exceptional physical and biological properties, such as high crystallinity degree, large specific surface area, high aspect ratio, high thermal resistance, good mechanical properties, abundance of surface hydroxyl groups, low toxicity, biodegradability, and biocompatibility. However, they still have drawbacks: (1) sources of raw materials and its utilization in the production of nanocomposites and (2) high chemical and energy consumption regarding the isolation of macro-sized fibers to nano-sized fibers. The incorporation of hydrophilic nanocrystalline cellulose within hydrophobic polymer limits the dispersion of nano-sized fibers, thus resulting in low mechanical properties of nanocomposites. Hence, surface modification on nano-sized fiber could be a solution to this problem. This review focuses on the advanced developments in pretreatment, nanocrystalline production and modifications, and its application in food packaging, biomedical materials, pharmaceutical, substitution biomaterials, drug excipient, drug delivery automotive, and nanopaper applications.",signatures:"R.A. Ilyas, S.M. Sapuan, R. Ibrahim, M.S.N. Atikah, A. Atiqah, M.N.M. Ansari and M.N.F. 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Ansari"}],corrections:null}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},subseries:null,tags:null},relatedBooks:[{type:"book",id:"7640",title:"Perspective of Carbon Nanotubes",subtitle:null,isOpenForSubmission:!1,hash:"8b85a9957fad5206369eadf0c1ffa27d",slug:"perspective-of-carbon-nanotubes",bookSignature:"Hosam El-Din Saleh and Said Moawad Mohamed El-Sheikh",coverURL:"https://cdn.intechopen.com/books/images_new/7640.jpg",editedByType:"Edited by",editors:[{id:"144691",title:"Prof.",name:"Hosam M.",surname:"Saleh",slug:"hosam-m.-saleh",fullName:"Hosam M. Saleh"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"6408",title:"Novel Nanomaterials",subtitle:"Synthesis and Applications",isOpenForSubmission:!1,hash:"f3585d338d78e4d31c200d9991b03692",slug:"novel-nanomaterials-synthesis-and-applications",bookSignature:"George Z. 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The well-known efficient market hypothesis precludes any possibility of accurate prediction of future stock prices since it assumes stock prices to be purely stochastic in nature. Numerous works in the finance literature have shown that robust and precise prediction of future stock prices is using sophisticated machine learning and deep learning algorithms, model architectures, and selection of appropriate variables in the models.
Technical analysis of stocks has been a very interesting area of work for the researchers engaged in security and portfolio analysis. Numerous approaches to technical analysis have been proposed in the literature. Most of the algorithms here work on searching and finding some pre-identified patterns and sequences in the time series of stock prices. Prior detection of such patterns can be useful for the investors in the stock market in formulating their investment strategies in the market to maximize their profit. A rich set of such patterns has been identified in the finance literature for studying the behavior of stock price time series.
In this chapter, we propose a collection of forecasting models for predicting the prices of a critical stock of the automobile sector of India. The predictive framework consists of four CNN regression models and six models of regression built on the
The current work has the following three contributions. First, unlike the currently existing works in the literature, which mostly deal with time-series data of daily or weekly stock prices, the models in this work are built and tested on stock price data at a small interval of 5 minutes. Second, our propositions exploit the power of deep learning, and hence, they achieve a very high degree of precision and robustness in their performance. Among all models proposed in this work, the lowest ratio of the
The chapter is organized as follows. Section 2 briefly discusses some related works in the literature. In Section 3, we discuss the method of data acquisition, the methodology followed, and the design details of the ten predictive models proposed by us. Section 4 exhibits the detailed experimental results and their analysis. A comparative study of the performance of the models is also made. In Section 5, we conclude the chapter and identify a few new directions of research.
The literature on systems and methods of stock price forecasting is quite rich. Numerous proposals exist on the mechanisms, approaches, and frameworks for predicting future stock prices and stock price movement patterns. At a broad level, these propositions can be classified into four categories. The proposals of the first category are based on different variants of univariate and multivariate regression models. Some of the notable approaches under this category are -
In the following, we briefly discuss the salient features of some of the works under each category. We start with the regression-based proposals.
Enke et al. propose a multi-step approach to stock price prediction using a multiple regression model [2]. The proposition is based on a
Among the econometric approaches, Du proposes an integrated model combining an ARIMA and a backpropagation neural network for predicting the future index values of the Shanghai Stock Exchange [6]. Jarrett and Kyper present an ARIMA-based model for predicting future stock prices [7]. The study conducted by the authors reveals two significant findings: (i) higher accuracy is achieved by models involving fewer parameters, and (ii) the daily return values exhibit a strong autoregressive property. Sen and Datta Chaudhuri different sectors of the Indian stock market using a time series decomposition approach and predict the future stock prices using different types of ARIMA and regression models [9, 10, 11, 12, 13, 14, 33]. Zhong and Enke present a gamut of econometric and statistical models, including ARIMA,
Machine learning and deep learning models have found widespread applications in designing predictive frameworks for stock prices. Baek and Kim propose a framework called ModAugNet, which is built on an LSTM deep learning model [17]. Chou and Nguyen preset a
The hybrid models use relevant information in the social web and exploit the power of machine learning and deep learning architectures and algorithms for making predictions with a high level of accuracy. Among some well-known hybrid models, Bollen et al. present a scheme for computing the mood states of the public from the Twitter feeds and use the mood states information as an input to a nonlinear regression model built on a
The most formidable challenge in designing a robust predictive model with a high level of precision for stock price forecasting is handling the randomness and the volatility exhibited by the time series. The current work utilizes the power of deep learning models in feature extraction and learning while exploiting their architectural diversity in achieving robustness and accuracy in stock price prediction on very granular time series data.
We propose a gamut of predictive models built on deep learning architectures. We train, validate, and then test the models based on the historical stock price records of a well-known stock listed in the NSE, viz.
In this chapter, we present ten regression models for stock price forecasting using a deep learning approach. For the univariate models, the objective is to forecast the future values of the variable
The suitability of CNNs in building predictive models for predicting future stock prices has been demonstrated in our previous work [22]. In the current work, we present a gamut of deep learning models built on CNN and LSTM architectures and illustrate their efficacy and effectiveness in solving the same problem.
