Properties of Nonnegative Matrix Factorization (NMF) as a clustering method are studied by relating its formulation to other methods such as K-means clustering. We show how interpreting the objective function of K-means as that of a lower rank approximation with special constraints allows comparisons between the constraints of NMF and K-means and provides the insight that some constraints can b...

Given electroencephalogram (EEG) data measured from several subjects under the same conditions, our goal is to estimate common task-related bases in a linear model that capture intra-subject variations as well as inter-subject variations. Such bases capture the common phenomenon in group data, which is a core of group analysis. In this paper we present a method of nonnegative matrix factorizati...

Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be partsbased in the human brain. However, when labeled and unlabeled images are sampled from different distributions, they may be quantized into different basis vector space and represented in different coding ...

Nonnegative matrix factorization NMF is a promising approach for local feature extraction in face recognition tasks. However, there are two major drawbacks in almost all existing NMFbased methods. One shortcoming is that the computational cost is expensive for large matrix decomposition. The other is that it must conduct repetitive learning, when the training samples or classes are updated. To ...

In this paper, we analyze character recognition performance of three different nonnegative matrix factorization (NMF) algorithms. These are multiplicative update (MU) rule known as standard NMF, alternating least square (NMF-ALS) and projected gradient descent (NMF-PGD). They are most preferred approaches in the literature. There are lots of application areas for NMF such as robotics, bioinform...

The equivalence can be formalized as follows: For a particular c in (21), there is a corresponding δ > 0 in the optimization in (A-1). We focus on `1-ARD where f(x) = ‖x‖1. Then the objective is concave in H. One natural way to solve (A-1) iteratively is to use an MM procedure by upper bounding the objective function with its tangent (first-order Taylor expansion) at the current iterate H. This...

Nonnegative matrix factorization (NMF) has become a popular technique for data analysis and dimensionality reduction. However, it is often assumed that the number of latent dimensions (or components) is given. In practice, one must choose a suitable value depending on the data and/or setting. In this paper, we address this important issue by using a Bayesian approach to estimate the latent dime...

In the paper we derive and discuss a wide class of algorithms for 3D Super-symmetric nonnegative Tensor Factorization (SNTF) or nonnegative symmetric PARAFAC, and as a special case: Symmetric Nonnegative Matrix Factorization (SNMF) that have many potential applications, including multi-way clustering, feature extraction, multisensory or multi-dimensional data analysis, and nonnegative neural sp...

Data analysis is pervasive throughout business, engineering and science. Very often the data to be analyzed is nonnegative, and it is often preferable to take this constraint into account in the analysis process. Here we are concerned with the application of analyzing data obtained using astronomical spectrometers, which provide spectral data which is inherently nonnegative. The identification ...

The conducted research project is concerned with image segmentation – one of the central problems of image analysis. A new model of segmented image is proposed and used to develop tools for analysis of image segmentations: image specific evaluation of segmentation algorithms’ performance, extraction of image segment descriptors, and extraction of image segments. Prevalent segmentation models ar...