We investigate the optimality of (1+ )-approximation algorithms obtained via the dimensionality reduction method. We show that: • Any data structure for the (1 + )-approximate n...
We present a unified duality view of several recently emerged spectral methods for nonlinear dimensionality reduction, including Isomap, locally linear embedding, Laplacian eigenm...
Non-linear dimensionality reduction of noisy data is a challenging problem encountered in a variety of data analysis applications. Recent results in the literature show that spect...
When only a small number of labeled samples are available, supervised dimensionality reduction methods tend to perform poorly due to overfitting. In such cases, unlabeled samples ...
Similarity search usually encounters a serious problem in the high dimensional space, known as the “curse of dimensionality”. In order to speed up the retrieval efficiency, p...