Asymmetric Principal Component and Discriminant Analyses for Pattern Classification

Jiang, Xudong

doi:10.1109/tpami.2008.258

Cited by 112 publications

(12 citation statements)

References 20 publications

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“…However, applying PCA-based method, the total covariance matrixes does not effectively remove the unreliable dimensions if one class is represented by its training data much better or much worse than the other class. The asymmetric principal component analysis (APCA) [8] and linear subspace learning-based dimensionality reduction [9] alleviate this problem by asymmetrically weighting the class conditional covariance matrices and by considering the important weak composition. Thus, we design an novel APCA-based method to identify the differentially expressed genes between patients with pmAF and the control group by combining the ideas in two works above [8], [9].…”

Section: Methodsmentioning

confidence: 99%

Analysis on Differential Gene Expression Data for Prediction of New Biological Features in Permanent Atrial Fibrillation

et al. 2013

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Permanent Atrial fibrillation (pmAF) has largely remained incurable since the existing information for explaining precise mechanisms underlying pmAF is not sufficient. Microarray analysis offers a broader and unbiased approach to identify and predict new biological features of pmAF. By considering the unbalanced sample numbers in most microarray data of case - control, we designed an asymmetric principal component analysis algorithm and applied it to re - analyze differential gene expression data of pmAF patients and control samples for predicting new biological features. Finally, we identified 51 differentially expressed genes using the proposed method, in which 42 differentially expressed genes are new findings compared with two related works on the same data and the existing studies. The enrichment analysis illustrated the reliability of identified differentially expressed genes. Moreover, we predicted three new pmAF – related signaling pathways using the identified differentially expressed genes via the KO-Based Annotation System. Our analysis and the existing studies supported that the predicted signaling pathways may promote the pmAF progression. The results above are worthy to do further experimental studies. This work provides some new insights into molecular features of pmAF. It has also the potentially important implications for improved understanding of the molecular mechanisms of pmAF.

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Section: Methodsmentioning

confidence: 99%

Analysis on Differential Gene Expression Data for Prediction of New Biological Features in Permanent Atrial Fibrillation

et al. 2013

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“…This bias is most pronounced when the population eigenvalues tend towards equality and is correspondingly less severe when their values are highly disparate. In all cases, this phenomenon becomes more pronounced as the sample size decreases [44–46]. Second, if there are very small eigenvalues in the sample covariance matrix, logarithm of these tiny eigenvalues will incur large disturbance that can dramatically degrade the generalization ability.…”

Section: Variants Of the Region Covariance Descriptormentioning

confidence: 99%

Object Tracking Using Adaptive Covariance Descriptor and Clustering-Based Model Updating for Visual Surveillance

Qin

Snoussi

Abdallah

2014

Sensors

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We propose a novel approach for tracking an arbitrary object in video sequences for visual surveillance. The first contribution of this work is an automatic feature extraction method that is able to extract compact discriminative features from a feature pool before computing the region covariance descriptor. As the feature extraction method is adaptive to a specific object of interest, we refer to the region covariance descriptor computed using the extracted features as the adaptive covariance descriptor. The second contribution is to propose a weakly supervised method for updating the object appearance model during tracking. The method performs a mean-shift clustering procedure among the tracking result samples accumulated during a period of time and selects a group of reliable samples for updating the object appearance model. As such, the object appearance model is kept up-to-date and is prevented from contamination even in case of tracking mistakes. We conducted comparing experiments on real-world video sequences, which confirmed the effectiveness of the proposed approaches. The tracking system that integrates the adaptive covariance descriptor and the clustering-based model updating method accomplished stable object tracking on challenging video sequences.

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“…However, this theoretical proof seems very often to be contradicted in practice as performance does decrease with increasing dimensionality (known as the curse of dimensionality [8]). In [9] it is argued that the proof is based on knowing the data structure of the data generating process, while in practice only a training set is available to inver this knowledge from. Several factors are known to corrupt this inference: incorrect sampling [9], errors in the measurements • A. Hendrikse, R. Veldhuis and L. Spreeuwers are with the Department of EEMCS, University of Twente, Enschede, the Netherlands.…”

Section: Introductionmentioning

confidence: 99%

“…In [9] it is argued that the proof is based on knowing the data structure of the data generating process, while in practice only a training set is available to inver this knowledge from. Several factors are known to corrupt this inference: incorrect sampling [9], errors in the measurements • A. Hendrikse, R. Veldhuis and L. Spreeuwers are with the Department of EEMCS, University of Twente, Enschede, the Netherlands. E-mail: a.j.hendrikse@ewi.utwente.nl [10], [11], modeling errors [12] and errors in the currently used estimators [13], [14].…”

Section: Introductionmentioning

confidence: 99%

“…In section 6 we present improvements to the individual SOS estimates. However, verification depends on two distribution estimates: one describing the variation between samples from one class and one describing the variation between samples from different classes (a major point in [9]). In the correction of the distribution estimates, the relation between the two should be taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Likelihood-Ratio-Based Verification in High-Dimensional Spaces

Hendrikse

Veldhuis

Spreeuwers

2014

IEEE Trans. Pattern Anal. Mach. Intell.

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The increase of the dimensionality of data sets often leads to problems during estimation, which are denoted as the curse of dimensionality. One of the problems of second-order statistics (SOS) estimation in high-dimensional data is that the resulting covariance matrices are not full rank, so their inversion, for example, needed in verification systems based on the likelihood ratio, is an ill-posed problem, known as the singularity problem. A classical solution to this problem is the projection of the data onto a lower dimensional subspace using principle component analysis (PCA) and it is assumed that any further estimation on this dimension-reduced data is free from the effects of the high dimensionality. Using theory on SOS estimation in high-dimensional spaces, we show that the solution with PCA is far from optimal in verification systems if the high dimensionality is the sole source of error. For moderate dimensionality, it is already outperformed by solutions based on euclidean distances and it breaks down completely if the dimensionality becomes very high. We propose a new method, the fixed-point eigenwise correction, which does not have these disadvantages and performs close to optimal.

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Asymmetric Principal Component and Discriminant Analyses for Pattern Classification

Cited by 112 publications

References 20 publications

Analysis on Differential Gene Expression Data for Prediction of New Biological Features in Permanent Atrial Fibrillation

Analysis on Differential Gene Expression Data for Prediction of New Biological Features in Permanent Atrial Fibrillation

Object Tracking Using Adaptive Covariance Descriptor and Clustering-Based Model Updating for Visual Surveillance

Likelihood-Ratio-Based Verification in High-Dimensional Spaces

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