Dimensional reduction may be effective in order to compress data without loss of essential information. Also, it may be useful in order to smooth data and reduce random noise. The...
This paper considers a recently proposed method for unsupervised learning and dimensionality reduction, locally linear embedding (LLE). LLE computes a compact representation of hi...
A K∗ -sparse vector x∗ ∈ RN produces measurements via linear dimensionality reduction as u = Φx∗ + n, where Φ ∈ RM×N (M < N), and n ∈ RM consists of independent ...
For supervised learning, feature selection algorithms attempt to maximise a given function of predictive accuracy. This function usually considers the ability of feature vectors t...
Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motiva...