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In human face image analysis, every face has common facial organs such as cheek, nose, eyes, and mouth, etc, and they often share some same features to some extend reflecting their shapes and locations, etc. Generally, their common features do not provide any discriminative information between them, while their individual features do. For this reason we proposed a scheme of common and individual feature analysis (CIFA) to extract separated common and individual features from multi-block linked data in order to improve data analysis performance.


CIFAfaces
Fig. 1. Common and individual features in face images.


Model

Given a set of matrices Yn, n=1,2,…,N, we seek their decomposition of Yn:

min Σn ||Yn - [Ac Ain][Bcn Bin]T ||2,
s.t.
AcTAc=I, AcTAin=0, and AinTAin=I, n=1,2,…,N.

In the above mode, matrix Ac denotes the common features presented in all data while the matrix Ain denotes individual features only presented in Yn.
flowdiagram
Fig. 2.
Flow diagram of the general common and individual feature analysis (CIFA)



Example


Given two 1000-by-10 matrices A1 and A2. The first column of A1 is generated as sin(0.01*t) while the first column of A2 is generated as sign(sin(0.01*t)). These two matrices were mixed by two different 10-by-10 matrices B1 and B2 whose entries were drawn from i.i.d. standard normal distribution to generate observation matrices Y1 and Y2. The comparison results between COBE (common orthogonal basis extraction), CCA, PCA, and JIVE are plotted in Fig.3 and Fig.4 below, respectively.

cobe_cca
Fig. 3.
Illustration of COBE as a high-correlation analysis tool.

cobepcajive
Fig. 4.
Comparison between COBE, PCA, and JIVE.


References:

  1. Guoxu Zhou, Qibin Zhao, Yu Zhang, Tulay Adalı, Shengli Xie, and Andrzej Cichocki, "Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data", Proceedings of the IEEE. Accepted. DOI: http://10.1109/JPROC.2015.2474704. 2015.

  2. Guoxu Zhou, Andrzej Cichocki, Yu Zhang, and Danilo Mandic. "Group Component Analysis from Multi-block Data: Common and Individual Feature Extraction,” IEEE Transactions on Neural Networks and Learning Systems, Accepted. DOI: 10.1109/TNNLS.2015.2487364. 2015.


[Draft] [Supplementary Information]

Code

Matlab codes (algorithms and some demos).