CNNs perform two critical functions for extracting rich feature sets from input data. These functions are: (1)
LSTM is an adapted form of a
The deep learning-based models we present in this paper differ in their design, structure, and dataflows. Our proposition includes four models based on the CNN architecture and six models built on the LSTM network architecture. The proposed models are as follows. The models have been named following a convention. The first part of the model’s name indicates the model type (CNN or LSTM), the second part of the name indicates the nature of the input data (univariate or multivariate). Finally, the third part is an integer indicating the size of the input data to the model (5 or 10). The ten models are as follows:
(i) CNN_UNIV_5 – a CNN model with an input of univariate open values of stock price records of the last week, (ii) CNN_UNIV_10 – a CNN model with an input of univariate open values of stock price records of the last couple of weeks, (iii) CNN_MULTV_10 – a CNN model with an input of multivariate stock price records consisting of five attributes of the last couple of weeks, where each variable is passed through a separate channel in a CNN, (iv) CNN_MULTH_10 – a CNN model with the last couple of weeks’ multivariate input data where each variable is used in a dedicated CNN and then combined in a multi-headed CNN architecture, (v) LSTM_UNIV_5 – an LSTM with univariate open values of the last week as the input, (vi) LSTM_UNIV_10 – an LSTM model with the last couple of weeks’ univariate open values as the input, (vii) LSTM_UNIV_ED_10 – an LSTM having an encoding and decoding ability with univariate open values of the last couple of weeks as the input, (viii) LSTM_MULTV_ED_10 – an LSTM based on encoding and decoding of the multivariate stock price data of five attributes of the last couple of weeks as the input, (ix) LSTM_UNIV_CNN_10 – a model with an encoding CNN and a decoding LSTM with univariate open values of the last couple of weeks as the input, and (x) LSTM_UNIV_CONV_10 – a model having a convolutional block for encoding and an LSTM block for decoding and with univariate open values of the last couple of weeks as the input.
We present a brief discussion on the model design. All the hyperparameters (i.e., the number of nodes in a layer, the size of a convolutional, LSTM or pooling layer, etc.) used in all the models are optimized using grid-search. However, we have not discussed the parameter optimization issues in this work.
This CNN model is based on a univariate input of
The schematic architecture of the model CNN_UNIV_5.
We compute the number of trainable parameters in the CNN_UNIV_5 model. As the role of the input layer is to provide the input data to the network, there is no learning involved in the input layer. There is no learning in the pooling layers as all these layers do is calculate the local aggregate features. The flatten layers do not involve any learning as well. Hence, in a CNN model, the trainable parameters are involved only in the convolutional layers and the dense layers. The number of trainable parameters (
The number of parameters (
The computation of the number of parameters in the CNN_UNIV_5 model is presented in Table 1. It is observed that the model involves 289 trainable parameters. The number of parameters in the convolutional layer is 64, while the two dense layers involve 170 and 55 parameters, respectively.
Layer | #params | |||||||
---|---|---|---|---|---|---|---|---|
Conv1D (conv1d) | 3 | 1 | 16 | 64 | 64 | |||
Dense (dense) | 16 | 10 | 170 | 170 | ||||
Dense (dense_1) | 10 | 5 | 55 | 55 | ||||
Computation of the number of params in the model CNN_UNIV_5.
This model is based on a univariate input of the
The architecture of the model CNN_UNIV_10.
Layer | #params | |||||||
---|---|---|---|---|---|---|---|---|
Conv1D (conv1d) | 3 | 1 | 16 | 64 | 64 | |||
Dense (dense) | 64 | 10 | 650 | 650 | ||||
Dense (dense_1) | 10 | 5 | 55 | 55 | ||||
The number of parameters in the model CNN_UNIV_10 model.
It is evident from Table 2 that the CNN_UNIV_10 involves 769 trainable parameters. The parameter counts for the convolutional layer, and the two dense layers are 64, 650, and 55 respectively.
This CNN model is built on the input of the last two weeks’ multivariate stock price records data. The five variables of the stock price time series are used in a CNN in five separate channels. The model uses a couple of convolutional layers, each of size (32, 3). The parameter values of the convolutional blocks indicate that 32 features are extracted from the input data by each convolutional layer using a feature map size of 32 and a filter size of 3. The input to the model has a shape of (10, 5), indicating ten records, each record having five features of the stock price data. After the first convolutional operation, the shape of the data is transformed to (8, 32). The value 32 corresponds to the number of features extracted, while the value 8 is obtained by the formula:
The schematic architecture of the model CNN_MULTV_10.
Layer | #params | |||||||
---|---|---|---|---|---|---|---|---|
Conv1D (conv1d_4) | 3*5 | 1 | 32 | 512 | 512 | |||
Conv1D (conv1d_5) | 3 | 32 | 32 | 3104 | 3014 | |||
Conv1D (conv1d_6) | 3 | 32 | 16 | 1552 | 1552 | |||
Dense (dense_3) | 16 | 100 | 1700 | 1700 | ||||
Dense (dense_4) | 100 | 5 | 505 | 505 | ||||
The number of parameters in the model CNN_MULTV_10.
From Table 3, it is observed that the total number of trainable parameters in the model CNN_MULTV_10 is 7373. The three convolutional layers
This CNN model uses a dedicated CNN block for each of the five input attributes in the stock price data. In other words, for each input variable, a separate CNN is used for feature extrication. We call this a multivariate and multi-headed CNN model. For each sub-CNN model, a couple of convolutional layers were used. The convolutional layers have a feature space dimension of 32 and a filter size (i.e., kernel size) of 3. The convolutional layers are followed by a max-pooling layer. The size of the feature space is reduced by a factor of 1/2 by the max-pooling layer. Following the computation rule discussed under the CNN_MULTV_10 model, the data shape of the output from the max-pooling layer for each sub-CNN model is (3, 32). A flatten operation follows converting the data into a single-dimensional array of size 96 for each input variable. A concatenation operation follows that concatenates the five arrays, each containing 96 values, into a single one-dimensional array of size 96*5 = 480. The output of the concatenation operation is passed successively through two dense layers containing 200 nodes and 100 nodes, respectively. In the end, the output layer having five nodes yields the forecasted five values as the daily
The schematic architecture of the model CNN_MULTH_10.
Table 4 presents the necessary calculations for finding the number of parameters in the CNN_MULTH_10 model. Each of the five convolutions layers,
Layer | #params | |||||||
---|---|---|---|---|---|---|---|---|
Conv1D (conv1d_1, conv1d_3, conv1d_5, conv1d_7, conv1d_9) | 3 | 1 | 32 | 640 | 640 | |||
Conv1D (conv1d_2, convid_4, conv1d_6, conv1d_8, conv1d_10) | 3 | 32 | 32 | 15520 | 15520 | |||
Dense (dense_1) | 480 | 200 | 96200 | 96200 | ||||
Dense (dense_2) | 200 | 100 | 20100 | 20100 | ||||
Dense (dense_3) | 100 | 5 | 505 | 505 | ||||
The number of parameters in the model CNN_MULTH_10 model.
