Investigating a Dictionary-Based Non-negative Matrix Factorization in Superimposed Digits Classification Tasks
Human visual system can recognize superimposed graphical components with ease while sophisticated computer vision systems still struggle to recognize them. This may be attributed to the fact that the image recognition task is framed as a classification task where a classification model is commonly constructed from appearance features. Hence, superimposed components are perceived as a single image unit. It seems logical to approach the recognition of superimposed digits by employing an approach that supports construction/deconstruction of superimposed components. Here, we resort to a dictionary-based non-negative matrix factorization (NMF). The dictionary-based NMF factors a given superimposed digit matrix, V, into the combination of entries in the dictionary matrix W. The H matrix from \(V \approx WH\) can be interpreted as corresponding superimposed digits. This work investigates three different dictionary representations: pixels’ intensity, Fourier coefficients and activations from RBM hidden layers. The results show that (i) NMF can be employed as a classifier and (ii) dictionary-based NMF is capable of classifying superimposed digits with only a small set of dictionary entries derived from single digits.
KeywordsDictionary-based NMF Classifying superimposed digits Restricted Boltzmann Machines
We wish to thank anonymous reviewers for their comments, which help improve this paper. We would like to thank the GSR office for their financial support given to this research.
- 2.Bottou, L., Cortes, C., Denker, J.S., Drucker, H., Guyon, I., Jackel, L.D., LeCun, Y., Müller, U.A., Säckinger, E., Simard, P., Vapnik, V.: Comparison of classifier methods: a case study in handwritten digit recognition. In: Proceedings of the 12th IAPR International. Conference on Pattern Recognition, vol. 2, pp. 77–82. Conference B: Computer Vision & Image Processing (1994)Google Scholar
- 3.Ciresan, D.C., Meier, U., Masci, J., Gambardella, L.M., Schmidhuber, J.: Flexible, high performance convolutional neural networks for image classification. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 1237–1242 (2011)Google Scholar
- 7.Sohn, K., Lee, H.: Learning invariant representations with local transformations. In: Proceedings of the 29th International Conference on Machine Learning, ICML 2012, Edinburgh (2012)Google Scholar
- 9.Lee, S.Y., Mozer, M.C.: Robust recognition of noisy and superimposed patterns via selective attention. In: Proceedings of the International Conference on Neural Information Processing Systems (NIPS 1999), pp. 31–37 (1999)Google Scholar
- 10.Zhou, Z., Wagner, A., Mobahi, H., Wright, J., Ma., Y.: Face recognition with contiguous occlusion using markov random fields. In: Proceedings of the International Conference on Computer Vision (ICCV 2009), pp. 1050–1057. IEEE (2009)Google Scholar
- 11.Tang, Y., Salakhutdinov, R., Hinton, G.: Robust Boltzmann machines for recognition and denoising. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2012), pp. 2264–2271. IEEE (2012)Google Scholar