Linear relations amongk sets of variables

Geer, Van de; John, P

doi:10.1007/bf02294207

Cited by 93 publications

(44 citation statements)

References 10 publications

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“…There are two important choices to make when considering multiblock methods: variance explained and fairness [3]. The first choice relates to whether only the relationship between blocks is interesting or whether the multiblock solution should also describe variation within each block of data.…”

Section: Properties Of Multiblock Modelsmentioning

confidence: 99%

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A framework for sequential multiblock component methods

Smilde

Westerhuis

Jong

2003

Journal of Chemometrics

194

135

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Multiblock or multiset methods are starting to be used in chemistry and biology to study complex data sets. In chemometrics, sequential multiblock methods are popular; that is, methods that calculate one component at a time and use deflation for finding the next component. In this paper a framework is provided for sequential multiblock methods, including hierarchical PCA (HPCA; two versions), consensus PCA (CPCA; two versions) and generalized PCA (GPCA). Properties of the methods are derived and characteristics of the methods are discussed. All this is illustrated with a real five-block example from chromatography. The only methods with clear optimization criteria are GPCA and one version of CPCA. Of these, GPCA is shown to give inferior results compared with CPCA.

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Section: Properties Of Multiblock Modelsmentioning

confidence: 99%

“…Multiblock analysis methods already have a long history in psychometrics [3,5,6] and are still the subject of active research [7][8][9][10][11]. Also in computational statistics and chemometrics, multiblock methods have been developed [4,[12][13][14][15][16] and investigated theoretically [17,18].…”

Section: Introductionmentioning

confidence: 99%

A framework for sequential multiblock component methods

Smilde

Westerhuis

Jong

2003

Journal of Chemometrics

194

135

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“…The notion of CCA has been applied to areas such as cluster analysis, data classification, pattern recognition, principal component analysis, and bioinformatics. Some general treatments as well as practicalities on this subject can be found in treatises [5,6,8,9,12,15,18]. One very early development of CCA is the maximal correlation problem (MCP) proposed by Hotelling [10,11] where the goal is to find the linear combination of one set of variables that correlates maximally with the linear combination of another set of variables.…”

Section: Introductionmentioning

confidence: 99%

“…[ni] ∈ R ni×ni denoting the n i × n i identity matrix [4,18]. We shall exploit this condition again in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Computing absolute maximum correlation

Zhang

Chu²

2011

IMA Journal of Numerical Analysis

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Abstract. Optimizing correlations between sets of variables is an important task in many areas of applications. There are plenty of algorithms for computing the maximum correlation. Most disappointedly, however, these methods typically cannot guarantee attaining the absolute maximum correlation which would have significant impact on practical applications. This paper makes two contributions. Firstly, some distinctive traits of the absolute maximum correlation are characterized. By exploiting these attributes, it is possible to propose an effective starting point strategy that significantly increases the likelihood of attaining the absolute maximum correlation. Numerical testing of the classical Horst algorithm with the starting point strategy seems to evince the potency of this approach. Secondly, the Horst algorithm is but one aggregated Jacobi-type power method. Following the innate iterative structure, a generalization to the Gauss-Seidel formulation is proposed as a natural improvement on the power method. Monotone convergence of the Gauss-Seidel algorithm is proved. When combined with the starting point strategy, the newer Gauss-Seidel approach leads to faster computation of the absolute maximum correlation.

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“…It is very popular also in the social sciences where it belongs to a class of methods of matching matrices. Van de Geer [12] referred to it as the MAXDIFF criterion. Previously, Tucker [13] introduced this method, with the name Inter-Battery Factor Analysis, in order to find common factors in two batteries of tests presented to the same group of statistical units.…”

Section: Introductionmentioning

confidence: 99%

Double restricted Co‐Inertia Analysis

Amenta

2007

Journal of Chemometrics

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In this paper, an extension of the Co‐Inertia Analysis 1 is proposed. This extension is based on an objective function which takes directly into account the external information, as linear restrictions, about parameters of both sets of variables, by rewriting the Co‐Inertia Analysis objective function according to the principle of Restricted Eigenvalue Problem 2. A restricted extension of Wold's two‐block ‘Mode A’ Partial Least Squares 3 is also proposed. Copyright © 2007 John Wiley & Sons, Ltd.

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Linear relations amongk sets of variables

Abstract: canonical correlation, linear relations between sets, multiple regression, redundancy analysis, ridge regression,

Cited by 93 publications

References 10 publications

A framework for sequential multiblock component methods

A framework for sequential multiblock component methods

Computing absolute maximum correlation

Double restricted Co‐Inertia Analysis

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