Clustering by non-negative matrix factorization with independent principal component initialization

Non negative matrix factorization (NMF) is a dimensionality reduction and clustering method, and has been applied to many areas such as bioinformatics, face images classification, and so on. Based on the traditional NMF, researchers recently have put forward several new algorithms on the initialization area to improve its performance. In this paper, we explore the clustering performance of the NMF algorithm, with emphasis on the initialization problem. We propose an initialization method based on independent principal component analysis (IPCA) for NMF. The experiments were carried out on the four real datasets and the results showed that the IPCA-based initialization of NMF gets better clustering of the datasets compared with both random and PCA-based initializations

Underdetermined blind source separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization

Conventional blind source separation is based on over-determined with more sensors than sources but the underdetermined is a challenging case and more convenient to actual situation. Non-negative Matrix Factorization (NMF) has been widely applied to Blind Source Separation (BSS) problems. However, the separation results are sensitive to the initialization of parameters of NMF. Avoiding the subjectivity of choosing parameters, we used the Fuzzy C-Means (FCM) clustering technique to estimate the mixing matrix and to reduce the requirement for sparsity. Also, decreasing the constraints is regarded in this paper by using Semi-NMF. In this paper we propose a new two-step algorithm in order to solve the underdetermined blind source separation. We show how to combine the FCM clustering technique with the gradient-based NMF with the multi-layer technique. The simulation results show that our proposed algorithm can separate the source signals with high signal-to-noise ratio and quite low cost time compared with some algorithms

An enhanced initialization method for non-negative matrix factorization

Non-negative matrix factorization (NMF) is a dimensionality reduction tool, and has been applied to many areas such as bioinformatics, face image classification, etc. However, it often converges to some local optima because of its random initial NMF factors (W and H matrices). To solve this problem, some researchers have paid much attention to the NMF initialization problem. In this paper, we first apply the k-means clustering to initialize the factor W, and then we calculate the initial factor H using four different initialization methods (three standard and one new). The experiments were carried out on the eight real datasets and the results showed that the proposed method (EIn-NMF) achieved less error and faster convergence compared with both random initialization based NMF and the three standard methods for k-means based NMF

New SVD based initialization strategy for Non-negative Matrix Factorization

There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems using Singular Value Decomposition (SVD). At first we extract the number of main components as the rank, actually this method is inspired from [1, 2]. Second, we use the singular value and its vectors to initialize NMF algorithm. In 2008, Boutsidis and Gollopoulos [3] provided the method titled NNDSVD to enhance initialization of NMF algorithms. They extracted the positive section and respective singular triplet information of the unit matrices {C(j)}k j=1 which were obtained from singular vector pairs. This strategy aims to use positive section to cope with negative elements of the singular vectors, but in experiments we found that even replacing negative elements by their absolute values could get better results than NNDSVD. Hence, we give another method based SVD to fulfil initialization for NMF algorithms (SVD-NMF). Numerical experiments on two face databases ORL and YALE [16, 17] show that our method is better than NNDSVD

A deep matrix factorization method for learning attribute representations

Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our original data matrix contains rather complex hierarchical information with implicit lower-level hidden attributes, that classical one level clustering methodologies can not interpret. In this work we propose a novel model, Deep Semi-NMF, that is able to learn such hidden representations that allow themselves to an interpretation of clustering according to different, unknown attributes of a given dataset. We also present a semi-supervised version of the algorithm, named Deep WSF, that allows the use of (partial) prior information for each of the known attributes of a dataset, that allows the model to be used on datasets with mixed attribute knowledge. Finally, we show that our models are able to learn low-dimensional representations that are better suited for clustering, but also classification, outperforming Semi-Non-negative Matrix Factorization, but also other state-of-the-art methodologies variants.Comment: Submitted to TPAMI (16-Mar-2015