This model is based on an input of the univariate information of the
The schematic architecture of the model LSTM_UNIV_5.
As we did in the case of the CNN models, we now compute the number of parameters involved in the LSTM model. The input layers do not have any parameters, as the role of these layers is to just receive and forward the data. There are four gates in an LSTM network that have the same number of parameters. These four gates are known as (i)
Hence, the total number of parameters in an LSTM layer will be given by 4 *
The computation of the number of parameters associated with the model LSTM_UNIV_5 is depicted in Table 5. In Table 5, the number of parameters in the LSTM layer is computed as follows: 4*[(200 + 1) * 200 + 200] = 161,600. The number of parameters in the dense layer, dens_4 is computed as: (200 * 100 + 100) = 20,100. Similarly, the parameters in the dense layers,
Layer | #params | ||||||
---|---|---|---|---|---|---|---|
LSTM (lstm_2) | 200 | 1 | 40,400 | 161600 | |||
Dense (dense_4) | 200 | 100 | 20100 | 20100 | |||
Dense (dense_5) | 100 | 5 | 505 | 505 | |||
Desne (dense_6) | 5 | 5 | 30 | 30 | |||
The number of parameters in the model LSTM_UNIV_5 model.
LSTM_UNIV_10 model: This univariate model uses the last couple of weeks’ open index input and yields the daily forecasted open values for the coming week. The same values of the parameters and hyperparameters of the model LSTM_UNIV_5 are used here. Only, the input data shape is different. The input data shape of this model is (10, 1). Figure 6 presents the architecture of this model.
The schematic architecture of the model LSTM_UNIV_10.
Table 6 presents the computation of the number of parameters involved in the modelLSTM_UNIV_10. Since the number of parameters in the LSTM layers depends only on the number of features in the input data and the node-count in the LSTM layer, and not on the number of input records in one epoch, the model LSTM_UNIV_10 has an identical number of parameters in the LSTM layer as that of the model LSTM_UNIV_5. Since both the models have the same number of dense layers and have the same architecture for those layers, the total number of parameters for both the models are the same.
Layer | #params | ||||||
---|---|---|---|---|---|---|---|
LSTM (lstm_2) | 200 | 1 | 40,400 | 161600 | |||
Dense (dense_4) | 200 | 100 | 20,100 | 20100 | |||
Dense (dense_5) | 100 | 5 | 505 | 505 | |||
Desne (dense_6) | 5 | 5 | 30 | 30 | |||
The number of parameters in the model LSTM_UNIV_10.
This LSTM model has an encoding and decoding capability and is based on the input of the
The decoded result is passed on to a dense layer. The dense layer learns from the decoded values and predicts the future five values of the target variable (i.e.,
The schematic architecture of the model LSTM_UNIV_ED_10.
The computation of the number of parameters in the LSTM_UNIV_ED_10 model is shown in Table 7. The input layer and the repeat vector layer do not involve any learning, and hence these layers have no parameters. On the other hand, the two LSTM layers,
Layer | #params | ||||||
---|---|---|---|---|---|---|---|
LSTM (lstm_3) | 200 | 1 | 40,400 | 161600 | |||
LSTM (lstm_4) | 200 | 200 | 80, 200 | 320800 | |||
Dense (time_dist_dense_3) | 200 | 100 | 20,100 | 20100 | |||
Dense (time_dist_dense_4) | 100 | 1 | 101 | 101 | |||
The number of parameters in the model LSTM_UNIV_ED_10.
This model is a multivariate version of LSTM_UNIV_ED_10. It uses the last couple of weeks’ stock price records and includes all the five attributes, i.e.,
The schematic architecture of the model LSTM_MULTV_ED_10.
Table 8 shows the number of parameters in the LSTM_MULTV_ED_10 model. The computation of the parameters for this model is exactly similar to that for the model LSTM_UNIV_ED_50 expect for the first LSTM layer. The number of parameters in the first LSTM (i.e., the encoder) layer for this model will be different since the number of parameters is dependent on the count of the features in the input data. The computation of the parameter counts in the encoder LSTM layer,
Layer | #params | ||||||
---|---|---|---|---|---|---|---|
LSTM (lstm_1) | 200 | 5 | 41200 | 164800 | |||
LSTM (lstm_2) | 200 | 200 | 80, 200 | 320800 | |||
Dense (time_dist_dense_1) | 200 | 100 | 20,100 | 20100 | |||
Dense (time_dist_dense_2) | 100 | 1 | 101 | 101 | |||
The number of parameters in the model LSTM_MULTV_ED_10.
This model is a modified version of the LSTM_UNIV_ED_N_10 model. A dedicated CNN block carries out the encoding operation. CNNs are poor in their ability to learn from sequential data. However, we exploit the power of a one-dimensional CNN in extracting important features from time-series data. After the feature extraction is done, the extracted features are provided as the input into an LSTM block. The LSTM block decodes the features and makes robust forecasting of the future values in the sequence. The CNN block consists of a couple of convolutional layers, each of which has a feature map size of 64 and a kernel size of 3. The input data shape is (10, 1) as the model uses univariate data of the target variable of the past couple of weeks. The output shape of the initial convolutional layer is (8, 64). The value of 8 is arrived at using the computation: (10–3 + 1), while 64 refers to the feature space dimension.
Similarly, the shape of the output of the next convolutional block is (6, 64). A max-pooling block follows, which contracts the feature-space dimension by 1/2. Hence, the output data shape of the max-pooling layer is (3, 64). The max-pooling layer’s output is flattened into an array of single-dimension and size 3*64 = 192. The flattened vector is fed into the decoder LSTM block consisting of 200 nodes. The decoder architecture remains identical to the decoder block of the LSTM_UNIV_ED_10 model. We train the model over 20 epochs, with each epoch using 16 records. The structure and the data flow of the model are shown in Figure 9.
The schematic architecture of the model LSTM_UNIV_CNN_10.
Table 9 presents the computation of the number of parameters in the model LSTM_UNIV_CNN_10. The input layer, the max-pooling layer, the flatten operation, and the repeat vector layer do not involve any learning, and hence they have no parameters. The number of parameters in the first convolutional layer is computed as follows: (3 + 1) * 64 = 256. For the second convolutional layer, the number of parameters is computed as: (3 * 64 + 1) * 64 = 12352. The number of parameters for the LSTM layer is computed as follows: 4 * [(200 + 192) * 200 + 200] = 314400. In the case of the first dense layer, the number of parameters is computed as follows: (200 * 100 + 100) = 20100. Finally, the number of parameters in the second dense layer is computed as (100 * 1 + 1) = 101. The total number of parameters in the model is found out to be 347209.
