Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations which are either specific or common to the classes, we derive class-specific alterations from common factorizations as well. Therewith, we broaden the applicability of our new method to datasets whose class-dependencies have a more complex structure. On the basis of synthetic and real-world datasets, we show on the one hand that our method is able to filter structure which corresponds to our model assumption, and on the other hand that our model assumption is justified in real-world application. Our method is parameter-free.
In the two-class nonnegative input matrices case, improve over RJSNMF by allowing small deviations from shared patterns in each class @cite_11 . They found that shared patterns are often marginally altered according to the class. In this paper, we aim at finding these overlooked variations of shared patterns together with strident differences among multiple classes, combining the strengths of MDL for rank detection and the latest results in NMF.
@cite_11
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In this paper, two supervised methods for enhancing the classification accuracy of the Nonnegative Matrix Factorization (NMF) algorithm are presented. The idea is to extend the NMF algorithm in order to extract features that enforce not only the spatial locality, but also the separability between classes in a discriminant manner. The first method employs discriminant analysis in the features derived from NMF. In this way, a two-phase discriminant feature extraction procedure is implemented, namely NMF plus Linear Discriminant Analysis (LDA). The second method incorporates the discriminant constraints inside the NMF decomposition. Thus, a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived. The introduced methods have been applied to the problem of frontal face verification using the well-known XM2VTS database. Both methods greatly enhance the performance of NMF for frontal face verification