Latent Fisher Discriminant Analysis

Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection and keyframe extraction cannot provide consistent instance-label pairs, while LDA requires labels on instance level for training. Thus it cannot be directly applied for semi-supervised classification problem. In this paper, we overcome this limitation and propose a latent variable Fisher discriminant analysis model. We relax the instance-level labeling into bag-level, is a kind of semi-supervised (video-level labels of event type are required for semantic frame extraction) and incorporates a data-driven prior over the latent variables. Hence, our method combines the latent variable inference and dimension reduction in an unified bayesian framework. We test our method on MUSK and Corel data sets and yield competitive results compared to the baseline approach. We also demonstrate its capacity on the challenging TRECVID MED11 dataset for semantic keyframe extraction and conduct a human-factors ranking-based experimental evaluation, which clearly demonstrates our proposed method consistently extracts more semantically meaningful keyframes than challenging baselines.Comment: 12 page

Enhanced protein fold recognition through a novel data integration approach

<p>Abstract</p> <p>Background</p> <p>Protein fold recognition is a key step in protein three-dimensional (3D) structure discovery. There are multiple fold discriminatory data sources which use physicochemical and structural properties as well as further data sources derived from local sequence alignments. This raises the issue of finding the most efficient method for combining these different informative data sources and exploring their relative significance for protein fold classification. Kernel methods have been extensively used for biological data analysis. They can incorporate separate fold discriminatory features into kernel matrices which encode the similarity between samples in their respective data sources.</p> <p>Results</p> <p>In this paper we consider the problem of integrating multiple data sources using a kernel-based approach. We propose a novel information-theoretic approach based on a Kullback-Leibler (KL) divergence between the output kernel matrix and the input kernel matrix so as to integrate heterogeneous data sources. One of the most appealing properties of this approach is that it can easily cope with multi-class classification and multi-task learning by an appropriate choice of the output kernel matrix. Based on the position of the output and input kernel matrices in the KL-divergence objective, there are two formulations which we respectively refer to as <it>MKLdiv-dc </it>and <it>MKLdiv-conv</it>. We propose to efficiently solve MKLdiv-dc by a difference of convex (DC) programming method and MKLdiv-conv by a projected gradient descent algorithm. The effectiveness of the proposed approaches is evaluated on a benchmark dataset for protein fold recognition and a yeast protein function prediction problem.</p> <p>Conclusion</p> <p>Our proposed methods MKLdiv-dc and MKLdiv-conv are able to achieve state-of-the-art performance on the SCOP PDB-40D benchmark dataset for protein fold prediction and provide useful insights into the relative significance of informative data sources. In particular, MKLdiv-dc further improves the fold discrimination accuracy to 75.19% which is a more than 5% improvement over competitive Bayesian probabilistic and SVM margin-based kernel learning methods. Furthermore, we report a competitive performance on the yeast protein function prediction problem.</p

Supervised classification and mathematical optimization

Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data.Ministerio de Ciencia e InnovaciónJunta de Andalucí

Supervised Classification and Mathematical Optimization

Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data