Distance Metric Learning for Ameliorated Nonnegative Matrix Factorization

Non-negative matrix factorization (NMF) is an unsupervised method whose aim is to find an approximate factorization V ¿ WH, which decomposes V = [v_ij] ¿ R^n*m into non-negative matrices W = [w_ij] ¿ R^n*r and H = [h_ij] ¿ R^r*m with w_ij, h_ij ¿ 0. In this paper, we present an extension to the non-negative matrix factorization called DMNMF and adopt the learned distance metric to measure the between-class similarity of two patterns and minimize F(V; WH) = ¿V - WH¿² _A, which is equivalent to finding a rescaling of a data, applying the standard Euclidean metric to the rescaled data, and this will later be useful in visualizing the learned metrics. DMNMF has been tested with color wood images after combining the statistical features based on energy extracted via dual-tree complex wavelet transform (DTCWT) from the feature spaces structured by the factorization process for wood image representation and defect detection. Based on visual valuation, it can effectively decrease the experimental errors and have better robust to the interferences on wood surfaces with better convergence property and similarity measures. The experimental results show the proposed method is effectual and practical with good research values and potential applications.