### 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.

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

## Model

Given a set of matrices Y* _{n}*,

*n=1,2,…,N*, we seek their decomposition of Y

*:*

_{n} min Σ* _{n} * ||Y

*- [Ac Ai*

_{n}*][Bc*

_{n}*Bi*

_{n}*]*

_{n}*||*

^{T}^{2},

s.t. Ac

*Ac=I, Ac*

^{T}*Ai*

^{T}*=0, and Ai*

_{n}*Ai*

_{n}^{T}*=I,*

_{n}*n=1,2,…,N*.

In the above mode, matrix Ac denotes the common features presented in all data while the matrix Ai

*denotes individual features only presented in Y*

_{n}*.*

_{n}Fig. 2. Flow diagram of the general common and individual feature analysis (CIFA)

## Example

Given two 1000-by-10 matrices A

_{1}and A

_{2}. The first column of A

_{1}is generated as

*sin*(0.01*

*t*) while the first column of A

_{2}is generated as

*sign*(

*sin*(0.01*

*t*)). These two matrices were mixed by two different 10-by-10 matrices B

_{1}and B

_{2}whose entries were drawn from i.i.d. standard normal distribution to generate observation matrices Y

_{1}and Y

_{2}. The comparison results between COBE (common orthogonal basis extraction), CCA, PCA, and JIVE are plotted in Fig.3 and Fig.4 below, respectively.

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

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

◦ References:

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.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.