Nonlinear Topological Component Analysis: Application to Age-Invariant Face Recognition

We introduce a novel formalism that performs dimensionality reduction and captures topological features (such as the shape of the observed data) to conduct pattern classification. This mission is achieved by: 1) reducing the dimension of the observed variables through a kernelized radial basis function technique and expressing the latent variables probability distribution in terms of the observed variables; 2) disclosing the data manifold as a 3-D polyhedron via the $\alpha $ -shape constructor and extracting topological features; and 3) classifying a data set using a mixture of multinomial distributions. We have applied our methodology to the problem of age-invariant face recognition. Experimental results obtained demonstrate the efficiency of the proposed methodology named nonlinear topological component analysis when compared with some state-of-the-art approaches.