A class of learning algorithms for principal component analysis and minor component analysis

2000 ◽  
Vol 11 (2) ◽  
pp. 529-533 ◽  
Author(s):  
Q. Zhang ◽  
Yiu-Wung Leung
Keyword(s):  
Principal Component Analysis ◽  
Learning Algorithms ◽  
Minor Component ◽  
Principal Component ◽  
Component Analysis ◽  
Minor Component Analysis

Products of Gaussians and Probabilistic Minor Component Analysis

2002 ◽  
Vol 14 (5) ◽  
pp. 1169-1182 ◽  
Author(s):  
C. K. I. Williams ◽  
F. V. Agakov
Keyword(s):  
Principal Component Analysis ◽  
Covariance Structure ◽  
Minor Component ◽  
Principal Component ◽  
Component Analysis ◽  
Minor Component Analysis ◽  
A Minor ◽  
Analysis Models ◽  
Probabilistic Principal Component Analysis ◽  
Individual Expert

Recently, Hinton introduced the products of experts architecture for density estimation, where individual expert probabilities are multiplied and renormalized. We consider products of gaussian “pancakes” equally elongated in all directions except one and prove that the maximum likelihood solution for the model gives rise to a minor component analysis solution. We also discuss the covariance structure of sums and products of gaussian pancakes or one-factor probabilistic principal component analysis models.

scholarly journals Modal Principal Component Analysis

2020 ◽  
Vol 32 (10) ◽  
pp. 1901-1935
Author(s):  
Keishi Sando ◽  
Hideitsu Hino
Keyword(s):  
Principal Component Analysis ◽  
Minor Component ◽  
Principal Component ◽  
Breakdown Point ◽  
Component Analysis ◽  
Finite Sample ◽  
Robust Pca ◽  
Theoretical Contribution ◽  
Mode Estimation ◽  
Finite Sample Breakdown Point

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.

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