Abstract: Non-linear dimensionality reduction techniques are affected by two critical aspects: (i) the design of the adjacency graphs, and (ii) the embedding of new test data-the out-of-sample problem. For the first aspect, the proposed solutions, in general, were heuristically driven. For the second aspect, the difficulty resides in finding an accurate mapping that transfers unseen data samples into an existing manifold. Past works addressing these two aspects were heavily parametric in the sense that the optimal performance is only achieved for a suitable parameter choice that should be known in advance. In this paper, we demonstrate that the sparse representation theory not only serves for automatic graph construction as shown in recent works, but also represents an accurate alternative for out-of-sample embedding. Considering for a case study the Laplacian Eigenmaps, we applied our method to the face recognition problem. To evaluate the effectiveness of the proposed out-of-sample embedding, experiments are conducted using the K-nearest neighbor (KNN) and Kernel Support Vector Machines (KSVM) classifiers on six public face datasets. The experimental results show that the proposed model is able to achieve high categorization effectiveness as well as high consistency with non-linear embeddings/manifolds obtained in batch modes.

Abstract: The problem of training classifiers only with target data arises in many applications where non-target data are too costly, difficult to obtain, or not available at all. Several one-class classification methods have been presented to solve this problem, but most of the methods are highly sensitive to the presence of outliers in the target class. Ensemble methods have therefore been proposed as a powerful way to improve the classification performance of binary/multi-class learning algorithms by introducing diversity into classifiers.
However, their application to one-class classification has been rather limited. In
this paper, we present a new ensemble method based on a non-parametric weighted bagging strategy for one-class classification, to improve accuracy in the presence of outliers. While the standard bagging strategy assumes a uniform data distribution, the method we propose here estimates a probability density based on a forest structure of the data. This assumption allows the estimation of data distribution from the computation of simple univariate and bivariate kernel densities. Experiments using original and noisy versions of 20 different datasets show that bagging ensemble methods applied to different one-class classifiers outperform base one-class classification methods. Moreover, we show that, in noisy versions of the datasets, the non-parametric weighted bagging strategy we propose outperforms the classical bagging strategy in a statistically significant way.