ISO-Container Projection for feature extraction

An interesting algorithm, ISO-Container Projection (ISOCP), is proposed for finding succinct representations in a supervised manner for feature extraction. Motivated by the assumption of manifold learning theory, we cast the recognition problem as finding highly symmetric transformations mapping all classes into the corresponding ISO-Containers based on regular simplex in low dimensional space. Given labeled input data, ISOCP discovers basis functions to map each data into its corresponding container while keeping the intrinsic structure of each class. The basis functions span the lower subspace, and can be computed by a convex optimization problem: an L₂-constrained least square problem. When recognizing a new sample, we map it into the lower subspace and just compare the distances to the centers of ISO-Containers, instead of all the training samples. Experiments were conducted on several data sets, and the results demonstrated the competence of the proposed algorithms.