Kernelization of locality preserving discriminant projection

In recent years, non-linear dimensionality reduction approaches have become popular due to their suitability to capture the non-linearities present in the data. However, these are not applicable for recognition related applications as representation of new data points is not defined in the reduced subspace. Hence, to explore the non-linearities of the data, local structure preserving approaches received considerable attention. These approaches keep the local information of the data points intact in the lower dimensional space as well. Locality Preserving Discriminant Projection (LPDP) not only preserves the neighborhood information for each data point, but also tries to discriminate data points from different classes using their class labels. The performance of such neighborhood information preserving dimensionality reduction techniques do not guarantee to capture complex non-linearities present in the data. To address this issue, kernel functions that map the data in a non-linear feature space before applying the dimensionality reduction approach are widely used. This article discusses Kernelization of LPDP which explores complex non-linear changes of face images due to facial expression, illumination, pose and environmental changes. The proposed approach is applied for face recognition on some of the benchmark databases with such variability.