Intrinsic Dimension Estimation via Nearest Constrained Subspace Classifier
This work addresses classification and dimension estimation problems for image data, representing an incremental improvement over existing subspace-based classifiers.
The paper tackles classification and intrinsic dimension estimation on image data by proposing a new subspace-based classifier that models each class as a union of affine subspaces, using L0-norm regression, and reports that it generally outperforms competitors in classification accuracy with an accurately estimated dimension parameter.
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 L0-norm. 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.