We revisit the classical technique of regularised least squares (RLS) for nonlinear classification in this paper. Specifically, we focus on a low-rank formulation of the RLS, which has linear time complexity in the size of data set only, independent of both the number of classes and number of features. This makes low-rank RLS particularly suitable for problems with large data and moderate feature dimensions. Moreover, we have proposed a general theorem for obtaining the closed-form estimation of prediction values on a holdout validation set given the low-rank RLS classifier trained on the whole training data. It is thus possible to obtain an error estimate for each parameter setting without retraining and greatly accelerate the process of cross-validation for parameter selection. Experimental results on several large-scale benchmark data sets have shown that low-rank RLS achieves comparable classification performance while being much more efficient than standard kernel SVM for nonlinear classification. The improvement in efficiency is more evident for data sets with higher dimensions.
In this paper, we propose a method for indexing and retrieval of images based on shapes of objects. The concept of connectivity is introduced. 3D models are used to represent 2D images. 2D images are decomposed a priori using connectivity which is followed by 3D model construction. 3D model descriptors are obtained for 3D models and used to represent the underlying 2D shapes. We have used spherical harmonics descriptors as the 3D model descriptors. Difference between two images is computed as the Euclidean distance between their descriptors. Experiments are performed to test the effectiveness of spherical harmonics for retrieval of 2D images. The proposed method is compared with methods based on principal components analysis (PCA) and generic Fourier descriptors (GFD). It is found that the proposed method is effective. Item S8 within the MPEG-7 still images content set is used for performing experiments.