Q. Q. SUN ET AL. 249

resul

ages and the

co

ts for the swimmer dataset. It could be observed that

as for this dataset, we also could find out the correct

bases via our algorithm. In this figure there are 25 base

images. The black ones correspond to irrelevant bases,

and the other 17 images depict the torso and the limbs at

each possible position. We can see that the correct torso

and limbs are discovered successfully.

The differences between the black im

rrect base images are shown in Figure 7. Figure 7

depicts L2-norm of each column of the base matrix. The

total number of points in this figure is the same to the

initial rank. Obviously, the points are classified into two

clusters. One is zero-value cluster, and the other is lar-

ger-value cluster. Thus the rank of base matrix in swim-

mer dataset is 117RB. The results of L2-norm of

base matrix not ow we could find the correct

bases, but also tell us how we could determine the correct

rank of base matrix.

only tell us h

Figure 6. The bases of swimmer dataset learned by our al-

gorithm.

05 10 15 20 25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Base ve ctor inde

Norm alized L2 nor m

Normalized L

2

norm

Figure 7. L2-norm of base vectors.

supervised multi-level non-

[1] D. D. Lee andhe Parts of Objects

5. Conclu

We have presented an un

sion

negative matrix factorization algorithm which is power-

ful and efficient to seek the correct rank of a data model.

This is achieved by introducing a multi-prior structure.

The experiment results on binary datasets adequately

demonstrate the efficacy of our algorithm. Compare to

the fully Bayesian method, it is simpler and more con-

venient. The crucial points of this method are how to

introduce the hyper-priors and what kind of prior is ap-

propriate to a certain data model. This algorithm also

could be extended to other data models and noise models.

Although our experiment is based on binary dataset, this

algorithm is suitable to other datasets such as gray-level

dataset, colorful dataset, etc.

REFERENCES

H. S. Seung, “Learning t

by Non-Negative Matrix Factorization,” Nature, Vol. 401,

No. 6755, 1999, pp. 788-791. doi:10.1038/44565

[2] Z. Yuan and E. Oja, “Projective Non-Negative Matrix

urrieu, “Non-Negative

Factorization for Image Compression and Feature Extrac-

tion,” Springer, Heidelberg, 2005.

[3] C. Fevotte, N. Bertin and J. L. D

Matrix Factorization with the Itakura-Saito Divergence,”

With Application to Music Analysis. Neural Computation,

Vol. 21, No. 3, 2009, pp. 793-830.

doi:10.1162/neco.2008.04-08-771

[4] M. W. Berry and M. Browne, “Email Surveillance Using

Non-Negative Matrix Factorization,” Computational and

Mathematical Organization Theory, Vol. 11, No. 3, 2005,

pp. 249-264. doi:10.1007/s10588-005-5380-5

[5] Q. Sun, F. Hu and Q. Hao, “Context Awareness Emer-

ile Targets Region-of-

“Clustering-

06

gence for Distributed Binary Pyroelectric Sensors,” Pro-

ceeding of 2010 IEEE Conference on Multisensor Fusion

and Integration for Intelligent Systems, Salt Lake City,

5-7 September 2010, pp. 162-167.

[6] F. Hu, Q. Sun and Q. Hao, “Mob

Interest via Distributed Pyroelectric Sensor Network:

Towards a Robust, Real-Pyroelectric Sensor Network,”

Proceeding of 2010 IEEE Conference on Sensors, Wai-

koloa, 1-4 November 2010, pp. 1832-1836.

[7] Y. Xue, C. S. Tong and Y. C. W. Chen,

Based Initialization for Non-Negative Matrix Factoriza-

tion,” Applied Mathematics and Computation, Vol. 205,

No. 2, 2008, pp. 525-536.

doi:10.1016/j.amc.2008.05.1

utomatic Rank Determi-

ative Ma-

[8] Z. Yang, Z. Zhu and E. Oja, “A

nation in Projective Non-Negative Matrix Factorization,”

Proceedings of 9th International Conference on LVA/ICA,

St. Malo, 27-30 September 2010, pp. 514-521.

[9] A. T. Cemgil, “Bayesian Inference for Non-Neg

trix Factorization Models,” Computational Intelligence

and Neuroscience, Vol. 2009, 2009, Article ID: 785152.

doi:10.1155/2009/785152

[10] M. Said, D. Brie, A. Mohammad-Djafari and C. Cedric,

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