Two Algorithms for Orthogonal Nonnegative Matrix Factorization with Application to Clustering

Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for clustering tasks such as document classification. In this paper, we introduce two new methods to solve ONMF. First, we show athematical equivalence between ONMF and a weighted variant of spherical k-means, from which we derive our first method, a simple EM-like algorithm. This also allows us to determine when ONMF should be preferred to k-means and spherical k-means. Our second method is based on an augmented Lagrangian approach. Standard ONMF algorithms typically enforce nonnegativity for their iterates while trying to achieve orthogonality at the limit (e.g., using a proper penalization term or a suitably chosen search direction). Our method works the opposite way: orthogonality is strictly imposed at each step while nonnegativity is asymptotically obtained, using a quadratic penalty. Finally, we show that the two proposed approaches compare favorably with standard ONMF algorithms on synthetic, text and image data sets.Comment: 17 pages, 8 figures. New numerical experiments (document and synthetic data sets

Balancing Speed and Quality in Online Learning to Rank for Information Retrieval

In Online Learning to Rank (OLTR) the aim is to find an optimal ranking model by interacting with users. When learning from user behavior, systems must interact with users while simultaneously learning from those interactions. Unlike other Learning to Rank (LTR) settings, existing research in this field has been limited to linear models. This is due to the speed-quality tradeoff that arises when selecting models: complex models are more expressive and can find the best rankings but need more user interactions to do so, a requirement that risks frustrating users during training. Conversely, simpler models can be optimized on fewer interactions and thus provide a better user experience, but they will converge towards suboptimal rankings. This tradeoff creates a deadlock, since novel models will not be able to improve either the user experience or the final convergence point, without sacrificing the other. Our contribution is twofold. First, we introduce a fast OLTR model called Sim-MGD that addresses the speed aspect of the speed-quality tradeoff. Sim-MGD ranks documents based on similarities with reference documents. It converges rapidly and, hence, gives a better user experience but it does not converge towards the optimal rankings. Second, we contribute Cascading Multileave Gradient Descent (C-MGD) for OLTR that directly addresses the speed-quality tradeoff by using a cascade that enables combinations of the best of two worlds: fast learning and high quality final convergence. C-MGD can provide the better user experience of Sim-MGD while maintaining the same convergence as the state-of-the-art MGD model. This opens the door for future work to design new models for OLTR without having to deal with the speed-quality tradeoff.Comment: CIKM 2017, Proceedings of the 2017 ACM on Conference on Information and Knowledge Managemen

Deep Divergence-Based Approach to Clustering

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effective in traditional clustering. We propose a novel loss function that incorporates geometric regularization constraints, thus avoiding degenerate structures of the resulting clustering partition. Experiments on synthetic benchmarks and real datasets show that the proposed network achieves competitive performance with respect to other state-of-the-art methods, scales well to large datasets, and does not require pre-training steps