This paper presents a novel matrix factorization method for effectively performing the image retrieval in large image databases. Non-negative Matrix Factorization (NMF) provides a parts-based representation of data by finding two non-negative matrices whose product can well approximate the original data matrix. Although it has been applied successfully for several applications, simply using NMF for image retrieval provides low performance results which results from the fact that NMF fails to consider the geometric structure that is contained within the data. To solve the above problem, we encode the geometrical information contained in the data by constructing a nearest neighbor graph and perform matrix factorization based on this graph structure. In this work, 500 images from Corel dataset have been taken into consideration. We compared NMF and GNMF based method in the context of image retrieval. Experimental results demonstrate the effectiveness and robustness of GNMF based approach.

1. D. Cai, X. He, J. Han, T. S. Huang. Graph Regularized Non-Negative Matrix Factorization for Data Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(33):1548-1560,2011.
2. E. Wachsmuth, M. W. Oram, and D. I. Perrett. Recognition of objects and their component parts: Responses of single units in the temporal cortex of the macaque. Cerebral Cortex, 4:509–522,1994.
3. D. D. Lee and H. S. Seung. Learning the parts of objects by nonnegative matrix factorization. Nature, 401:788–791, 1999.
4. Guillamet, D. , Vitria, J. , Schiele, B. : Introducing a weighted non-negative matrix factoriza-tion for image classification. Pattern Recognition Letters 24 (2003) 2447-2454.
5. Buciu, I. , Pitas,I. : Application of non-negative and local non-negative matrix factorization to facial expression recognition. In: ICPR, Cambridge, 2004.
6. Chen, X. , Gu, L. , Li, S. Z. , Zhang, H. J. : Learning representative local features for face detec-tion. In: CVPR, Hawaii, 2001.
7. F. Shahnaza, M. W. Berrya, V. Paucab, and R. J. Plemmonsb. Document clustering using nonnegative matrix factorization. Information Processing & Management, 42(2):373–386, 2006.
8. R. Hadsell, S. Chopra, and Y. LeCun. Dimensionality reduction by learning an invariant mapping. In Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR'06), pages 1735–1742, 2006.
9. D. D. Lee and H. S. Seung. Algorithms for non-negative matrix factorization. In Advances in Neural Information Processing Systems13. 2001.
10. C. -J. Lin. On the convergence of multiplicative update algorithms for non-negative matrix factorization. IEEE Transactions on Neural Networks, 18(6):1589–1596, 2007.
11. F. R. K. Chung. Spectral Graph Theory, volume 92 of Regional Conference Series in Mathematics. AMS, 1997.
12. Carlos Ordonez and Edward Omiecinski. Image Mining: A New Approach for Data Mining Proceedings of National Academy of Sciences,103(12) 3164-3169.
13. Denis Filimonov, Touradj Ebrahimi, Ivan Ivanov. Automatic Extraction of Interesting Image Content. OpiCS,Lausanne. ,June. 2011

Non-negative Matrix Factorization Local Invariance Assumption Graph Laplacian