Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain setups, one wishes to extract the most significant information of one dataset relative to other datasets. Specifically, the interest may be on identifying, namely extracting features that are specific to a single target dataset but not the others. This paper develops a novel approach for such so-termed discriminative data analysis, and establishes its optimality in the least-squares (LS) sense under suitable data modeling assumptions. The criterion reveals linear combinations of variables by maximizing the ratio of the variance of the target data to that of the remainders. The novel approach solves a generalized eigenvalue problem by performing SVD just once. Numerical tests using synthetic and real datasets showcase the merits of the proposed approach relative to its competing alternatives.

What happened during the Boston Marathon in 2013? Nowadays, at any major event, lots of people take videos and share them on social media. To fully understand exactly what happened in these major events, researchers and analysts often have to examine thousands of these videos manually. To reduce this manual effort, we present an investigative system that automatically synchronizes these videos to a global timeline and localizes them on a map. In addition to alignment in time and space, our system combines various functions for analysis, including gunshot detection, crowd size estimation, 3D reconstruction and person tracking. To our best knowledge, this is the first time a unified framework has been built for comprehensive event reconstruction for social media videos.

Advertising in the case of textual Web pages has been studied extensively by many researchers. However, with the increasing amount of multimedia data such as image, audio and video on the Web, the need for recommending advertisement for the multimedia data is becoming a reality. In this paper, we address the novel problem of visual contextual advertising, which is to directly advertise when users are viewing images which do not have any surrounding text. A key challenging issue of visual contextual advertising is that images and advertisements are usually represented in image space and word space respectively, which are quite different with each other inherently. As a result, existing methods for Web page advertising are inapplicable since they represent both Web pages and advertisement in the same word space. In order to solve the problem, we propose to exploit the social Web to link these two feature spaces together. In particular, we present a unified generative model to integrate advertisements, words and images. Specifically, our solution combines two parts in a principled approach: First, we transform images from a image feature space to a word space utilizing the knowledge from images with annotations from social Web. Then, a language model based approach is applied to estimate the relevance between transformed images and advertisements. Moreover, in this model, the probability of recommending an advertisement can be inferred efficiently given an image, which enables potential applications to online advertising.