Layer | #param | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Conv1D (conv1d_4) | 3 | 1 | 64 | 256 | 256 | |||||
Conv1D (conv1d_5) | 3 | 64 | 64 | 12352 | 12352 | |||||
LSTM (lstm_2) | 200 | 192 | 78600 | 314400 | ||||||
Dense (time_dist_4) | 200 | 100 | 20,100 | 20100 | ||||||
Dense (time_dist_5) | 100 | 1 | 101 | 101 | ||||||
The number of parameters in the model LSTM_UNIV_CNN_10.
This model is a modification of the LSTM_UNIV_CNN_10 model. The encoder CNN’s convolution operations and the decoding operations of the LSTM sub-module are integrated for every round of the sequence in the output. This encoder-decoder model is also known as the Convolutional-LSTM model [58]. This integrated model reads sequential input data, performs convolution operations on the data without any explicit CNN block, and decodes the extracted features using a dedicated LSTM block. The Keras framework contains a class,
The schematic architecture of the model LSTM_UNIV_CONV_10.
The computation of the number of parameters for the LSTM_UNIV_CONV_10 model is shown in Table 10. While the input layer, the flatten operation, and the repeat vector layer do not involve any learning, the other layers include trainable parameters. The number of parameters in the convolutional LSTM layer (i.e.,
Layer | #param | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
ConvLSTM2D(conv_1st_m2d) | 3 | 1 | 64 | 64 | 1 | 12544 | 50176 | |||
LSTM (lstm) | 200 | 192 | 78600 | 314400 | ||||||
Dense (time_dist) | 200 | 100 | 20,100 | 20100 | ||||||
Dense (time_dist_1) | 100 | 1 | 101 | 101 | ||||||
Computation of the no. of params in the model LSTM_UNIV_CONV_10.
We present the results on the performance of the ten deep learning models on the dataset we prepared. We also compare the performances of the models. For designing a robust evaluation framework, we execute every model over ten rounds. The average performance of the ten rounds is considered as the overall performance of the model. We use four metrics for evaluation: (i) average RMSE, (ii) the RMSE for different days (i.e., Monday to Friday) of a week, (iii) the time needed for execution of one round, and (iv) the ratio of the RMSE to the response variable’s (i.e.,
Table 11 shows the results of the performance of the CNN_UNIV_5 model. The model takes, on average, 174.78 seconds to finish its one cycle of execution. For this model, the ratio of RMSE to the mean
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 4.058 | 4.00 | 3.40 | 3.90 | 4.40 | 4.50 | 173.95 |
2 | 3.782 | 3.10 | 3.30 | 3.80 | 4.10 | 4.40 | 176.92 |
3 | 3.378 | 2.80 | 3.00 | 3.40 | 3.60 | 3.90 | 172.21 |
4 | 3.296 | 2.60 | 3.00 | 3.30 | 3.60 | 3.90 | 173.11 |
5 | 3.227 | 2.60 | 3.00 | 3.30 | 3.50 | 3.70 | 174.72 |
6 | 3.253 | 2.60 | 3.00 | 3.30 | 3.50 | 3.70 | 183.77 |
7 | 3.801 | 3.60 | 3.60 | 3.80 | 3.80 | 4.10 | 172.29 |
8 | 3.225 | 2.60 | 2.90 | 3.30 | 3.50 | 3.70 | 171.92 |
9 | 3.306 | 2.80 | 3.00 | 3.30 | 3.50 | 3.70 | 174.92 |
10 | 3.344 | 2.70 | 3.10 | 3.40 | 3.60 | 3.80 | 174.01 |
2.94 | 3.13 | 3.48 | 3.71 | 3.94 | |||
0.0062 | 0.0066 | 0.0073 | 0.0078 | 0.0083 |
The RMSE and the execution time of the CNN_UNIV_5 model.
RMSE vs. day plot of CNN_UNIV_5 (depicted by tuple#2 in
Table 12 depicts the performance results of the model CNN_UNIV_10. The model needs 185.01 seconds on average for one round. The ratio of the RMSE to the average of the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 3.165 | 2.50 | 3.20 | 3.10 | 3.50 | 3.50 | 177.86 |
2 | 3.813 | 3.30 | 3.90 | 3.30 | 3.60 | 4.80 | 202.25 |
3 | 3.230 | 2.60 | 2.90 | 3.30 | 3.50 | 3.80 | 183.45 |
4 | 3.209 | 2.50 | 3.10 | 3.40 | 3.40 | 3.60 | 188.35 |
5 | 3.176 | 2.80 | 3.00 | 3.10 | 3.40 | 3.60 | 180.30 |
6 | 3.233 | 2.60 | 3.00 | 3.30 | 3.50 | 3.70 | 181.20 |
7 | 3.312 | 2.70 | 3.20 | 3.20 | 3.50 | 3.80 | 188.81 |
8 | 3.082 | 2.20 | 2.80 | 3.30 | 3.30 | 3.50 | 180.89 |
9 | 3.772 | 2.80 | 3.70 | 3.90 | 4.30 | 4.10 | 186.23 |
10 | 3.150 | 2.40 | 2.90 | 3.20 | 3.50 | 3.60 | 180.78 |
2.64 | 3.17 | 3.31 | 3.55 | 3.80 | |||
0.0056 | 0.0067 | 0.0070 | 0.0075 | 0.0080 |
The RMSE and the execution time of the CNN_UNIV_10 model.
RMSE vs. day plot of CNN_UNIV_10 (depicted by tuple#7 in
Table 13 depicts the performance results of the model CNN_MULTV_10. One round of execution of the model requires 202.78 seconds. The model yields a value of 0.009420 for the ratio of the RMSE to the average of the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 4.525 | 4.00 | 4.30 | 4.50 | 4.70 | 5.00 | 206.92 |
2 | 3.606 | 3.10 | 3.30 | 3.70 | 3.80 | 4.00 | 202.61 |
3 | 4.830 | 4.60 | 4.70 | 4.70 | 5.10 | 5.00 | 202.87 |
4 | 4.938 | 4.40 | 4.80 | 4.70 | 5.30 | 5.40 | 201.49 |
5 | 4.193 | 3.50 | 4.00 | 4.10 | 4.60 | 4.60 | 214.66 |
6 | 5.101 | 4.70 | 4.90 | 5.20 | 5.30 | 5.30 | 190.73 |
7 | 4.751 | 4.40 | 4.50 | 4.80 | 5.00 | 5.00 | 201.73 |
8 | 3.927 | 3.20 | 3.70 | 4.00 | 4.30 | 4.40 | 200.04 |
9 | 4.267 | 3.90 | 3.80 | 4.50 | 4.60 | 4.40 | 199.09 |
10 | 4.661 | 4.40 | 4.50 | 4.60 | 4.90 | 4.90 | 207.62 |
4.02 | 4.25 | 4.53 | 4.76 | 4.80 | |||
0.0085 | 0.0089 | 0.0095 | 0.0100 | 0.0101 |
The RMSE and the execution time of the CNN_MULTV_10 model.
