This paper investigates recommendation fairness among new items. While previous efforts have studied fairness in recommender systems and shown success in improving fairness, they mainly focus on scenarios where unfairness arises due to biased prior user-feedback history (like clicks or views). Yet, it is unknown whether new items without any feedback history can be recommended fairly, and if unfairness does exist, how can we provide fair recommendations among these new items in such a cold-start scenario. In detail, we first formalize fairness among new items with the well-known concepts of equal opportunity and Rawlsian Max-Min fairness. We empirically show the prevalence of unfairness in cold start recommender systems. Then we propose a novel learnable post-processing framework as a model blueprint for enhancing fairness, with which we propose two concrete models: a joint-learning generative model, and a score scaling model. Extensive experiments over four public datasets show the effectiveness of the proposed models for enhancing fairness while also preserving recommendation utility.

Understanding large-scale document collections in an efficient manner is an important problem. Usually, document data are associated with other information (e.g., an author's gender, age, and location) and their links to other entities (e.g., co-authorship and citation networks). For the analysis of such data, we often have to reveal common as well as discriminative characteristics of documents with respect to their associated information, e.g., male- vs. female-authored documents, old vs. new documents, etc. To address such needs, this paper presents a novel topic modeling method based on joint nonnegative matrix factorization, which simultaneously discovers common as well as discriminative topics given multiple document sets. Our approach is based on a block-coordinate descent framework and is capable of utilizing only the most representative, thus meaningful, keywords in each topic through a novel pseudo-deflation approach. We perform both quantitative and qualitative evaluations using synthetic as well as real-world document data sets such as research paper collections and nonprofit micro-finance data. We show our method has a great potential for providing in-depth analyses by clearly identifying common and discriminative topics among multiple document sets.

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.

The nonnegative least squares problems are useful in applications where the physical nature of problem domain permits only additive linear combinations. We discuss the l1-regularized nonnegative least squares (L1-NLS) problem, where l1-regularization is used to induce sparsity. Although l1-regularization has been successfully used in least squares regression, when combined with nonnegativity constraints, developments of algorithms and their understandings have been limited. We propose an algorithm that generates the entire regularization paths of the L1-NLS problem. We prove the correctness of the proposed algorithm and illustrate a novel application in environmental sustainability. The application relates to life cycle assessment (LCA), a technique used to estimate environmental impact during the entire lifetime of a product. We address an inverse problem in LCA. Given environmental impact factors of a target product and of a large library of constituents, the goal is to reverse engineer an inventory tree for the product. Using real-world data sets, we demonstrate how our L1-NLS approach controls the size of discovered trees, and how the full regularization paths effectively illustrate the spectrum of discovered trees with varying sparsity and compositions.

A recent challenge in data analysis for science and engineering is that data are often represented in a structured way. In particular, many data mining tasks have to deal with group-structured prior information, where features or data items are organized into groups. In this paper, we develop group sparsity regularization methods for nonnegative matrix factorization (NMF). NMF is an effective data mining tool that has been widely adopted in text mining, bioinformatics, and clustering, but a principled approach to incorporating group information into NMF has been lacking in the literature. Motivated by an observation that features or data items within a group are expected to share the same sparsity pattern in their latent factor representation, we propose mixed-norm regularization to promote group sparsity in the factor matrices of NMF. Group sparsity improves the interpretation of latent factors. Efficient convex optimization methods for dealing with the mixed-norm term are presented along with computational comparisons between them. Application examples of the proposed method in factor recovery, semi-supervised clustering, and multilingual text analysis are demonstrated.

Nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used for various tasks including text mining, pattern analysis, clustering, and cancer class discovery. The mathematical formulation for NMF appears as a non-convex 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 some limitations of active set methods. We introduce ideas to efficiently extend the block principal pivoting method within the context of NMF computation. Our algorithm inherits the convergence theory of the ANLS framework and can easily be extended to other constrained NMF formulations. Comparisons of algorithms using datasets that are from real life applications as well as those artificially generated show that the proposed new algorithm outperforms existing ones in computational speed.