Loading and correlations in the interpretation of principle compenents

Cadima, Jorge

doi:10.1080/757584614

Cited by 288 publications

(216 citation statements)

References 8 publications

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“…In other words, only a subset of features is selected. We compare our performance against the simple thresholding method [32]. Table 6 reports the classification error.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Supervised dimensionality reduction via sequential semidefinite programming

Shen

Brooks

2008

Pattern Recognition

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Cite this article as: Chunhua Shen, Hongdong Li and Michael J. Brooks, Supervised dimensionality reduction via sequential semidefinite programming, Pattern Recognition (2008Recognition ( ), doi:10.1016Recognition ( /j.patcog.2008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractMany dimensionality reduction problems end up with a trace quotient formulation. Since it is difficult to directly solve the trace quotient problem, traditionally the trace quotient cost function is replaced by an approximation such that generalized eigenvalue decomposition can be applied. In contrast, we directly optimize the trace quotient in this work. It is reformulated as a quasi-linear semidefinite optimization problem, which can be solved globally and efficiently using standard off-the-shelf semidefinite programming solvers. Also this optimization strategy allows one to enforce additional constraints (for example, sparseness constraints) on the projection matrix. We apply this optimization framework to a novel dimensionality reduction algorithm. The performance of the proposed algorithm is demonstrated in experiments on several UCI machine learning benchmark examples, USPS handwritten digits as well as ORL and Yale face data.

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“…In other words, only a subset of features is selected. We compare our performance against the simple thresholding method [32]. Table 6 reports the classification error.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Supervised dimensionality reduction via sequential semidefinite programming

Shen

Brooks

2008

Pattern Recognition

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“…Jolliffe (1972Jolliffe ( , 1973 examined methods that discard irrelevant variables based on threshold values using multiple correlations, PCA itself, and clustering.These methods are very simple; however, this might be misleading as pointed out by Cadima and Jolliffe (1995). Other methods that aid in the interpretation of principal components include orthogonal rotation, similar to those used in factor analysis (Jolliffe, 1989(Jolliffe, , 1995, that restrict the coefficients of the components to a small set of possible values such as −1, 0, 1 (Hausman, 1982;Vines, 2000) and to introduce penalty functions to force the coefficients of irrelevant variables to zero (Jolliffe, 2002).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic penalized principal component analysis

Park

Wang

2017

CSAM

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A variable selection method based on probabilistic principal component analysis (PCA) using penalized likelihood method is proposed. The proposed method is a two-step variable reduction method. The first step is based on the probabilistic principal component idea to identify principle components. The penalty function is used to identify important variables in each component. We then build a model on the original data space instead of building on the rotated data space through latent variables (principal components) because the proposed method achieves the goal of dimension reduction through identifying important observed variables. Consequently, the proposed method is of more practical use. The proposed estimators perform as the oracle procedure and are root-n consistent with a proper choice of regularization parameters. The proposed method can be successfully applied to high-dimensional PCA problems with a relatively large portion of irrelevant variables included in the data set. It is straightforward to extend our likelihood method in handling problems with missing observations using EM algorithms. Further, it could be effectively applied in cases where some data vectors exhibit one or more missing values at random.

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“…These interpretable factors are sparse principal components (spca). There are many heuristics for obtaining sparse factors [3,17,18,6,5,12,16] as well as some approximation algorithms with provable guarantees [2]. Our goal in this short paper is to establish the NP-hardness and inapproximability of spca using a reduction from clique.…”

Section: Introductionmentioning

confidence: 99%