Learning non-negative sparse image codes by convex programming

Example-based learning of codes that statistically encode general image classes is of vital importance for computational vision. Recently non negative matrix factorization (NMF) was suggested to provide image code that was both sparse and localized, in contrast to established non local methods like PCA. In this paper, we adopt and generalize this approach to develop a novel learning framework that allows to efficiently compute sparsity-controlled invariant image codes by a well defined sequence of convex conic programs. Applying the corresponding parameter-free algorithm to various image classes results in semantically relevant and transformation-invariant image representations that are remarkably robust against noise and quantization

[1]  Yunde Jia,et al.  FISHER NON-NEGATIVE MATRIX FACTORIZATION FOR LEARNING LOCAL FEATURES , 2004 .

[2]  A. Hyvärinen,et al.  A multi-layer sparse coding network learns contour coding from natural images , 2002, Vision Research.

[3]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[4]  B. Frey,et al.  Transformation-Invariant Clustering Using the EM Algorithm , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Xin Liu,et al.  Document clustering based on non-negative matrix factorization , 2003, SIGIR.

[6]  K. Kreutz-Delgado,et al.  A General Approach to Sparse Basis Selection : Majorization , Concavity , and Affine Scaling — — — — — – , 1997 .

[7]  P. Paatero.  Least squares formulation of robust non-negative factor analysis , 1997 .

[8]  H. Tuy.  Convex programs with an additional reverse convex constraint , 1987 .

[9]  Brendan J. Frey,et al.  Fast, Large-Scale Transformation-Invariant Clustering , 2001, NIPS.

[10]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[11]  Stan Z. Li,et al.  Learning spatially localized, parts-based representation , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[12]  Patrik O. Hoyer,et al.  Non-negative sparse coding , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[13]  Yee Whye Teh,et al.  Learning to Parse Images , 1999, NIPS.

[14]  Stephen J. Wright.  Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[15]  D. Field,et al.  Natural image statistics and efficient coding. , 1996, Network.

[16]  G. W. Israel,et al.  A receptor model using a specific non-negative transformation technique for ambient aerosol , 1989 .

[17]  Ole Winther,et al.  Mean-Field Approaches to Independent Component Analysis , 2002, Neural Computation.

[18]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[19]  P. Smaragdis,et al.  Non-negative matrix factorization for polyphonic music transcription , 2003, 2003 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE Cat. No.03TH8684).

[20]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[21]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[22]  Andrew McCallum,et al.  Using Maximum Entropy for Text Classification , 1999 .