RMSE vs. day plot of CNN_MULTV_10 (based on tuple#6 in
Table 14 depicts the results of the model CNN_MULTH_10. The model needs, on average, 215.07 seconds to execute its one round. The ratio of the RMSE to the average of the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 3.338 | 2.70 | 2.80 | 3.30 | 3.70 | 4.00 | 224.63 |
2 | 3.264 | 2.80 | 3.10 | 3.30 | 3.50 | 3.70 | 216.44 |
3 | 3.015 | 2.30 | 2.70 | 3.10 | 3.30 | 3.50 | 218.14 |
4 | 3.692 | 3.20 | 3.40 | 4.00 | 3.80 | 4.00 | 220.01 |
5 | 3.444 | 2.80 | 3.20 | 3.40 | 3.80 | 3.90 | 212.54 |
6 | 4.019 | 4.50 | 3.70 | 3.70 | 4.20 | 3.90 | 210.95 |
7 | 6.988 | 6.40 | 7.40 | 7.20 | 6.80 | 7.10 | 210.24 |
8 | 3.133 | 2.50 | 2.80 | 3.20 | 3.40 | 3.60 | 214.48 |
9 | 3.278 | 2.40 | 3.10 | 3.70 | 3.40 | 3.60 | 211.53 |
10 | 4.469 | 5.90 | 3.60 | 4.00 | 4.10 | 4.40 | 211.78 |
3.55 | 3.58 | 3.89 | 4.00 | 4.17 | |||
0.0076 | 0.0075 | 0.0082 | 0.0084 | 0.0088 |
The RMSE and the execution time of the CNN_MULTH_10 model.
RMSE vs. day plot of CNN_MULTH_10 (based on tuple#4 in
The results of the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 3.125 | 2.40 | 2.90 | 3.00 | 3.50 | 3.70 | 372.28 |
2 | 3.376 | 3.00 | 2.90 | 3.40 | 3.90 | 3.70 | 371.73 |
3 | 2.979 | 2.10 | 2.60 | 3.00 | 3.30 | 3.70 | 368.72 |
4 | 3.390 | 3.20 | 3.40 | 3.30 | 3.60 | 3.50 | 368.58 |
5 | 4.387 | 4.20 | 4.60 | 4.10 | 4.40 | 4.60 | 379.10 |
6 | 5.173 | 4.40 | 5.10 | 4.60 | 5.20 | 6.30 | 373.84 |
7 | 3.434 | 4.30 | 2.60 | 2.90 | 3.70 | 3.50 | 368.91 |
8 | 3.979 | 3.70 | 3.10 | 4.60 | 4.30 | 4.10 | 371.02 |
9 | 2.892 | 1.90 | 2.50 | 2.90 | 3.30 | 3.50 | 371.95 |
10 | 3.683 | 2.70 | 4.00 | 3.30 | 3.50 | 4.60 | 370.07 |
3.19 | 3.37 | 3.51 | 3.87 | 4.12 | |||
0.0067 | 0.0071 | 0.0074 | 0.0081 | 0.0086 |
The RMSE and the execution time of the LSTM_UNIV_5 model.
RMSE vs. day plot of LSTM_UNIV_5 (depicted by tuple#9 in
Table 16 exhibits the results of the model
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 3.005 | 2.40 | 2.40 | 2.80 | 3.70 | 3.50 | 547.22 |
2 | 3.859 | 3.50 | 3.30 | 3.80 | 3.90 | 4.70 | 554.03 |
3 | 4.601 | 4.50 | 4.50 | 4.60 | 4.80 | 4.60 | 550.24 |
4 | 3.342 | 2.70 | 4.00 | 3.10 | 3.40 | 3.50 | 555.50 |
5 | 4.714 | 4.80 | 4.40 | 4.70 | 4.60 | 5.10 | 563.44 |
6 | 3.336 | 2.50 | 3.20 | 3.30 | 3.60 | 3.90 | 553.83 |
7 | 3.711 | 3.10 | 4.00 | 4.00 | 3.60 | 3.90 | 559.31 |
8 | 2.795 | 1.90 | 2.40 | 2.80 | 3.20 | 3.40 | 552.50 |
9 | 3.012 | 1.80 | 2.80 | 2.90 | 3.60 | 3.50 | 551.20 |
10 | 2.751 | 1.70 | 2.30 | 3.00 | 3.00 | 3.30 | 557.39 |
2.89 | 3.33 | 3.50 | 3.74 | 3.94 | |||
0.0061 | 0.0070 | 0.0074 | 0.0079 | 0.0083 |
The RMSE and the execution time of the LSTM_UNIV_10 model.
RMSE vs. day plot of LSTM_UNIV_10 (depicted by tuple#10 in
Table 17 shows that the model LSTM_UNIV_ED_10 needs, on average, 307.27 seconds to execute its one round. The average value of the ratio of the RMSE to the average value of the target variable (i.e., the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 2.975 | 2.00 | 2.70 | 3.00 | 3.40 | 3.60 | 310.28 |
2 | 4.856 | 4.10 | 4.60 | 5.00 | 5.20 | 5.30 | 306.22 |
3 | 5.500 | 4.30 | 5.20 | 5.50 | 6.00 | 6.40 | 306.08 |
4 | 3.656 | 3.20 | 3.40 | 3.70 | 3.90 | 4.10 | 305.64 |
5 | 2.859 | 1.90 | 2.60 | 2.90 | 3.20 | 3.40 | 306.03 |
6 | 3.887 | 3.30 | 3.60 | 3.90 | 4.20 | 4.40 | 305.34 |
7 | 4.007 | 3.60 | 3.70 | 4.00 | 4.10 | 4.50 | 304.69 |
8 | 3.489 | 2.70 | 3.20 | 3.60 | 3.80 | 3.90 | 305.26 |
9 | 2.944 | 2.10 | 2.80 | 3.00 | 3.20 | 3.50 | 314.37 |
10 | 5.497 | 4.70 | 5.10 | 5.60 | 6.00 | 5.90 | 308.78 |
3.19 | 3.69 | 4.02 | 4.30 | 4.50 | |||
0.0067 | 0.0078 | 0.0085 | 0.0090 | 0.0095 |
The RMSE and the execution time of the LSTM_UNIV_ED_10 model.
