Approximation errors of online sparsification criteria

Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict the model definition on a subset of samples. The most known criterion is the (linear) approximation criterion, which discards any sample that can be well represented by the already contributing samples, an operation with excessive computational complexity. Several computationally efficient sparsification criteria have been introduced in the literature, such as the distance, the coherence and the Babel criteria. In this paper, we provide a framework that connects these sparsification criteria to the issue of approximating samples, by deriving theoretical bounds on the approximation errors. Moreover, we investigate the error of approximating any feature, by proposing upper-bounds on the approximation error for each of the aforementioned sparsification criteria. Two classes of features are described in detail, the empirical mean and the principal axes in the kernel principal component analysis.Comment: 10 page

Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data

Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the robust \emph{time series cluster kernel} (TCK). The approach taken leverages the missing data handling properties of Gaussian mixture models (GMM) augmented with informative prior distributions. An ensemble learning approach is exploited to ensure robustness to parameters by combining the clustering results of many GMM to form the final kernel. We evaluate the TCK on synthetic and real data and compare to other state-of-the-art techniques. The experimental results demonstrate that the TCK is robust to parameter choices, provides competitive results for MTS without missing data and outstanding results for missing data.Comment: 23 pages, 6 figure

Unsupervised Adaptive Re-identification in Open World Dynamic Camera Networks

Person re-identification is an open and challenging problem in computer vision. Existing approaches have concentrated on either designing the best feature representation or learning optimal matching metrics in a static setting where the number of cameras are fixed in a network. Most approaches have neglected the dynamic and open world nature of the re-identification problem, where a new camera may be temporarily inserted into an existing system to get additional information. To address such a novel and very practical problem, we propose an unsupervised adaptation scheme for re-identification models in a dynamic camera network. First, we formulate a domain perceptive re-identification method based on geodesic flow kernel that can effectively find the best source camera (already installed) to adapt with a newly introduced target camera, without requiring a very expensive training phase. Second, we introduce a transitive inference algorithm for re-identification that can exploit the information from best source camera to improve the accuracy across other camera pairs in a network of multiple cameras. Extensive experiments on four benchmark datasets demonstrate that the proposed approach significantly outperforms the state-of-the-art unsupervised learning based alternatives whilst being extremely efficient to compute.Comment: CVPR 2017 Spotligh