Andersen Ang

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• PhD
• Assistant professor at University of Southampton

ABSTRACT In recent years, nonnegative matrix factorization (NMF) with volume regularization has been shown to be a powerful identifiable model; for example for hyperspectral unmixing, document classification, community detection and hidden Markov models. In this paper, we show that minimum-volume NMF (min-volNMF) can also be used when the basis matri...

We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate d...

This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates the empirical convergence speed...

Considering a mixed signal composed of various audio sources and recorded with a single microphone, we consider on this paper the blind audio source separation problem which consists in isolating and extracting each of the sources. To perform this task, nonnegative matrix factorization (NMF) based on the Kullback-Leibler and Itakura-Saito $\beta$-d...

Low-rank optimization problems with sparse simplex constraints involve vari- ables that must satisfy nonnegativity, sparsity, and sum-to-one conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints. These problems arise in various applica- tions, including machine learning, sign...

The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between the reconstruction accuracy and the adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence , effective for extracting low spectral d...

We study estimation of piecewise smooth signals over a graph. We propose a $\ell _{2,0}$ -norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the nodes. We prove that the proposed GTF model is simultaneously a k-means clustering on the signal over the nod...

When applying nonnegative matrix factorization (NMF), generally the rank parameter is unknown. Such rank in NMF, called the nonnegative rank, is usually estimated heuristically since computing the exact value of it is NP-hard. In this work, we propose an approximation method to estimate such rank while solving NMF on-the-fly. We use sum-of-norm (SO...

Nonnegative Matrix Factorization (NMF) is the problem of approximating a given nonnegative matrix M through the conic combination of two nonnegative low-rank matrices W and H. Traditionally NMF is tackled by optimizing a specific objective function evaluating the quality of the approximation. This assessment is often done based on the Frobenius nor...

We study the combination of proximal gradient descent with multigrid for solving a class of possibly nonsmooth strongly convex optimization problems. We propose a multigrid proximal gradient method called MG- Prox, which accelerates the proximal gradient method by multigrid, based on using hierarchical information of the optimization problem. MGPro...

Paper https://www.researchgate.net/publication/370766076_Inexact_higher-order_proximal_algorithms_for_tensor_factorization

In the last decades, Matrix Factorization (MF) models and their multilinear extension-Tensor Factorization (TF) models have been shown to be powerful tools for high dimensional data analysis and features extraction. Computing MF's or TF's are commonly achieved by solving a constrained optimization subproblem on each block of variables, where the su...

We study estimation of piecewise smooth signals over a graph. We propose a l2,0-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit in- homogeneous levels of smoothness across the nodes. We prove that the proposed GTF model is simultaneously a k-means clustering on the signal over the nodes and a...

We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's method is able to solve the projection problem to high precision with a complexity roughly about O(n), which has a...

We introduce a new Nonnegative Matrix Factorization (NMF) model called Nonnegative Unimodal Matrix Factorization (NuMF), which adds on top of NMF the unimodal condition on the columns of thebasis matrix. NuMF finds applications for example in analytical chemistry. We propose a simple but naive brute-force heuristics strategy based on accelerated pr...

This paper is concerned with improving the empirical convergence speed of block‐coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in‐between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates the empirical convergence speed...

In this paper we consider a Nonnegative Matrix Factorization (NMF) model on complex numbers, in particular, we propose a group complex-NMF (cNMF) model that subsumes the phase-consistency complex NMF for the audio Blind Source Separation (aBSS). Using Wirtinger calculus, we propose a gradient-based algorithm to solve cNMF. The algorithm is then fur...

Nonnegative matrix factorization with the minimum-volume criterion (min-vol NMF) guarantees that, under some mild and realistic conditions, the factorization has an essentially unique solution. This result has been successfully leveraged in many applications, including topic modeling, hyperspectral image unmixing, and audio source separation. In th...

We introduce a new Nonnegative Matrix Factorization (NMF) model called Nonnegative Unimodal Matrix Factorization (NuMF), which adds on top of NMF the unimodal condition on the columns of the basis matrix. NuMF finds applications for example in analytical chemistry. We propose a simple but naive brute-force heuristics strategy based on accelerated p...

Tensor decompositions have become a central tool in machine learn-ing to extract interpretable patterns from multiway arrays of data.However, computing the approximate Canonical Polyadic Decom-position (aCPD), one of the most important tensor decompositionmodel, remains a challenge. In this work, we propose several algo-rithms based on extrapolatio...

Considering a mixed signal composed of various audio sources and recorded with a single microphone, we consider on this paper the blind audio source separation problem which consists in isolating and extracting each of the sources. To perform this task, nonnegative matrix factorization (NMF) based on the Kullback-Leibler and Itakura-Saito β-diverge...

Tensor decompositions have become a central tool in machine learning to extract interpretable patterns from multiway arrays of data. However, computing the approximate Canonical Polyadic Decomposition (aCPD), one of the most important tensor decomposition model, remains a challenge. In this work, we propose several algorithms based on extrapolation...

In this paper, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume regularizers, and compare them on endmember recovery in hyperspectral unmixing. The NMF algorithms developed in this pape...

In this work, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume regularizers, and compare them on endmember recovery in hyperspectral unmixing. The NMF algorithms developed in this work...

In this work, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume regularizers, and compare them on endmember recovery in hyperspectral unmixing. The NMF algorithms developed in this work...

Abstract Audio source separation concerns techniques used to extract unknown signals called sources from a mixed signal. In this paper, we assume that the audio signal is recorded with a single microphone. Considering a mixed signal composed of various audio sources, the blind audio source separation consists in isolating and extracting each of the...

In this work, we consider the problem of approximate Nonnegative Canonical Polyadic Decomposition (aNCPD) of third-order nonnegative tensors, which boils down to minimizing ||T − (U ⊗ V ⊗ W)Ir||_F^2 over element-wise nonnegative matrices U , V and W. We present an accelerated block coordinate descent algorithm that uses Nesterov-like extrapolation...

This work considers two volume regularized non-negative matrix factorization (NMF) problems that decompose a non-negative matrix X into the product of two nonnegative matrices W and H with a regularization on the volume of the convex hull spanned by the columns of W. This regularizer takes two forms: the determinant (det) and logarithm of the deter...

In this paper, we propose a general framework to accelerate significantly the algorithms for non-negative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the tw...

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the two...

The learning process on Massive Open Online Courses (MOOCs) is learner-driven, where face-to-face interactions are limited. Because of this, instructional videos and forum discussions in MOOCs become critical points of contact. However, in on-campus teaching, some courses (such as philosophy) are often taught in a small-class tutorial setting. How...

In this paper, a decomposition method is proposed for Separable Non-negative Tensor Factorization (SNTF), which yields a structure similar to the PARATUCK2 model for the decomposition of non-negative tensors. Among many different possibilities for performing tensor factorization, we develop a specific procedure for SNTF with an aim to decompose mul...

This paper presents a novel wearable single-channel electrooculography (EOG) based human-computer interface (HCI) with a simple system design and robust performance. In the proposed system, EOG signals are generated from double eye blinks, collected by a commercial wearable device (the NeuroSky MindWave headset), and then converted into a sequence...

This brief introduces a new and practical human-machine interface (HMI) system based on single-channel electrooculography (EOG) signals. The proposed system uses a consumer wireless recording device to collect EOG and employs new encoding/decoding paradigms to covey users’ intentions with EOG from eye movements including blinking and looking up. Th...