Multiclass latent locally linear support vector machines

Kernelized Support Vector Machines (SVM) have gained the status of off-the-shelf classifiers, able to deliver state of the art performance on almost any problem. Still, their practical use is constrained by their computational and memory complexity, which grows super-linearly with the number of training samples. In order to retain the low training and testing complexity of linear classifiers and the exibility of non linear ones, a growing, promising alternative is represented by methods that learn non-linear classifiers through local combinations of linear ones. In this paper we propose a new multi class local classifier, based on a latent SVM formulation. The proposed classifier makes use of a set of linear models that are linearly combined using sample and class specific weights. Thanks to the latent formulation, the combination coefficients are modeled as latent variables. We allow soft combinations and we provide a closed-form solution for their estimation, resulting in an efficient prediction rule. This novel formulation allows to learn in a principled way the sample specific weights and the linear classifiers, in a unique optimization problem, using a CCCP optimization procedure. Extensive experiments on ten standard UCI machine learning datasets, one large binary dataset, three character and digit recognition databases, and a visual place categorization dataset show the power of the proposed approach

Semi-supervised Eigenvectors for Large-scale Locally-biased Learning

In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that prespecified target region. For example, one might be interested in the clustering structure of a data graph near a prespecified "seed set" of nodes, or one might be interested in finding partitions in an image that are near a prespecified "ground truth" set of pixels. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities, thus limiting the applicability of eigenvector-based methods in situations where one is interested in very local properties of the data. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We show that these semi-supervised eigenvectors can be computed quickly as the solution to a system of linear equations; and we also describe several variants of our basic method that have improved scaling properties. We provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning; and we discuss the relationship between our results and recent machine learning algorithms that use global eigenvectors of the graph Laplacian

CAFÉ-Map : context aware feature mapping for mining high dimensional biomedical data

Feature selection and ranking is of great importance in the analysis of biomedical data. In addition to reducing the number of features used in classification or other machine learning tasks, it allows us to extract meaningful biological and medical information from a machine learning model. Most existing approaches in this domain do not directly model the fact that the relative importance of features can be different in different regions of the feature space. In this work, we present a context aware feature ranking algorithm called CAFÉ-Map. CAFÉ-Map is a locally linear feature ranking framework that allows recognition of important features in any given region of the feature space or for any individual example. This allows for simultaneous classification and feature ranking in an interpretable manner. We have benchmarked CAFÉ-Map on a number of toy and real world biomedical data sets. Our comparative study with a number of published methods shows that CAFÉ-Map achieves better accuracies on these data sets. The top ranking features obtained through CAFÉ-Map in a gene profiling study correlate very well with the importance of different genes reported in the literature. Furthermore, CAFÉ-Map provides a more in-depth analysis of feature ranking at the level of individual examples

Adaptive Locality Preserving Regression

This paper proposes a novel discriminative regression method, called adaptive locality preserving regression (ALPR) for classification. In particular, ALPR aims to learn a more flexible and discriminative projection that not only preserves the intrinsic structure of data, but also possesses the properties of feature selection and interpretability. To this end, we introduce a target learning technique to adaptively learn a more discriminative and flexible target matrix rather than the pre-defined strict zero-one label matrix for regression. Then a locality preserving constraint regularized by the adaptive learned weights is further introduced to guide the projection learning, which is beneficial to learn a more discriminative projection and avoid overfitting. Moreover, we replace the conventional `Frobenius norm' with the special l21 norm to constrain the projection, which enables the method to adaptively select the most important features from the original high-dimensional data for feature extraction. In this way, the negative influence of the redundant features and noises residing in the original data can be greatly eliminated. Besides, the proposed method has good interpretability for features owing to the row-sparsity property of the l21 norm. Extensive experiments conducted on the synthetic database with manifold structure and many real-world databases prove the effectiveness of the proposed method.Comment: The paper has been accepted by IEEE Transactions on Circuits and Systems for Video Technology (TCSVT), and the code can be available at https://drive.google.com/file/d/1iNzONkRByIaUhXwdEhOkkh_0d2AAXNE8/vie