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Gaussian processes are widely used for the analysis of spatial data due to their nonparametric flexibility and ability to quantify uncertainty, and recently developed scalable approximations have facilitated application to massive datasets.…
Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in…
Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…
We present a novel graphical framework for modeling non-negative sequential data with hierarchical structure. Our model corresponds to a network of coupled non-negative matrix factorization (NMF) modules, which we refer to as a positive…
Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA),…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…
There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…
Non-negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi-Nonnegative Matrix Factorization…
Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, $X$, by the product of two nonnegative factors, $WH$, where $W$ has $r$ columns and $H$ has $r$ rows. In this paper, we consider NMF using the component-wise L1 norm…
Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational…
Sparse representations using overcomplete dictionaries have proved to be a powerful tool in many signal processing applications such as denoising, super-resolution, inpainting, compression or classification. The sparsity of the…
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative…
We consider the general problem of utilizing both labeled and unlabeled data to improve data representation performance. A new semi-supervised learning framework is proposed by combing manifold regularization and data representation methods…
In probabilistic classification, a discriminative model based on the softmax function has a potential limitation in that it assumes unimodality for each class in the feature space. The mixture model can address this issue, although it leads…
The spectrum of mutations in a collection of cancer genomes can be described by a mixture of a few mutational signatures. The mutational signatures can be found using non-negative matrix factorization (NMF). To extract the mutational…
Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…
We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a Beta Process. It also…
This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still…
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications…