22 papers · ranked by Valyu relevance
Jyothi Rikhab Chand, Prabhu Babu
—We consider the problem of localizing the source using range and range-difference measurements. Both the problems are non-convex and non-smooth and are challenging to solve. In this paper, we develop an iterative algorithm - Source Localization Via an Iterative technique (SOLVIT) to localize the source using all the…
Astha Saini, Petre Stoica, Prabhu Babu, Aakash Arora
| 1 | Introduction | 312 | | --- | --- | --- | | | 1.1 | MM Summary 313 | | | 1.2 | Need for MM4MM 314 | | | 1.3 | Organization 315 | | | 1.4 | Notation 316 | | 2 | | Max Formulation 318 | | | 2.1 | Conjugate Function 319 | | | 2.2 | Max Formulation for Certain Non-Convex Functions 320 | | | 2.3 | Illustrative Examples…
Jyothi Rikhab Chand, Prabhu Babu, Rajendar Bahl
Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a nonnegative matrix into a product of two nonnegative matrices which gives some meaningful…
Ali Hashemi, Chang Cai, Gitta Kutyniok, Klaus-Robert Müller + 2 more
Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of…
Bangyue Ren, Yansong Hao, Huaqing Wang, Liuyang Song + 2 more
'Hongfang Yuan'] Fault transient impulses induced by faulty components in rotating machinery usually contain substantial interference. Fault features are comparatively weak in the initial fault stage, which renders fault diagnosis more difficult. In this case, a sparse representation method based on the…
Junxiao Song, Prabhu Babu, Daniel P. Palomar
—In this paper, we consider an ℓ 0-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a discontinuous nonconcave objective function over a nonconvex constraint set, and is…
Paul Magron, Cédric Févotte
This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an…
Mehrsa Pourya, Sebastian Neumayer, Michael Unser
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In contrast, our scheme is interpretable because it corresponds to the…
C. Eric, Hua Zhou, Kenneth Lange
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's…
Kevin L. Keys, Hua Zhou, Kenneth Lange
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss…
Yuxue Chen, Shuisheng Zhou, Boris Ryabko
Possibilistic fuzzy c-means (PFCM) clustering is a kind of hybrid clustering method based on fuzzy c-means (FCM) and possibilistic c-means (PCM), which not only has the stability of FCM but also partly inherits the robustness of PCM. However, as an extension of FCM on the objective function, PFCM tends to find a…
Charles L. Byrne, Jong‐Soo Lee
Let Φ : X × Y → R+, where X and Y are arbitrary nonempty sets. The objective in alternating minimization (AM) is to find ˆx ∈ X and ˆy ∈ Y such that Φ(ˆx, yˆ) ≤ Φ(x, y) for all x ∈ X and y ∈ Y . For each k we minimize Φ(x, yk−1 ) to get x k−1 and then minimize Φ(x k−1 , y) to get y k . For each x ∈ X, let y(x) ∈ Y be…
Rui Liang, Hui Li, Yingli Dong, Guodong Xue + 2 more
'Luca Barletta'] The practical implementation of massive multi-user multi-input-multi-output (MU-MIMO) downlink communication systems power amplifiers that are energy efficient; otherwise, the power consumption of the base station (BS) will be prohibitive. Constant envelope (CE) precoding is gaining increasing interest…
Alfonso Landeros, Oscar Hernan Madrid Padilla, Hua Zhou, Kenneth Lange
'Kenneth Lange'] The current paper studies the problem of minimizing a loss f(x) subject to constraints of the form Dx ∈ S, where S is a closed set, convex or not, and D is a matrix that fuses parameters. Fusion constraints can capture smoothness, sparsity, or more general constraint patterns. To tackle this generic…
Gustavo M. Bosyk, Hector Freytes, Guido Bellomo, Giuseppe Sergioli
The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization…
Gilles Delmaire, Mahmoud Omidvar, Matthieu Puigt, Frédéric Ledoux + 3 more
'Abdelhakim Limem' 'Gilles Roussel' 'Dominique Courcot'] In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an $αβ$-divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization-which are used to…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Anqi Wu, Samuel A. Nastase, Christopher A. Baldassano, Nicholas B. Turk-Browne + 3 more
A key problem in functional magnetic resonance imaging (fMRI) is to estimate spatial activity patterns from noisy high-dimensional signals. Spatial smoothing provides one approach to regularizing such estimates. However, standard smoothing methods ignore the fact that correlations in neural activity may fall off at…
David M. Bradley, J. Andrew Bagnell
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Michael Cho + 2 more
High dimensional linear regression problems are often fitted using LASSO-type approaches. Although the LASSO objective function is convex, it is not differentiable everywhere, making the use of gradient descent methods for minimization not straightforward. To avoid this technical issue, we apply Nesterov smoothing to…