國立虎尾科技大學 |

Nonlinear Principal Component Analysis and Its Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Nonlinear Principal Component Analysis and Its Applications/ by Yuichi Mori, Masahiro Kuroda, Naomichi Makino.
作者:	Mori, Yuichi.
其他作者:	Kuroda, Masahiro.
面頁冊數:	X, 80 p. 17 illus., 8 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Statistics . -
電子資源:	https://doi.org/10.1007/978-981-10-0159-8
ISBN:	9789811001598

Nonlinear Principal Component Analysis and Its Applications
Mori, Yuichi.

Nonlinear Principal Component Analysis and Its Applications[electronic resource] /by Yuichi Mori, Masahiro Kuroda, Naomichi Makino. - 1st ed. 2016. - X, 80 p. 17 illus., 8 illus. in color.online resource. - JSS Research Series in Statistics,2364-0057. - JSS Research Series in Statistics,.

1. Introduction -- 2. Nonlinear Principal Component Analysis -- 3. Application.

This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.

ISBN: 9789811001598

Standard No.: 10.1007/978-981-10-0159-8doiSubjects--Topical Terms:

1253516
Statistics .

LC Class. No.: QA276-280

Dewey Class. No.: 519.5

Nonlinear Principal Component Analysis and Its Applications
LDR:03452nam a22003975i 4500 001 974008
003 DE-He213
005 20200703012019.0
007 cr nn 008mamaa
008 201211s2016 si | s |||| 0|eng d
020 $a 9789811001598 $9 978-981-10-0159-8
024 7 $a 10.1007/978-981-10-0159-8 $2 doi
035 $a 978-981-10-0159-8
050 4 $a QA276-280
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.5 $2 23
100 1 $a Mori, Yuichi. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 884210
245 1 0 $a Nonlinear Principal Component Analysis and Its Applications $h [electronic resource] / $c by Yuichi Mori, Masahiro Kuroda, Naomichi Makino.
250 $a 1st ed. 2016.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2016.
300 $a X, 80 p. 17 illus., 8 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a JSS Research Series in Statistics, $x 2364-0057
505 0 $a 1. Introduction -- 2. Nonlinear Principal Component Analysis -- 3. Application.
520 $a This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.
650 0 $a Statistics . $3 1253516
650 1 4 $a Statistical Theory and Methods. $3 671396
650 2 4 $a Statistics and Computing/Statistics Programs. $3 669775
650 2 4 $a Statistics for Social Sciences, Humanities, Law. $3 1211304
700 1 $a Kuroda, Masahiro. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1116529
700 1 $a Makino, Naomichi. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1116530
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811001574
776 0 8 $i Printed edition: $z 9789811001581
830 0 $a JSS Research Series in Statistics, $x 2364-0057 $3 1255493
856 4 0 $u https://doi.org/10.1007/978-981-10-0159-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)