RMSE vs. day plot of LSTM_UNIV_ED_10 (as per tuple#5 in
Table 18 shows that the model LSTM_MULTV_ED_10, on average, requires 634.34 seconds to complete the execution of its one round. For this model, the ratio of the RMSE to the average value of the target variable (i.e., the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 5.858 | 5.50 | 5.70 | 5.90 | 6.00 | 6.20 | 631.53 |
2 | 4.062 | 3.60 | 3.90 | 4.00 | 4.20 | 4.50 | 617.62 |
3 | 6.623 | 6.20 | 6.50 | 6.60 | 6.80 | 6.90 | 640.09 |
4 | 3.661 | 3.20 | 3.30 | 3.60 | 3.90 | 4.10 | 624.22 |
5 | 5.879 | 5.80 | 5.90 | 5.70 | 6.00 | 6.10 | 632.34 |
6 | 4.808 | 4.20 | 4.60 | 4.80 | 5.10 | 5.20 | 644.48 |
7 | 4.657 | 4.10 | 4.50 | 4.70 | 4.90 | 5.10 | 631.72 |
8 | 3.866 | 3.30 | 3.60 | 3.90 | 4.10 | 4.30 | 633.28 |
9 | 3.910 | 3.30 | 3.70 | 3.90 | 4.20 | 4.40 | 647.29 |
10 | 5.644 | 5.30 | 5.50 | 5.60 | 5.90 | 6.00 | 640.86 |
4.50 | 4.72 | 4.87 | 5.11 | 5.28 | |||
0.0094 | 0.0099 | 0.0102 | 0.0107 | 0.0111 |
The RMSE and the execution time of the LSTM_MULTV_ED_10 model.
RMSE vs. day plot of LSTM_MULTV_ED_10 (as per tuple#10 in
Table 19 depicts that the model LSTM_UNIV_CNN_N_10 requires, on average, 222.48 seconds to finish one round. For this model, the ratio of the RMSE to the average value of the target variable (i.e., the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 3.832 | 3.30 | 3.50 | 3.90 | 4.10 | 4.30 | 221.18 |
2 | 3.256 | 2.50 | 3.00 | 3.30 | 3.60 | 3.80 | 219.74 |
3 | 4.308 | 3.80 | 4.00 | 4.40 | 4.60 | 4.60 | 222.59 |
4 | 4.081 | 3.30 | 4.00 | 4.10 | 4.30 | 4.50 | 227.95 |
5 | 3.325 | 2.60 | 3.00 | 3.30 | 3.60 | 3.90 | 224.46 |
6 | 3.870 | 3.20 | 3.70 | 3.90 | 4.10 | 4.10 | 223.40 |
7 | 3.688 | 3.10 | 3.40 | 3.80 | 4.00 | 4.10 | 222.89 |
8 | 3.851 | 3.20 | 3.60 | 3.80 | 4.20 | 4.40 | 221.87 |
9 | 3.710 | 2.60 | 3.40 | 4.00 | 4.00 | 4.40 | 219.74 |
10 | 3.736 | 3.30 | 3.70 | 3.70 | 3.90 | 4.10 | 220.96 |
3.09 | 3.53 | 3.82 | 4.04 | 4.22 | |||
0.0065 | 0.0074 | 0.0080 | 0.0085 | 0.0089 |
The RMSE and the execution time of the LSTM_UNIV_CNN_10 model.
RMSE vs. day plot of LSTM_UNIV_CNN_10 (as per tuple#3 in
The results of the model LSTM_UNIV_CONV_N_10 are presented in Table 20. The model completes its one round, on average, in 265.97 seconds. The ratio of the RMSE to the average of the
No. | Agg RMSE | Day1 | Day2 | Day3 | Day4 | Day5 | Time (sec) |
---|---|---|---|---|---|---|---|
1 | 3.971 | 3.00 | 3.60 | 4.00 | 4.40 | 4.60 | 263.84 |
2 | 3.103 | 2.40 | 2.80 | 3.20 | 3.40 | 3.60 | 262.06 |
3 | 3.236 | 2.30 | 2.90 | 3.30 | 3.60 | 3.80 | 266.47 |
4 | 4.347 | 3.10 | 4.00 | 4.60 | 4.70 | 5.00 | 257.43 |
5 | 2.860 | 2.20 | 2.50 | 2.80 | 3.20 | 3.40 | 260.05 |
6 | 3.525 | 2.50 | 3.60 | 3.50 | 3.80 | 4.00 | 282.27 |
7 | 3.163 | 2.30 | 2.80 | 3.20 | 3.50 | 3.80 | 265.26 |
8 | 2.870 | 2.00 | 2.60 | 2.90 | 3.20 | 3.50 | 272.18 |
9 | 3.504 | 2.20 | 3.10 | 3.70 | 3.70 | 4.40 | 265.46 |
10 | 5.053 | 4.70 | 4.40 | 5.20 | 5.30 | 5.60 | 264.66 |
2.67 | 3.23 | 3.64 | 3.88 | 4.17 | |||
0.0056 | 0.0068 | 0.0077 | 0.0082 | 0.0088 |
The RMSE and the execution time of the LSTM_UNIV_CONV_10 model.
RMSE vs. day plot of LSTM_UNIV_CONV_10 (as per tuple#8 in
Table 21 summarizes the performance of the ten models proposed in this chapter. We evaluate the models on two metrics and then rank the models on the basis of each metric. The two metrics used for the model evaluation are: (i) an accuracy matric computed as the ratio of the RMSE to the mean value of the target variable (i.e.,
No. | Model | #param | RMSE/Mean | Rank | Exec. Time (s) | Rank |
---|---|---|---|---|---|---|
1 | CNN_UNIV_5 | 289 | 0.007288 | 2 | 174.78 | 1 |
2 | CNN_UNIV_10 | 769 | 0.006967 | 1 | 180.01 | 2 |
3 | CNN_MULTV_10 | 7373 | 0.009420 | 9 | 202.78 | 3 |
4 | CNN_MULTH_10 | 132965 | 0.008100 | 7 | 215.07 | 4 |
5 | LSTM_UNIV_5 | 182235 | 0.007770 | 5 | 371.62 | 8 |
6 | LSTM_UNIV_10 | 182235 | 0.007380 | 3 | 554.47 | 9 |
7 | LSTM_UNIV_ED_10 | 502601 | 0.008350 | 8 | 307.27 | 7 |
8 | LSTM_MULTV_ED_10 | 505801 | 0.010294 | 10 | 634.34 | 10 |
9 | LSTM_UNIV_CNN_10 | 347209 | 0.007916 | 6 | 222.48 | 5 |
10 | LSTM_UNIV_CONV_10 | 384777 | 0.007490 | 4 | 265.97 | 6 |
Comparative analysis of the accuracy and execution speed of the models.
