MSdB-NMF: MultiSpectral Document Image Binarization Framework via Non-negative Matrix Factorization Approach

Entropy Minimizing Matrix Factorization

Nonnegative matrix factorization (NMF) is a widely used data analysis technique and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids and find the optimal centroids by minimizing the sum of the residual errors. However, outliers deviating from the normal data distribution may have large residues and then dominate the objective value. In this study, an entropy minimizing matrix factorization (EMMF) framework is developed to tackle the above problem. Considering that outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization, which minimizes the entropy of the residue distribution and allows a few samples to have large errors. In this way, the outliers do not affect the approximation of normal samples. Multiplicative updating rules for EMMF are derived, and the convergence is proven theoretically. In addition, a Graph regularized version of EMMF (G-EMMF) is also presented, which uses a data graph to capture the data relationship. Clustering results on various synthetic and real-world datasets demonstrate the advantages of the proposed models, and the effectiveness is also verified through the comparison with state-of-the-art methods.

Feature Weighted Non-Negative Matrix Factorization

Non-negative matrix factorization (NMF) is one of the most popular techniques for data representation and clustering and has been widely used in machine learning and data analysis. NMF concentrates the features of each sample into a vector and approximates it by the linear combination of basis vectors, such that the low-dimensional representations are achieved. However, in real-world applications, the features usually have different importance. To exploit the discriminative features, some methods project the samples into the subspace with a transformation matrix, which disturbs the original feature attributes and neglects the diversity of samples. To alleviate the above problems, we propose the feature weighted NMF (FNMF) in this article. The salient properties of FNMF can be summarized as three-fold: 1) it learns the weights of features adaptively according to their importance; 2) it utilizes multiple feature weighting components to preserve the diversity; and 3) it can be solved efficiently with the suggested optimization algorithm. The performance on synthetic and real-world datasets demonstrates that the proposed method obtains the state-of-the-art performance.