Canonical Divergence Analysis

We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical domains, including biology and architecture. Existing techniques assume the vectors to have the same domain or to be jointly distributed, and hence are not applicable. To address this, we propose Canonical Divergence Analysis (CDA). We introduce three instantiations, each of which permits practical implementation. Extensive empirical evaluation shows the potential of our method.Comment: Submission to AISTATS 201

An Information Retrieval Approach to Finding Dependent Subspaces of Multiple Views

Finding relationships between multiple views of data is essential both for exploratory analysis and as pre-processing for predictive tasks. A prominent approach is to apply variants of Canonical Correlation Analysis (CCA), a classical method seeking correlated components between views. The basic CCA is restricted to maximizing a simple dependency criterion, correlation, measured directly between data coordinates. We introduce a new method that finds dependent subspaces of views directly optimized for the data analysis task of \textit{neighbor retrieval between multiple views}. We optimize mappings for each view such as linear transformations to maximize cross-view similarity between neighborhoods of data samples. The criterion arises directly from the well-defined retrieval task, detects nonlinear and local similarities, is able to measure dependency of data relationships rather than only individual data coordinates, and is related to well understood measures of information retrieval quality. In experiments we show the proposed method outperforms alternatives in preserving cross-view neighborhood similarities, and yields insights into local dependencies between multiple views.Comment: 9 pages, 15 figures. Submitted for ICLR 2016; the authors contributed equall