Bo Yang

Ahmed S. Zamzam, Bo Yang, Nicholas D. Sidiropoulos

In this paper, we address the challenge of recovering an accurate breakdown of aggregated tensor data using disaggregation examples. This problem is motivated by several applications. For example, given the breakdown of energy consumption at some homes, how can we disaggregate the total energy consumed during the same period at other homes? In order to address this challenge, we propose GRATE, a principled method that turns the ill-posed task at hand into a constrained tensor factorization problem. Then, this optimization problem is tackled using an alternating least-squares algorithm. GRATE has the ability to handle exact aggregated data as well as inexact aggregation where some unobserved quantities contribute to the aggregated data. Special emphasis is given to the energy disaggregation problem where the goal is to provide energy breakdown for consumers from their monthly aggregated consumption. Experiments on two real datasets show the efficacy of GRATE in recovering more accurate disaggregation than state-of-the-art energy disaggregation methods.

Songtao Lu, Meisam Razaviyayn, Bo Yang et al.

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally intractable, we first show that generic instances of the problem can be solved efficiently. More specifically, for a generic problem instance, certain strict complementarity (SC) condition holds for all Karush-Kuhn-Tucker (KKT) solutions (with probability one). The SC condition is then used to establish an equivalence relationship between two different notions of SOSPs, one of which is computationally easy to verify. Based on this particular notion of SOSP, we design an algorithm named the Successive Negative-curvature grAdient Projection (SNAP), which successively performs either conventional gradient projection or some negative curvature based projection steps to find SOSPs. SNAP and its first-order extension SNAP$^+$, require $\mathcal{O}(1/ε^{2.5})$ iterations to compute an $(ε, \sqrtε)$-SOSP, and their per-iteration computational complexities are polynomial in the number of constraints and problem dimension. To our knowledge, this is the first time that first-order algorithms with polynomial per-iteration complexity and global sublinear rate have been designed to find SOSPs of the important class of non-convex problems with linear constraints.

Bo Yang, Xiao Fu, Nicholas D. Sidiropoulos et al.

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is well-studied, under frameworks such as independent component analysis and constrained matrix factorization. Nevertheless, when the linear mixtures are distorted by an unknown nonlinear functions -- which is well-motivated and more realistic in many cases -- the identifiability issues are much less studied. This work proposes an identification criterion for a nonlinear mixture model that is well grounded in many real-world applications, and offers identifiability guarantees. A practical implementation based on a judiciously designed neural network is proposed to realize the criterion, and an effective learning algorithm is proposed. Numerical results on synthetic and real-data corroborate effectiveness of the proposed method.

Xiao Fu, Kejun Huang, Bo Yang et al.

This paper considers \emph{volume minimization} (VolMin)-based structured matrix factorization (SMF). VolMin is a factorization criterion that decomposes a given data matrix into a basis matrix times a structured coefficient matrix via finding the minimum-volume simplex that encloses all the columns of the data matrix. Recent work showed that VolMin guarantees the identifiability of the factor matrices under mild conditions that are realistic in a wide variety of applications. This paper focuses on both theoretical and practical aspects of VolMin. On the theory side, exact equivalence of two independently developed sufficient conditions for VolMin identifiability is proven here, thereby providing a more comprehensive understanding of this aspect of VolMin. On the algorithm side, computational complexity and sensitivity to outliers are two key challenges associated with real-world applications of VolMin. These are addressed here via a new VolMin algorithm that handles volume regularization in a computationally simple way, and automatically detects and {iteratively downweights} outliers, simultaneously. Simulations and real-data experiments using a remotely sensed hyperspectral image and the Reuters document corpus are employed to showcase the effectiveness of the proposed algorithm.

Bo Yang, Xiao Fu, Nicholas D. Sidiropoulos

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations that are well-suited for the intended task is more appealing. This paper proposes a joint factor analysis and latent clustering framework, which aims at learning cluster-aware low-dimensional representations of matrix and tensor data. The proposed approach leverages matrix and tensor factorization models that produce essentially unique latent representations of the data to unravel latent cluster structure -- which is otherwise obscured because of the freedom to apply an oblique transformation in latent space. At the same time, latent cluster structure is used as prior information to enhance the performance of factorization. Specific contributions include several custom-built problem formulations, corresponding algorithms, and discussion of associated convergence properties. Besides extensive simulations, real-world datasets such as Reuters document data and MNIST image data are also employed to showcase the effectiveness of the proposed approaches.