Another interesting observation is that the multivariate models are found to be inferior to the corresponding univariate models on the basis of the accuracy metric. The multivariate models, CNN_MULTV_10 and LSTM_MULTV_ED_10, are ranked 9 and 10, respectively, under the accuracy metric.
Finally, it is observed that the number of parameters in a model has an effect on its execution time, barring some notable exceptions. For the four CNN models, it is noted that with the increase in the number of parameters, there is a monotone increase in the execution time of the models. For the LSTM models, even though the models, LSTM_UNIV_CNN_10, LSTM_UNIV_CONV_10, and LSTM_UNIV_ED_10, have higher number of parameters than the vanilla LSTM models (i.e., LSTM_UNIV_5 and LSTM_UNIV_10), they are faster in execution. Evidently, the univariate encoder-decoder LSTM models are faster even when they involve a higher number of parameters than the vanilla LSTM models.
Prediction of future stock prices and price movement patterns is a challenging task if the stock price time series has a large amount of volatility. In this chapter, we presented ten deep learning-based regression models for robust and precise prediction of stock prices. Among the ten models, four of them are built on variants of CNN architectures, while the remaining six are constructed using different LSTM architectures. The historical stock price records are collected using the Metastock tool over a span of two years at five minutes intervals. The models are trained using the records of the first year, and then they are tested on the remaining records. The testing is carried out using an approach known as walk-forward validation, in which, based on the last one- or two-weeks historical stock prices, the predictions of stock prices for the five days of the next week are made. The overall RMSE and the RMSE for each day in a week are computed to evaluate the prediction accuracy of the models. The time needed to complete one round of execution of each model is also noted in order to measure the speed of execution of the models. The results revealed some very interesting observations. First, it is found that while the CNN models are faster, in general, the accuracies of both CNN and LSTM models are comparable. Second, the univariate models are faster and more accurate than their multivariate counterparts. And finally, the number of variables in a model has a significant effect on its speed of execution except for the univariate encoder-decoder LSTM models. As a future scope of work, we will design optimized models based on
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This problematic is particularly relevant with medical imaging data, where linear techniques are frequently unsuitable for capturing variations in anatomical structures. In many cases, there is enough structure in the data (CT, MRI, ultrasound) so a lower dimensional object can describe the degrees of freedom, such as in a manifold structure. Still, complex, multivariate distributions tend to demonstrate highly variable structural topologies that are impossible to capture with a single manifold learning algorithm. This chapter will present recent techniques developed in manifold theory for medical imaging analysis, to allow for statistical organ shape modeling, image segmentation and registration from the concept of navigation of manifolds, classification, as well as disease prediction models based on discriminant manifolds. We will present the theoretical basis of these works, with illustrative results on their applications from various organs and pathologies, including neurodegenerative diseases and spinal deformities.",book:{id:"7342",slug:"manifolds-ii-theory-and-applications",title:"Manifolds II",fullTitle:"Manifolds II - Theory and Applications"},signatures:"Samuel Kadoury",authors:null},{id:"62804",doi:"10.5772/intechopen.79383",title:"Recent Advances of Manifold Regularization",slug:"recent-advances-of-manifold-regularization",totalDownloads:1096,totalCrossrefCites:0,totalDimensionsCites:3,abstract:"Semi-supervised learning (SSL) that can make use of a small number of labeled data with a large number of unlabeled data to produce significant improvement in learning performance has been received considerable attention. Manifold regularization is one of the most popular works that exploits the geometry of the probability distribution that generates the data and incorporates them as regularization terms. There are many representative works of manifold regularization including Laplacian regularization (LapR), Hessian regularization (HesR) and p-Laplacian regularization (pLapR). Based on the manifold regularization framework, many extensions and applications have been reported. In the chapter, we review the LapR and HesR, and we introduce an approximation algorithm of graph p-Laplacian. We study several extensions of this framework for pairwise constraint, p-Laplacian learning, hypergraph learning, etc.",book:{id:"7342",slug:"manifolds-ii-theory-and-applications",title:"Manifolds II",fullTitle:"Manifolds II - Theory and Applications"},signatures:"Xueqi Ma and Weifeng Liu",authors:null},{id:"52886",doi:"10.5772/65903",title:"Head Pose Estimation via Manifold Learning",slug:"head-pose-estimation-via-manifold-learning",totalDownloads:1854,totalCrossrefCites:4,totalDimensionsCites:3,abstract:"For the last decades, manifold learning has shown its advantage of efficient non-linear dimensionality reduction in data analysis. Based on the assumption that informative and discriminative representation of the data lies on a low-dimensional smooth manifold which implicitly embedded in the original high-dimensional space, manifold learning aims to learn the low-dimensional representation following some geometrical protocols, such as preserving piecewise local structure of the original data. Manifold learning also plays an important role in the applications of computer vision, i.e., face image analysis. According to the observations that many face-related research is benefitted by the head pose estimation, and the continuous variation of head pose can be modelled and interpreted as a low-dimensional smooth manifold, we will focus on the head pose estimation via manifold learning in this chapter. Generally, head pose is hard to directly explore from the high-dimensional space interpreted as face images, which is, however, can be efficiently represented in low-dimensional manifold. Therefore, in this chapter, classical manifold learning algorithms are introduced and the corresponding application on head pose estimation are elaborated. Several extensions of manifold learning algorithms which are developed especially for head pose estimation are also discussed and compared.",book:{id:"5488",slug:"manifolds-current-research-areas",title:"Manifolds",fullTitle:"Manifolds - Current Research Areas"},signatures:"Chao Wang, Yuanhao Guo and Xubo Song",authors:[{id:"190308",title:"Dr.",name:"Chao",middleName:null,surname:"Wang",slug:"chao-wang",fullName:"Chao Wang"},{id:"190461",title:"Prof.",name:"Xubo",middleName:null,surname:"Song",slug:"xubo-song",fullName:"Xubo