Supervised Locally Linear Embedding Algorithm for Pattern Recognition

The dimensionality of the input data often far exceeds their intrinsic dimensionality. As a result, it may be difficult to recognize multidimensional data, especially if the number of samples in a dataset is not large. In addition, the more dimensions the data have, the longer the recognition time is. This leads to the necessity of performing dimensionality reduction before pattern recognition. Locally linear embedding (LLE) 5,6 is one of the methods intended for this task. In this paper, we investigate its extension, called supervised locally linear embedding (SLLE), using class labels of data points in their mapping into a low-dimensional space. An efficient eigendecomposition scheme for SLLE is derived. Two variants of SLLE are analyzed coupled with a k nearest neighbor classifier and tested on real-world images. Preliminary results demonstrate that both variants yield identical best accuracy, despite of being conceptually different.