Effective Distance based Low Rank Representation for Image Classification Lowrank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring lowdimensional subspace structures embedded in data. However, conventional LRR methods simply use Euclidean distance to measure the similarity of samples, ignoring the dynamic structure information of data. Meanwhile, recent studies have shown that a probabilistically motivated distance measurement (called effective distance) can model the dynamic structure information of data. In this paper, we propose an effective distance based LRR (EDLRR)method for representation learning. The proposed EDLRR method can not only represent the dynamic structure of data, but also capture the geometric information in the inherent nonlinear data. Our method mainly uses Effective Distance Computation and Effective Distance based LowRank Representation. We evaluate our method on datasets in the task of image classification, with results demonstrating the effectiveness of the method.

Intrinsic Dimension Estimation via Nearest Constrained Subspace Classifier We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each class is modeled by a union of of a finite number ofaffine subspaces of the feature space. The affine subspaces have a common dimension, which is assumed to be much less than the dimension of the feature space. The subspaces are found using regression based on the L0norm. The proposed method is a generalisation of classical NN (Nearest Neighbor), NFL (Nearest Feature Line) classifiers and has a close relationship to NS (Nearest Subspace) classifier. The proposed classifier with an accurately estimated dimension parameter generally outperforms its competitors in terms of classification accuracy. We also propose a fast version of the classifier using a neighborhood representation to reduce its computational complexity. Experiments on publicly available datasets corroborate these claims.