Song"},{id:"191562",title:"MSc.",name:"Yuanhao",middleName:null,surname:"Guo",slug:"yuanhao-guo",fullName:"Yuanhao Guo"}]},{id:"53713",doi:"10.5772/67008",title:"An Intrinsic Characterization of Bonnet Surfaces Based on a Closed Differential Ideal",slug:"an-intrinsic-characterization-of-bonnet-surfaces-based-on-a-closed-differential-ideal",totalDownloads:1497,totalCrossrefCites:2,totalDimensionsCites:2,abstract:"The structure equations for a two‐dimensional manifold are introduced and two results based on the Codazzi equations pertinent to the study of isometric surfaces are obtained from them. Important theorems pertaining to isometric surfaces are stated and a theorem due to Bonnet is obtained. A transformation for the connection forms is developed. It is proved that the angle of deformation must be harmonic, and that the differentials of many of the important variables generate a closed differential ideal. This implies that a coordinate system exists in which many of the variables satisfy particular ordinary differential equations, and these results can be used to characterize Bonnet surfaces.",book:{id:"5488",slug:"manifolds-current-research-areas",title:"Manifolds",fullTitle:"Manifolds - Current Research Areas"},signatures:"Paul Bracken",authors:[{id:"92883",title:"Prof.",name:"Paul",middleName:null,surname:"Bracken",slug:"paul-bracken",fullName:"Paul Bracken"}]},{id:"72257",doi:"10.5772/intechopen.92441",title:"Quasiconformal Reflections across Polygonal Lines",slug:"quasiconformal-reflections-across-polygonal-lines",totalDownloads:466,totalCrossrefCites:1,totalDimensionsCites:1,abstract:"An important open problem in geometric complex analysis is to establish algorithms for explicit determination of the basic curvelinear and analytic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmüller and Grunsky norms, Fredholm eigenvalues and the quasireflection coefficient. This has not been solved even for convex polygons. This case has intrinsic interest in view of the connection of polygons with the geometry of the universal Teichmüller space and approximation theory. This survey extends our previous survey of 2005 and presents the new approaches and recent essential progress in this field of geometric complex analysis, having various important applications. Another new topic concerns quasireflections across finite collections of quasiintervals.",book:{id:"8760",slug:"structure-topology-and-symplectic-geometry",title:"Structure Topology and Symplectic Geometry",fullTitle:"Structure Topology and Symplectic Geometry"},signatures:"Samuel L. 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Clifford algebra unifies and generalizes real number, complex, quaternion, and vector algebra and converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant, and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So, Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.",book:{id:"8760",slug:"structure-topology-and-symplectic-geometry",title:"Structure Topology and Symplectic Geometry",fullTitle:"Structure Topology and Symplectic Geometry"},signatures:"Ying-Qiu Gu",authors:[{id:"314607",title:"Dr.",name:"Ying-Qiu",middleName:null,surname:"Gu",slug:"ying-qiu-gu",fullName:"Ying-Qiu Gu"}]},{id:"52596",title:"Symplectic Manifolds: Gromov-Witten Invariants on Symplectic and Almost Contact Metric Manifolds",slug:"symplectic-manifolds-gromov-witten-invariants-on-symplectic-and-almost-contact-metric-manifolds",totalDownloads:1520,totalCrossrefCites:0,totalDimensionsCites:0,abstract:"In this chapter, we introduce Gromov-Witten invariant, quantum cohomology, Gromov-Witten potential, and Floer cohomology on symplectic manifolds, and in connection with these, we describe Gromov-Witten type invariant, quantum type cohomology, Gromov-Witten type potential and Floer type cohomology on almost contact metric manifolds. On the product of a symplectic manifold and an almost contact metric manifold, we induce some relations between Gromov-Witten type invariant and quantum cohomology and quantum type invariant. We show that the quantum type cohomology is isomorphic to the Floer type cohomology.",book:{id:"5488",slug:"manifolds-current-research-areas",title:"Manifolds",fullTitle:"Manifolds - Current Research Areas"},signatures:"Yong Seung Cho",authors:[{id:"62522",title:"Prof.",name:"Yong Seung",middleName:null,surname:"Cho",slug:"yong-seung-cho",fullName:"Yong Seung Cho"}]},{id:"62804",title:"Recent Advances of Manifold Regularization",slug:"recent-advances-of-manifold-regularization",totalDownloads:1096,totalCrossrefCites:0,totalDimensionsCites:3,abstract:"Semi-supervised learning (SSL) that can make use of a small number of labeled data with a large number of unlabeled data to produce significant improvement in learning performance has been received considerable attention. 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We study several extensions of this framework for pairwise constraint, p-Laplacian learning, hypergraph learning, etc.",book:{id:"7342",slug:"manifolds-ii-theory-and-applications",title:"Manifolds II",fullTitle:"Manifolds II - Theory and Applications"},signatures:"Xueqi Ma and Weifeng Liu",authors:null},{id:"79892",title:"βI-Compactness, βI*-Hyperconnectedness and βI-Separatedness in Ideal Topological Spaces",slug:"-em-em-sub-em-i-em-sub-compactness-em-em-sub-em-i-em-sub-hyperconnectedness-and-em-em-sub-em-i-em-su",totalDownloads:76,totalCrossrefCites:0,totalDimensionsCites:0,abstract:"Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it is said to be βI-open if there is a set O∈τ with the property 1 O−A∈I and 2 A−clintclO∈I. The set A is called βI-compact if every cover of A by βI-open sets has a finite sub-cover. The set A is said to be cβI-compact, if every cover Oλ:λ∈Λ of A by β-open sets, Λ has a finite subset Λ0 such that A−∪Oλ:λ∈Λ0∈I. The set A is said to be countably βI-compact if every countable cover of A by βI-open sets has a finite sub-cover. An ideal topological space XτI is said to be βI∗-hyperconnected if X−cl∗A∈I for every non-empty βI-open subset A of X. Two subsets A and B of X is said to be βI-separated if clβIA∩B=∅=A∩clβB. Moreover, A is called a βI-connected set if it can’t be written as a union of two βI-separated subsets. An ideal topological space XτI is called βI-connected space if X is βI-connected. In this article, we give some important properties of βI-open sets, βI-compact spaces, cβI-compact spaces, βI∗-hyperconnected spaces, and βI-connected spaces.",book:{id:"10677",slug:"advanced-topics-of-topology",title:"Advanced Topics of Topology",fullTitle:"Advanced Topics of Topology"},signatures:"Glaisa T. Catalan, Michael P. Baldado Jr and Roberto N. 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According to the behaviour of the tangent bundle of a sub-manifold, with respect to the action of almost Riemannian product structure of the ambient manifolds, we have three typical classes of sub-manifolds such as invariant sub-manifolds, anti-invariant sub-manifolds and semi-invariant sub-manifolds. 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