The First Discriminant Theory Of Linearly Separable Data
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The First Discriminant Theory Of Linearly Separable Data
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Author : Shuichi Shinmura
language : en
Publisher: Springer Nature
Release Date : 2024-04-12
The First Discriminant Theory Of Linearly Separable Data written by Shuichi Shinmura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-12 with Mathematics categories.
This book deals with the first discriminant theory of linearly separable data (LSD), Theory3, based on the four ordinary LSD of Theory1 and 169 microarrays (LSD) of Theory2. Furthermore, you can quickly analyze the medical data with the misclassified patients which is the true purpose of diagnoses. Author developed RIP (Optimal-linear discriminant function finding the combinatorial optimal solution) as Theory1 in decades ago, that found the minimum misclassifications. RIP discriminated 63 (=26−1) models of Swiss banknote (200*6) and found the minimum LSD: basic gene set (BGS). In Theory2, RIP discriminated Shipp microarray (77*7129) which was LSD and had only 32 nonzero coefficients (first Small Matryoshka; SM1). Because RIP discriminated another 7,097 genes and found SM2, the author developed the Matryoshka feature selection Method 2 (Program 3), that splits microarray into many SMs. Program4 can split microarray into many BGSs. Then, the wide columnLSD (Revolution-0), such as microarray (np), is found to have several Matryoshka dolls, including SM up to BGS./p Theory3 shows the surprising results of six ordinary data re-analyzed by Theory1 and Theory2 knowledge. Essence of Theory3 is described by using cephalopelvic disproportion (CPD) data. RIP discriminates CPD data (240*19) and finds two misclassifications unique for cesarean and natural-born groups. CPD238 omitting two patients becomes LSD, which is the first case selection method. Program4 finds BGS (14 vars.) the only variable selection method for Theory3. 32 (=25) models, including BGS, become LSD among (219−1) models. Because Program2 confirms BGS has the minimum average error rate, BGS is the most compact and best model satisfying Occam’s Razor. With this book, physicians obtain complete diagnostic results for disease, and engineers can become a true data scientist, by obtaining integral knowledge ofstatistics and mathematical programming with simple programs.
New Theory Of Discriminant Analysis After R Fisher
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Author : Shuichi Shinmura
language : en
Publisher: Springer
Release Date : 2016-12-27
New Theory Of Discriminant Analysis After R Fisher written by Shuichi Shinmura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-27 with Mathematics categories.
This is the first book to compare eight LDFs by different types of datasets, such as Fisher’s iris data, medical data with collinearities, Swiss banknote data that is a linearly separable data (LSD), student pass/fail determination using student attributes, 18 pass/fail determinations using exam scores, Japanese automobile data, and six microarray datasets (the datasets) that are LSD. We developed the 100-fold cross-validation for the small sample method (Method 1) instead of the LOO method. We proposed a simple model selection procedure to choose the best model having minimum M2 and Revised IP-OLDF based on MNM criterion was found to be better than other M2s in the above datasets. We compared two statistical LDFs and six MP-based LDFs. Those were Fisher’s LDF, logistic regression, three SVMs, Revised IP-OLDF, and another two OLDFs. Only a hard-margin SVM (H-SVM) and Revised IP-OLDF could discriminate LSD theoretically (Problem 2). We solved the defect of the generalized inverse matrices (Problem 3). For more than 10 years, many researchers have struggled to analyze the microarray dataset that is LSD (Problem 5). If we call the linearly separable model "Matroska," the dataset consists of numerous smaller Matroskas in it. We develop the Matroska feature selection method (Method 2). It finds the surprising structure of the dataset that is the disjoint union of several small Matroskas. Our theory and methods reveal new facts of gene analysis.
Big Data Cloud Computing And Data Science Engineering
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Author : Roger Lee
language : en
Publisher: Springer
Release Date : 2019-07-30
Big Data Cloud Computing And Data Science Engineering written by Roger Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-30 with Computers categories.
This edited book presents the scientific outcomes of the 4th IEEE/ACIS International Conference on Big Data, Cloud Computing, Data Science & Engineering (BCD 2019) which was held on May 29–31, 2019 in Honolulu, Hawaii. The aim of the conference was to bring together researchers and scientists, businessmen and entrepreneurs, teachers, engineers, computer users and students to discuss the numerous fields of computer science and to share their experiences and exchange new ideas and information in a meaningful way. Presenting 15 of the conference’s most promising papers, the book discusses all aspects (theory, applications and tools) of computer and information science, the practical challenges encountered along the way, and the solutions adopted to solve them.
Advanced Intelligent Computing Theories And Applications
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Author : De-Shuang Huang
language : en
Publisher: Springer
Release Date : 2007-07-31
Advanced Intelligent Computing Theories And Applications written by De-Shuang Huang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-31 with Computers categories.
This volume, in conjunction with the two volumes CICS 0002 and LNCS 4681, constitutes the refereed proceedings of the Third International Conference on Intelligent Computing held in Qingdao, China, in August 2007. The 139 full papers published here were carefully reviewed and selected from among 2,875 submissions. These papers offer important findings and insights into the field of intelligent computing.
Backpropagation
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Author : Yves Chauvin
language : en
Publisher: Psychology Press
Release Date : 2013-02-01
Backpropagation written by Yves Chauvin and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-01 with Psychology categories.
