Local tangent space alignment

Local tangent space alignment (LTSA) is a method for <a href="/facts/Manifold_learning/1lL1Y0vN">manifold learning</a>, which can efficiently learn a <a href="/facts/Nonlinear_system/4aYItALC">nonlinear</a> embedding into <a href="/facts/Dimension/0ktmUyac">low-dimensional</a> coordinates from <a href="/facts/High-dimensional/0ktmUyac">high-dimensional</a> data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a <a href="/facts/Manifold/rXPERJtu">manifold</a> is correctly unfolded, all of the <a href="/facts/Tangent/sF0jH3EI">tangent</a> <a href="/facts/Hyperplane/2s2ycYYd">hyperplanes</a> to the manifold will become aligned. It begins by computing the <a href="/facts/K-nearest_neighbors_algorithm/Bs1UaAmE">k-nearest neighbors</a> of every point. It computes the <a href="/facts/Tangent_space/crvpbSeG">tangent space</a> at every point by computing the d-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by <a href="/facts/Sample_(statistics)/URCwKNge">data samples</a>, and thus can not be used for classification directly.

Local tangent space alignment open-in-new

Local tangent space alignment