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Nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used for numerous applications, including text mining, computer vision, pattern discovery, and bioinformatics. A mathematical formulation for NMF appears as a nonconvex optimization problem, and various types of algorithms have been devised to solve the problem. The alternating nonnegative least squares (ANLS) framework is a block coordinate descent approach for solving NMF, which was recently shown to be theoretically sound and empirically efficient. In this paper, we present a novel algorithm for NMF based on the ANLS framework. Our new algorithm builds upon the block principal pivoting method for the nonnegativity-constrained least squares problem that overcomes a limitation of the active set method. We introduce ideas that efficiently extend the block principal pivoting method within the context of NMF computation. Our algorithm inherits the convergence property of the ANLS framework and can easily be extended to other constrained NMF formulations. Extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state-of-the-art performance in terms of computational speed. [PUBLICATION ABSTRACT]

We review algorithms developed for nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) from a unified view based on the block coordinate descent (BCD) framework. NMF and NTF are low-rank approximation methods for matrices and tensors in which the low-rank factors are constrained to have only nonnegative elements. The nonnegativity constraints have been shown to enable natural interpretations and allow better solutions in numerous applications including text analysis, computer vision, and bioinformatics. However, the computation of NMF and NTF remains challenging and expensive due the constraints. Numerous algorithmic approaches have been proposed to efficiently compute NMF and NTF. The BCD framework in constrained non-linear optimization readily explains the theoretical convergence properties of several efficient NMF and NTF algorithms, which are consistent with experimental observations reported in literature. In addition, we discuss algorithms that do not fit in the BCD framework contrasting them from those based on the BCD framework. With insights acquired from the unified perspective, we also propose efficient algorithms for updating NMF when there is a small change in the reduced dimension or in the data. The effectiveness of the proposed updating algorithms are validated experimentally with synthetic and real-world data sets.

Nonnegative matrix factorization (NMF) provides a lower rank approximation of a matrix by a product of two nonnegative factors. NMF has been shown to produce clustering results that are often superior to those by other methods such as K-means. In this paper, we provide further interpretation of NMF as a clustering method and study an extended formulation for graph clustering called Symmetric NMF (SymNMF). In contrast to NMF that takes a data matrix as an input, SymNMF takes a nonnegative similarity matrix as an input, and a symmetric nonnegative lower rank approximation is computed. We show that SymNMF is related to spectral clustering, justify SymNMF as a general graph clustering method, and discuss the strengths and shortcomings of SymNMF and spectral clustering. We propose two optimization algorithms for SymNMF and discuss their convergence properties and computational efficiencies. Our experiments on document clustering, image clustering, and image segmentation support SymNMF as a graph clustering method that captures latent linear and nonlinear relationships in the data.

Nonnegative matrix factorization (NMF) determines a lower rank approximation of a matrix $A \\in \\mathbb{R}^{m \\times n} \\approx WH$ where an integer $k \\ll \\min(m,n)$ is given and nonnegativity is imposed on all components of the factors $W \\in \\mathbb{R}^{m \\times k}$ and $H \\in \\mathbb{R}^{k \\times n}$. NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. In applications where the components of the data are necessarily nonnegative, such as chemical concentrations in experimental results or pixels in digital images, NMF provides a more relevant interpretation of the results since it gives nonsubtractive combinations of nonnegative basis vectors. In this paper, we introduce an algorithm for NMF based on alternating nonnegativity constrained least squares (NMF/ANLS) and the active set-based fast algorithm for nonnegativity constrained least squares with multiple right-hand side vectors, and we discuss its convergence properties and a rigorous convergence criterion based on the Karush-Kuhn-Tucker (KKT) conditions. In addition, we also describe algorithms for sparse NMFs and regularized NMF. We show how we impose a sparsity constraint on one of the factors by $L_1$-norm minimization and discuss its convergence properties. Our algorithms are compared to other commonly used NMF algorithms in the literature on several test data sets in terms of their convergence behavior.

Prophylactic vaccination of rhesus macaques with rhesus cytomegalovirus (RhCMV) vectors expressing simian immunodeficiency virus (SIV) antigens (RhCMV/SIV) elicits immune responses that stringently control highly pathogenic SIV infection, with subsequent apparent clearance of the infection, in ~50% of vaccinees. In contrast, here, we show that therapeutic RhCMV/SIV vaccination of rhesus macaques previously infected with SIV and given continuous combination antiretroviral therapy (cART) beginning 4–9 d post-SIV infection does not mediate measurable SIV reservoir clearance during over 600 d of follow-up on cART relative to RhCMV/control vaccination. However, none of the six animals started on cART on day four or five, across both RhCMV/SIV- and RhCMV/control-vaccinated groups, those rhesus macaques with SIV reservoirs most closely resembling those of prophylactically RhCMV/SIV-vaccinated and protected animals early in their course, showed post-cART viral rebound with up to nine months of follow-up. Moreover, at necropsy, these rhesus macaques showed little to no evidence of replication-competent SIV. These results suggest that the early SIV reservoir is limited in durability and that effective blockade of viral replication and spread in this critical time window by either pharmacologic or immunologic suppression may result in reduction, and potentially loss, of rebound-competent virus over a period of ~two years. Early and prolonged administration of antiretroviral therapy to SIV-infected and post-exposure-vaccinated rhesus macaques was associated with absence or delay of detectable virus after therapy interruption.

