Da Kuang

Da Kuang, Barry Drake, Haesun Park

The importance of unsupervised clustering and topic modeling is well recognized with ever-increasing volumes of text data. In this paper, we propose a fast method for hierarchical clustering and topic modeling called HierNMF2. Our method is based on fast Rank-2 nonnegative matrix factorization (NMF) that performs binary clustering and an efficient node splitting rule. Further utilizing the final leaf nodes generated in HierNMF2 and the idea of nonnegative least squares fitting, we propose a new clustering/topic modeling method called FlatNMF2 that recovers a flat clustering/topic modeling result in a very simple yet significantly more effective way than any other existing methods. We implement highly optimized open source software in C++ for both HierNMF2 and FlatNMF2 for hierarchical and partitional clustering/topic modeling of document data sets. Substantial experimental tests are presented that illustrate significant improvements both in computational time as well as quality of solutions. We compare our methods to other clustering methods including K-means, standard NMF, and CLUTO, and also topic modeling methods including latent Dirichlet allocation (LDA) and recently proposed algorithms for NMF with separability constraints. Overall, we present efficient tools for analyzing large-scale data sets, and techniques that can be generalized to many other data analytics problem domains.

Kai Yuan, Da Kuang

Autocomplete (a.k.a "Query Auto-Completion", "AC") suggests full queries based on a prefix typed by customer. Autocomplete has been a core feature of commercial search engine. In this paper, we propose a novel context-aware neural network based pairwise ranker (DeepPLTR) to improve AC ranking, DeepPLTR leverages contextual and behavioral features to rank queries by minimizing a pairwise loss, based on a fully-connected neural network structure. Compared to LambdaMART ranker, DeepPLTR shows +3.90% MeanReciprocalRank (MRR) lift in offline evaluation, and yielded +0.06% (p < 0.1) Gross Merchandise Value (GMV) lift in an Amazon's online A/B experiment.

Wei Zhu, Victoria Chayes, Alexandre Tiard et al.

In this paper, a graph-based nonlocal total variation method (NLTV) is proposed for unsupervised classification of hyperspectral images (HSI). The variational problem is solved by the primal-dual hybrid gradient (PDHG) algorithm. By squaring the labeling function and using a stable simplex clustering routine, an unsupervised clustering method with random initialization can be implemented. The effectiveness of this proposed algorithm is illustrated on both synthetic and real-world HSI, and numerical results show that the proposed algorithm outperforms other standard unsupervised clustering methods such as spherical K-means, nonnegative matrix factorization (NMF), and the graph-based Merriman-Bence-Osher (MBO) scheme.

Da Kuang, Zuoqiang Shi, Stanley Osher et al.

We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank approximation methods using convex optimization and the nuclear norm, we formulate matrix completion as a series of semi-supervised learning problems, and propagate the known ratings to the missing ones on the user-user or item-item graph globally. The semi-supervised learning problems are expressed as Laplace-Beltrami equations on a manifold, or namely, harmonic extension, and can be discretized by a point integral method. We show that our approach does not impose a low-rank Euclidean subspace on the data points, but instead minimizes the dimension of the underlying manifold. Our method, named LDM (low dimensional manifold), turns out to be particularly effective in generating rankings of items, showing decent computational efficiency and robust ranking quality compared to state-of-the-art methods.

Da Kuang, Alex Gittens, Raffay Hamid

The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($λ$). We propose an efficient way to interpolate the Cholesky factors of the Hessian matrix computed over a small set of $λ$ values. This approximation enables us to optimally minimize the hold-out error while incurring only a fraction of the cost compared to exact cross-validation. We provide a formal error bound for our approximation scheme and present solutions to a set of key implementation challenges that allow our approach to maximally exploit the compute power of modern architectures. We present a thorough empirical analysis over multiple datasets to show the effectiveness of our approach.