In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by certain Indepenent Component Analysis techniques, are simple, easy to implement and efficient. Geometrically, the proposed algorithms can be interpreted as hidden basis recovery by means of function optimization. We give a complete characterization of the contrast functions admissible for provable basis recovery. We show how these conditions can be interpreted as a "hidden convexity" of our optimization problem on the sphere; interestingly, we use efficient convex maximization rather than the more common convex minimization. We also show encouraging experimental results on real and simulated data.

This Blue Sky presentation focuses on a major shift toward a notion of “ambient intelligence” that transcends general applications targeted at the general population.  The focus is on highly personalized agents that accommodate individual differences and changes over time.  This notion of Extended Ambient Intelligence (EAI) concerns adaptation to a person’s preferences and experiences, as well as changing capabilities, most notably in an environment where conversational engagement is central.  An important step in moving this research forward is the accommodation of different degrees of cognitive capability (including speech processing) that may vary over time for a given user—whether through improvement or through deterioration. We suggest that the application of divergence detection to speech patterns may enable adaptation to a speaker’s increasing or decreasing level of speech impairment over time. Taking an adaptive approach toward technology development in this arena may be a first step toward empowering those with special needs so that they may live with a high quality of life.  It also represents an important step toward a notion of ambient intelligence that is personalized beyond what can be achieved by mass-produced, one-size-fits-all software currently in use on mobile devices.

Location sharing services (LSS) like Foursquare, Gowalla, and Facebook Places support hundreds of millions of user-driven footprints (i.e., "checkins"). Those global-scale footprints provide a unique opportunity to study the social and temporal characteristics of how people use these services and to model patterns of human mobility, which are significant factors for the design of future mobile+location-based services, traffic forecasting, urban planning, as well as epidemiological models of disease spread. In this paper, we investigate 22 million checkins across 220,000 users and report a quantitative assessment of human mobility patterns by analyzing the spatial, temporal, social, and textual aspects associated with these footprints. We find that: (i) LSS users follow the “Levy Flight” mobility pattern and adopt periodic behaviors; (ii) While geographic and economic constraints affect mobility patterns, so does individual social status; and (iii) Content and sentiment-based analysis of posts associated with checkins can provide a rich source of context for better understanding how users engage with these services.

We present a new framework for semi-supervised learning with sparse eigenfunction bases of kernel matrices. It turns out that when the cluster assumption holds, that is, when the high density regions are sufficiently separated by low density valleys, each high density area corresponds to a unique representative eigenvector. Linear combination of such eigenvectors (or, more precisely, of their Nystrom extensions) provide good candidates for good classification functions. By first choosing an appropriate basis of these eigenvectors from unlabeled data and then using labeled data with Lasso to select a classifier in the span of these eigenvectors, we obtain a classifier, which has a very sparse representation in this basis. Importantly, the sparsity appears naturally from the cluster assumption. Experimental results on a number of real-world datasets show that our method is competitive with the state of the art semi-supervised learning algorithms and out-performs the natural base-line algorithm (Lasso in the Kernel PCA basis).