Fukazawa et al . report that SIV persists in follicular helper T cells in elite controller macaques, evading clearance by CD8+ T cells Chronic-phase HIV and simian immunodeficiency virus (SIV) replication is reduced by as much as 10,000-fold in elite controllers (ECs) compared with typical progressors (TPs), but sufficient viral replication persists in EC tissues to allow viral sequence evolution and induce excess immune activation. Here we show that productive SIV infection in rhesus monkey ECs, but not TPs, is markedly restricted to CD4 + follicular helper T (T FH ) cells, suggesting that these EC monkeys' highly effective SIV-specific CD8 + T cells can effectively clear productive SIV infection from extrafollicular sites, but their relative exclusion from B cell follicles prevents their elimination of productively infected T FH cells. CD8 + lymphocyte depletion in EC monkeys resulted in a dramatic re-distribution of productive SIV infection to non-T FH cells, with restriction of productive infection to T FH cells resuming upon CD8 + T cell recovery. Thus, B cell follicles constitute 'sanctuaries' for persistent SIV replication in the presence of potent anti-viral CD8 + T cell responses, potentially complicating efforts to cure HIV infection with therapeutic vaccination or T cell immunotherapy.

Purpose - The purpose of this study is to investigate the relationships between fashion innovativeness opinion leadership and utilitarian hedonic shopping motivations. This study seeks to develop a better understanding of fashion leadership and determine the primary shopping motivations associated with fashion leadership.Design methodology approach - A survey was completed by a total of 150 students at a large university in the southeastern USA. Multiple regression analyses, MANCOVA, and ANCOVA were employed to test the research hypotheses.Findings - The results indicated that fashion innovativeness was significantly related to various hedonic shopping motivations; fashion innovativeness was positively associated with adventure and idea shopping motivations, whereas it was negatively associated with value shopping motivation. Fashion opinion leadership was positively associated with utilitarian shopping motivation.Practical implications - The results of the study help to suggest various marketing and retailing strategies to stimulate fashion innovative behaviors through adventurous, stimulating, and up-to-date new fashions. They also suggest that fashion opinion leadership could be activated by focusing proper shopping environments or advertising on information features for cognitive stimulation.Originality value - The study investigated a direct relationship between fashion leadership and shopping motivations for the first time. The findings of the study strengthen academic research on fashion leadership by identifying pre-positioned shopping motivations that trigger fashion leadership, as well as practical applications.

Achieving stable cyclability in initially anode-free all-solid-state batteries is challenging due to non-uniform Li (de)plating, especially under practical operating conditions. Here, we introduce a bilayer comprising a silver(Ag)-doped Li-argyrodite electrolyte layer in contact with the undoped Li-argyrodite electrolyte. During charging, electrochemical exsolution of Ag + from the silver-doped Li argyrodite forms nanoscale, lithiophilic silver seeds along grain boundaries and in pores where they are accessible for electron transfer. These silver seeds alloy with Li to induce uniform Li plating underneath and return to the electrolyte layer upon Li stripping to enhance the reversibility during cycling. With silver exsolution, a pouch-type full-cell with a volumetric energy density of 1312 Wh L −1 (excluding the packaging materials) and areal discharge capacity of 7.0 mAh cm −2 at 0.7 mA cm −2 , demonstrated stable cycling at a practical stack pressure of 2.0 MPa. This study highlights that Ag + diffusion in the Li-argyrodite solid electrolyte and its electrochemical exsolution are an effective strategy for robust, high-energy-density initially anode-free all-solid-state batteries. Achieving uniform Li plating in solid-state batteries is key for their practical application. Here, the authors integrate a silver-doped lithium argyrodite layer in initially anode-free all-solid-state batteries, promoting uniform lithium plating and cell operation under a low stack pressure of 2 MPa through silver exsolution.

Programmed cell death protein 1 (PD-1) is an immune checkpoint marker commonly expressed on memory T cells and enriched in latently HIV-infected CD4+ T cells. We engineered an anti-PD-1 chimeric antigen receptor (CAR) to assess the impact of PD-1 depletion on viral reservoirs and rebound dynamics in SIVmac239-infected rhesus macaques (RMs). Adoptive transfer of anti-PD-1 CAR T cells was done in 2 SIV-naive and 4 SIV-infected RMs on antiretroviral therapy (ART). In 3 of 6 RMs, anti-PD-1 CAR T cells expanded and persisted for up to 100 days concomitant with the depletion of PD-1+ memory T cells in blood and tissues, including lymph node CD4+ follicular helper T (TFH) cells. Loss of TFH cells was associated with depletion of detectable SIV RNA from the germinal center (GC). However, following CAR T infusion and ART interruption, there was a marked increase in SIV replication in extrafollicular portions of lymph nodes, a 2-log higher plasma viremia relative to controls, and accelerated disease progression associated with the depletion of CD8+ memory T cells. These data indicate anti-PD-1 CAR T cells depleted PD-1+ T cells, including GC TFH cells, and eradicated SIV from this immunological sanctuary.

Matrix factorization has been widely utilized as a latent factor model for solving the recommender system problem using collaborative filtering. For a recommender system, all the ratings in the rating matrix are bounded within a pre-determined range. In this paper, we propose a new improved matrix factorization approach for such a rating matrix, called Bounded Matrix Factorization (BMF), which imposes a lower and an upper bound on every estimated missing element of the rating matrix. We present an efficient algorithm to solve BMF based on the block coordinate descent method. We show that our algorithm is scalable for large matrices with missing elements on multicore systems with low memory. We present substantial experimental results illustrating that the proposed method outperforms the state of the art algorithms for recommender system such as stochastic gradient descent, alternating least squares with regularization, SVD++ and Bias-SVD on real-world datasets such as Jester, Movielens, Book crossing, Online dating and Netflix.