Functional Locality Preserving Projection for Dimensionality Reduction

Dimensionality Reduction (DR) which tries to discover low-dimensional feature representation embedded into the high-dimensional observations are significant for data visualization and data preprocessing. However, most DR models are designed for vector-valued data while only few of them are for functional data where samples are considered as continuous data such as curves or surfaces compared to discrete vector-valued data. Motivated by Functional Principal Component Analysis (FPCA), which generalizes the idea of Principal Component Analysis (PCA) to the Hilbert space of square-integrable functions, in this paper we propose Functional Locality Preserving Projection (FLPP), where classic Locality Preserving Projection (LPP) is extended for functional data analysis. Different from FPCA which only focuses on the global structure, FLPP could preserve local manifold structure embedded into the functional data, thus FLPP is capable of dealing with noise data. Experimental results on both synthetic data and real-world data verify that FLPP outperforms FPCA and typical LPP.