机器学习 -- Unsupervised Learning: Neighbor Embedding

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Unsupervised Learning: Neighbor Embedding Manifold Learning Locally Linear Embedding (LLE) Laplacian Eigenmaps T-distributed Stochastic Neighbor Embedding (t-SNE)
Locally linear embedding (ley Wii represents the relation between xt and x Wi Find a set of wii minimizing Wii 2 Then find the dimension reduction results z and z based on w Find a set of z minimizing Keep wii unchanged ∑|-∑ WiiZ Original space New(Low-dim space 在在 x°,x 地天 願碩 為作 更 理 校|篤 Source of image http://feetsprint.blogspot.tw/2016 /02/blog-post 29 html Lawrence K Saul, Sam T Roweis, Think Globally, fit locally Unsupervised learning of low dimensional manifolds JMLR, 2013 c K=5 K=6 K=8 K=10 是 K=12 K=14 K=16 K=18 一是· K=20 K=30 K=40 K=60 Laplacian eigenmaps Graph-based approach Distance detined by graph approximate the distance on manifold Construct the data points as a graph similarity Laplacian eigenmaps wi If connected 0 otherwise Review in semi-supervised learning: If x and x are close in a high density region, y and y< are probably the same c(yr,yr)l+as As a regularization term 2 L L:(R+U)X(R+U)matrix Evaluates how smooth your label is Graph Laplacian L=D-W Laplacian eigenmaps Dimension reduction If x 1 and x2 h are close in a nigl density region, z and z are close to each other. 2 Wi, i (z-Z J Any problem? How about_7j=0? Giving some constraints to z If the dim of z is M, Span(z,z2,.z]=RM Spectral clustering: clustering on z Belkin, M, niyogi, P. Laplacian eigenmaps and spectral techniques for embedding and clustering. Advances in neural information processing systems. 2002 T-distributed Stochastic Neighbor Embedding(t-SNE Problem of the previous approaches Similar data are close, but different data may collapse 十 ●X费 丰 ▲ LLE oN mnist LLE on coil-20

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