Facial Expression Recognition Based on PCA and NMFIntelligent Control and Automation, 2008. WCICA 2008.

Outline• Introduction• Principal Component Analysis (PCA) Method• Non-negative Matrix Factorization (NMF) Method• PCA-NMF Method• Experiments Result and Analysis• Conclusion

Introduction• In this paper, we have detailed PCA and NMF, and

applied them to feature extraction of facial expression images.

• We also try to process basic image matrix and weight matrix of PCA and make them as the initialization of NMF.

• The experiments demonstrate that the method has got a better recognition rate than PCA and NMF.

Principal Component Analysis MethodLet’s suppose that m expression images are selected to take part in training, the training set X is defined by

Covariance matrix corresponding to all training samples is obtained as

u, average face, is defined by

Principal Component Analysis Method

# of training data

𝑥1 𝑥2 𝑥3 𝑥4

average face

𝑟𝑜𝑤+ + +

𝟒

𝑢

𝑐𝑜𝑙𝑛=𝑟𝑜𝑤×𝑐𝑜𝑙

Training Data Set

Principal Component Analysis Method

LetThen (2) becomes𝐴∈𝑅𝑛×𝑚

𝐶∈𝑅𝑛×𝑛❑⇒Matrix has eigenvectors

and eigenvalues.

Principal Component Analysis Method

Image50x50

⇒𝑛=50×50=2500

It is difficult to get 2500 eigenvectors and eigenvalues.

Therefore, we get eigenvectors and eigenvalues of by solving eigenvectors and eigenvalues of .

𝐴𝑇 𝐴∈𝑅𝑚×𝑚

Principal Component Analysis Method

The vectors and scalars are the eigenvectors and eigenvalues of covariance matrix . Then, eigenvectors of are defined by

Sorting by size: Generally, the scale is capacity that eigenvalues occupied:

Principal Component Analysis Method

Set is a projection matrix,

And then, every facial expression image feature can be denoted by following equation

PCA basic images

Non-negative Matrix Factorization MethodGiven a non-negative matrix , the NMF algorithms seek to find non-negative factors and of ,such that :

where is the number of feature vector satisfies

Non-negative Matrix Factorization MethodIterative update formulae are given as follow:

set hen define objective function

Non-negative Matrix Factorization Method

And then, every facial expression image feature can be denoted by following equation

NMF basic images

PCA-NMF Method

First, get projective matrix and weight matrix by PCA method.

Initialization is performed for matrices and by following

PCA-NMF Method

PCA-NMF basic imagesNMF basic images

Experiments Result And Analysis

anger disgust fear happy neutral sad surprise

anger disgust fear happy neutral sad surprise

Experiments Result And Analysis

The comparison of recognition rate for every expression( The training set comprises 70 images and the test set of 70 images)

Experiments Result And Analysis

The comparison of recognition rate for every expression( The training set comprises 70 images and the test set of 143 images)

Experiments Result And Analysis

The comparison of recognition rate for every expression( The training set comprises 140 images and the test set of 73 images)

Experiments Result And Analysis

The discussion or r

Conclusion

The results of experiments demonstrate that NMF and PCA-NMF can outperform PCA. The best recognition rate of facial expression image is 93.72%. On the whole, our approach provides good recognition rates.