Locally principal component analysis based on L1-norm maximisation

Locally principal component analysis (LPCA) is a popular method of dimensionality reduction, which takes locality of data points into account. In this study, by using the L1-norm instead of the L2-norm in LPCA, the authors introduce a new formulation of LPCA based on the L1-norm maximisation, referred to as LPCA-L1. Compared with the conventional L2-norm LPCA, the proposed LPCA-L1 approach is more robust to outliers. Experiments of classification and recognition on the UCI, Yale and ORL data sets confirm the effectiveness of the proposed method.