Mining Subspace Correlations

Abstract—In recent applications of clustering such as gene expression microarray analysis, collaborative filtering, text and web mining, object similarity is no longer measured by physical distance, but rather by the behavior patterns objects manifest or the magnitude of correlations they induce. Current state of the art algorithms aiming at this type of clustering typically postulate specific cluster models that are able to capture only specific behavior patterns or correlations, and omit the possibility that other information carrying patterns or correlations may coexist in the data. In this paper we present a new clustering method that is able to cluster simultaneously different types of patterns or correlations that may coexist in the data. This is achieved by casting the problem into a problem of searching for groups of points that fit lines in subspaces of the data. A formal stochastic line cluster model is presented. Based on this model an algorithm which uses feature selection in conjunction with a line detector subroutine is discussed. I

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Temporal Cross-Media Retrieval with Soft-Smoothing

Multimedia information have strong temporal correlations that shape the way modalities co-occur over time. In this paper we study the dynamic nature of multimedia and social-media information, where the temporal dimension emerges as a strong source of evidence for learning the temporal correlations across visual and textual modalities. So far, cross-media retrieval models, explored the correlations between different modalities (e.g. text and image) to learn a common subspace, in which semantically similar instances lie in the same neighbourhood. Building on such knowledge, we propose a novel temporal cross-media neural architecture, that departs from standard cross-media methods, by explicitly accounting for the temporal dimension through temporal subspace learning. The model is softly-constrained with temporal and inter-modality constraints that guide the new subspace learning task by favouring temporal correlations between semantically similar and temporally close instances. Experiments on three distinct datasets show that accounting for time turns out to be important for cross-media retrieval. Namely, the proposed method outperforms a set of baselines on the task of temporal cross-media retrieval, demonstrating its effectiveness for performing temporal subspace learning.Comment: To appear in ACM MM 201