Constrained Nonnegative Matrix Factorization for Image Representation

Abstract

Nonnegative matrix factorization (NMF) is a popular technique for finding parts-based, linear representations of nonnegative data. It has been successfully applied in a wide range of applications such as pattern recognition, information retrieval, and computer vision. However, NMF is essentially an unsupervised method and cannot make use of label information. In this paper, we propose a novel semi-supervised matrix decomposition method, called Constrained Nonnegative Matrix Factorization (CNMF), which incorporates the label information as additional constraints. Specifically, we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition. We explore the proposed CNMF method with two cost function formulations and provide the corresponding update solutions for the optimization problems. Empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state-of-the-art approaches through a set of evaluations based on real-world applications.

Robust nonnegative matrix factorization with ordered structure constraints

“…These NMF methods, which are referred as unsupervised learning methods, are not optimal to many real-world problems where limited knowledge (such as label information) from domain experts is available. To address this limitation, Liu et al [2] extended NMF to the semi-supervised setting and proposed the constrained NMF (CNMF). It takes the label information as hard constraints by enforcing data with the same label to have the same new representations, thus, the obtained representations may have more discriminating power.…”

“…Similar to the experimental setting in [2], we conduct the experiments for each method on the different number of clusters from 2 to 10 to make a thorough comparison. For a fixed cluster number k, we randomly choose k categories from the dataset, and mix the images of these k categories as the collection V for clustering.…”

“…Finding an optimal data representation is a fundamental problem in many data analysis tasks [1], [2]. A good data representation can typically reveal the latent structure of data and facilitate further processes such as clustering, classification and recognition.…”

Learning convolutive features for storage and transmission between networked sensors

“…Donoho and Stodden showed that NMF only gives the exact and unique solution for certain classes of partsbased data-sets [6]. Nevertheless, the popularity of NMF in recent years has grown unabated due to the simplicity of its updates and the success of its application in areas such as bioinformatics [8] and computer vision [9]. In this paper, we consider Donoho and Stodden's parts-based explanation for the success of NMF and posit that there exists, in some sense, an even simpler representation of the data.…”

Group Sparsity and Graph Regularized Semi-Nonnegative Matrix Factorization with Discriminability for Data Representation

“…Usually, exploiting label information in the framework of NMF can allow obtaining discriminative information. For example, Liu et al [9] proposed Constrained Nonnegative Matrix Factorization (CNMF), which imposes the label information for the objective function as hard constraints. Li et al [10] developed a semi-supervised robust structured NMF, which exploited the block-diagonal structure in the framework of NMF.…”