Publication
Over the past few decades we have been experiencing a data explosion; massive amounts of data are increasingly collected and multimedia databases, such as YouTube and Flickr, are rapidly expanding. At the same time rapid technological advancements in mobile devices and vision sensors have led to the emergence of novel multimedia mining architectures. These produce even more multimedia data, which are possibly captured under geometric transformations and need to be efficiently stored and analyzed. It is also common in such systems that data are collected distributively. This very fact poses great challenges in the design of effective methods for analysis and knowledge discovery from multimedia data. In this thesis, we study various instances of the problem of classification of visual data under the viewpoint of modern challenges. Roughly speaking, classification corresponds to the problem of categorizing an observed object to a particular class (or category), based on previously seen examples. We address important issues related to classification, namely flexible data representation for joint coding and classification, robust classification in the case of large geometric transformations and classification with multiple object observations in both centralized and distributed settings. We start by identifying the need for flexible data representation methods that are efficient in both storage and classification of multimedia data. Such flexible schemes offer the potential to significantly impact the efficiency of current multimedia mining systems, as they permit the classification of multimedia patterns directly in their compressed form, without the need for decompression. We propose a framework, called semantic approximation, which is based on sparse data representations. It formulates dimensionality reduction as a matrix factorization problem, under hybrid criteria that are posed as a trade-off between approximation for efficient compression and discrimination for effective classification. We demonstrate that the proposed methodology competes with state-of-the-art solutions in image classification and face recognition, implying that compression and classification can be performed jointly without performance penalties with respect to expensive disjoint solutions. Next, we allow the multimedia patterns to be geometrically transformed and we focus on transformation invariance issues in pattern classification. When a pattern is transformed, it spans a manifold in a high dimensional space. We focus on the problem of computing the distance of a certain test pattern from the manifold, which is also closely related to the image alignment problem. This is a hard non-convex problem that has only been sub-optimally addressed before. We represent transformation manifolds based on sparse geometric expansions, which results in a closed-form representation of the manifold equation with respect to the transformation parameters. When the transformation consists of