Composed of three sections, this book presents the most popular training algorithm for neural networks: backpropagation. The first section presents the theory and principles behind backpropagation as seen from different perspectives such as statistics, machine learning, and dynamical systems. The second presents a number of network architectures that may be designed to match the general concepts of Parallel Distributed Processing with backpropagation learning. Finally, the third section shows how these principles can be applied to a number of different fields related to the cognitive sciences, including control, speech recognition, robotics, image processing, and cognitive psychology. The volume is designed to provide both a solid theoretical foundation and a set of examples that show the versatility of the concepts. Useful to experts in the field, it should also be most helpful to students seeking to understand the basic principles of connectionist learning and to engineers wanting to add neural networks in general -- and backpropagation in particular -- to their set of problem-solving methods.
Operations Research And Enterprise Systems
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Author : Eric Pinson
language : en
Publisher: Springer
Release Date : 2015-04-16
Operations Research And Enterprise Systems written by Eric Pinson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Computers categories.
This book constitutes the refereed proceedings of the Third International Conference on Operations Research and Enterprise Systems, ICORES 2014, held in Angers, France, in March 2014. The 18 revised full papers presented together with an invited paper were carefully reviewed and selected from 96 submissions. The papers are organized in topical sections on Methodologies and Technologies and Applications.
Data Complexity In Pattern Recognition
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Author : Mitra Basu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-22
Data Complexity In Pattern Recognition written by Mitra Basu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-22 with Computers categories.
Machines capable of automatic pattern recognition have many fascinating uses in science & engineering as well as in our daily lives. Algorithms for supervised classification, where one infers a decision boundary from a set of training examples, are at the core of this capability. This book takes a close view of data complexity & its role in shaping the theories & techniques in different disciplines & asks: What is missing from current classification techniques? When the automatic classifiers are not perfect, is it a deficiency of the algorithms by design, or is it a difficulty intrinsic to the classification task? How do we know whether we have exploited to the fullest extent the knowledge embedded in the training data? Uunique in its comprehensive coverage & multidisciplinary approach from various methodological & practical perspectives, researchers & practitioners will find this book an insightful reference to learn about current available techniques as well as application areas.
High Dimensional Microarray Data Analysis
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Author : Shuichi Shinmura
language : en
Publisher: Springer
Release Date : 2019-05-14
High Dimensional Microarray Data Analysis written by Shuichi Shinmura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-14 with Medical categories.
This book shows how to decompose high-dimensional microarrays into small subspaces (Small Matryoshkas, SMs), statistically analyze them, and perform cancer gene diagnosis. The information is useful for genetic experts, anyone who analyzes genetic data, and students to use as practical textbooks. Discriminant analysis is the best approach for microarray consisting of normal and cancer classes. Microarrays are linearly separable data (LSD, Fact 3). However, because most linear discriminant function (LDF) cannot discriminate LSD theoretically and error rates are high, no one had discovered Fact 3 until now. Hard-margin SVM (H-SVM) and Revised IP-OLDF (RIP) can find Fact3 easily. LSD has the Matryoshka structure and is easily decomposed into many SMs (Fact 4). Because all SMs are small samples and LSD, statistical methods analyze SMs easily. However, useful results cannot be obtained. On the other hand, H-SVM and RIP can discriminate two classes in SM entirely. RatioSV is the ratioof SV distance and discriminant range. The maximum RatioSVs of six microarrays is over 11.67%. This fact shows that SV separates two classes by window width (11.67%). Such easy discrimination has been unresolved since 1970. The reason is revealed by facts presented here, so this book can be read and enjoyed like a mystery novel. Many studies point out that it is difficult to separate signal and noise in a high-dimensional gene space. However, the definition of the signal is not clear. Convincing evidence is presented that LSD is a signal. Statistical analysis of the genes contained in the SM cannot provide useful information, but it shows that the discriminant score (DS) discriminated by RIP or H-SVM is easily LSD. For example, the Alon microarray has 2,000 genes which can be divided into 66 SMs. If 66 DSs are used as variables, the result is a 66-dimensional data. These signal data can be analyzed to find malignancy indicators by principal component analysis and cluster analysis.
Rough Sets And Knowledge Technology
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Author : James F. Peters
language : en
Publisher: Springer
Release Date : 2006-09-27
Rough Sets And Knowledge Technology written by James F. Peters and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-27 with Computers categories.
This book constitutes the refereed proceedings of the First International Conference on Rough Sets and Knowledge Technology, RSKT 2006, held in Chongqing, China in July 2006. The volume presents 43 revised full papers and 58 revised short papers, together with 15 commemorative and invited papers. Topics include rough computing, evolutionary computing, fuzzy sets, granular computing, neural computing, machine learning and KDD, logics and reasoning, multiagent systems and Web intelligence, and more.
Face Detection And Recognition
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Author : Asit Kumar Datta
language : en
Publisher: CRC Press
Release Date : 2015-10-28
Face Detection And Recognition written by Asit Kumar Datta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-28 with Computers categories.
Face detection and recognition are the nonintrusive biometrics of choice in many security applications. Examples of their use include border control, driver's license issuance, law enforcement investigations, and physical access control.Face Detection and Recognition: Theory and Practice elaborates on and explains the theory and practice of face de