Clustering and Inference From Pairwise Comparisons

Given a set of pairwise comparisons, the classical ranking problem computes a single ranking that best represents the preferences of all users. In this paper, we study the problem of inferring individual preferences, arising in the context of making personalized recommendations. In particular, we assume that there are $n$ users of $r$ types; users of the same type provide similar pairwise comparisons for $m$ items according to the Bradley-Terry model. We propose an efficient algorithm that accurately estimates the individual preferences for almost all users, if there are $r \max \{m, n\}\log m \log^2 n$ pairwise comparisons per type, which is near optimal in sample complexity when $r$ only grows logarithmically with $m$ or $n$. Our algorithm has three steps: first, for each user, compute the \emph{net-win} vector which is a projection of its $\binom{m}{2}$-dimensional vector of pairwise comparisons onto an $m$-dimensional linear subspace; second, cluster the users based on the net-win vectors; third, estimate a single preference for each cluster separately. The net-win vectors are much less noisy than the high dimensional vectors of pairwise comparisons and clustering is more accurate after the projection as confirmed by numerical experiments. Moreover, we show that, when a cluster is only approximately correct, the maximum likelihood estimation for the Bradley-Terry model is still close to the true preference.Comment: Corrected typos in the abstrac

Matching Image Sets via Adaptive Multi Convex Hull

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image set. Existing multi-model approaches extract local models by clustering each image set individually only once, with fixed clusters used for matching with various image sets. This may not be optimal for discrimination, as undesirable environmental conditions (eg. illumination and pose variations) may result in the two closest clusters representing different characteristics of an object (eg. frontal face being compared to non-frontal face). To address the above problem, we propose a novel approach to enhance nearest points based methods by integrating affine/convex hull classification with an adapted multi-model approach. We first extract multiple local convex hulls from a query image set via maximum margin clustering to diminish the artificial variations and constrain the noise in local convex hulls. We then propose adaptive reference clustering (ARC) to constrain the clustering of each gallery image set by forcing the clusters to have resemblance to the clusters in the query image set. By applying ARC, noisy clusters in the query set can be discarded. Experiments on Honda, MoBo and ETH-80 datasets show that the proposed method outperforms single model approaches and other recent techniques, such as Sparse Approximated Nearest Points, Mutual Subspace Method and Manifold Discriminant Analysis.Comment: IEEE Winter Conference on Applications of Computer Vision (WACV), 201

Group-In: Group Inference from Wireless Traces of Mobile Devices

This paper proposes Group-In, a wireless scanning system to detect static or mobile people groups in indoor or outdoor environments. Group-In collects only wireless traces from the Bluetooth-enabled mobile devices for group inference. The key problem addressed in this work is to detect not only static groups but also moving groups with a multi-phased approach based only noisy wireless Received Signal Strength Indicator (RSSIs) observed by multiple wireless scanners without localization support. We propose new centralized and decentralized schemes to process the sparse and noisy wireless data, and leverage graph-based clustering techniques for group detection from short-term and long-term aspects. Group-In provides two outcomes: 1) group detection in short time intervals such as two minutes and 2) long-term linkages such as a month. To verify the performance, we conduct two experimental studies. One consists of 27 controlled scenarios in the lab environments. The other is a real-world scenario where we place Bluetooth scanners in an office environment, and employees carry beacons for more than one month. Both the controlled and real-world experiments result in high accuracy group detection in short time intervals and sampling liberties in terms of the Jaccard index and pairwise similarity coefficient.Comment: This work has been funded by the EU Horizon 2020 Programme under Grant Agreements No. 731993 AUTOPILOT and No.871249 LOCUS projects. The content of this paper does not reflect the official opinion of the EU. Responsibility for the information and views expressed therein lies entirely with the authors. Proc. of ACM/IEEE IPSN'20, 202