Robust embedded projective nonnegative matrix factorization for image analysis and feature extraction

Abstract

Nonnegative matrix factorization (NMF) is an unsupervised learning method for decomposing high-dimensional nonnegative data matrices and extracting basic and intrinsic features. Since image data are described and stored as nonnegative matrices, the mining and analysis process usually involves the use of various NMF strategies. NMF methods have well-known applications in face recognition, image reconstruction, handwritten digit recognition, image denoising and feature extraction. Recently, several projective NMF (P-NMF) methods based on positively constrained projections have been proposed and were found to perform better than the standard NMF approach in some aspects. However, some drawbacks still affect the existing NMF and P-NMF algorithms; these include dense factors, slow convergence, learning poor local features, and low reconstruction accuracy. The aim of this paper is to design algorithms that address the aforementioned issues. In particular, we propose two embedded P-NMF algorithms: the first method combines the alternating least squares (ALS) algorithm with the P-NMF update rules of the Frobenius norm and the second one embeds ALS with the P-NMF update rule of the Kullback–Leibler divergence. To assess the performances of the proposed methods, we conducted various experiments on four well-known data sets of faces. The experimental results reveal that the proposed algorithms outperform other related methods by providing very sparse factors and extracting better localized features. In addition, the empirical studies show that the new methods provide highly orthogonal factors that possess small entropy values

Retinal vessel segmentation with constrained-based nonnegative matrix factorization and 3D modified attention U-Net

“…Therefore, NMF [15], a linear dimensionality reduction technique commonly used for extracting basic and latent features from high-dimensional data matrices, is wildly adopted. However, latent semantic structure within data set may not be discovered well by the basis vectors in classical NMF while high-dimensional data are represented by low-dimensional vectors [16]. In addition, since features are extracted from similar images, some inherent relations should have existed in these features whereas sometimes failed to.…”

Globality constrained adaptive graph regularized non‐negative matrix factorization for data representation

“…This non-negativity constraints result in the parts-based representation of NMF. In practice, NMF has been applied to many applications, such as document clustering [6], image segmentation [7], text mining [8], image clustering [9,10] and biological data mining [11].…”

Retinal vessel segmentation with constrained-based nonnegative matrix factorization and 3D modified Attention U-Net

“…For further utilization of this contributing low dimension feature description method, we convert matrix Algorithm 1 The optimizing scheme of constrained-based NMF Input: X, L; Output: V ; 1: Initial: U by using the random initialization, V and G with one. Construct matrices A and B; 2: Repeat: Update U according to (16); Update V using (16); Update G by using (18); 3: Until the objective function (9) convergence; 4: Return V ;…”