Unsupervised Learning: Neighbor Embedding
Unsupervised Learning: Neighbor Embedding
Manifold Learning Suitable for clustering or following supervised learning
Manifold Learning Suitable for clustering or following supervised learning
Locally Linear Embedding (LLE) Wij represents the relation between xl and x Find a set of wii minimizing k-yl Then find the dimension reduction results zi and z based on wij
Locally Linear Embedding (LLE) 𝑥 𝑖 𝑥 𝑗 𝑤𝑖𝑗 𝑤𝑖𝑗 represents the relation between 𝑥 𝑖 and 𝑥 𝑗 Find a set of 𝑤𝑖𝑗 minimizing 𝑖 𝑥 𝑖 − 𝑗 𝑤𝑖𝑗𝑥 𝑗 2 Then find the dimension reduction results 𝑧 𝑖 and 𝑧 𝑗 based on 𝑤𝑖𝑗
LLE Find a set of z minimizing Keep wij unchanged -Σ Wi Original Space New (Low-dim)Space
LLE 𝑥 𝑖 𝑥 𝑗 𝑤𝑖𝑗 𝑤𝑖𝑗 𝑧 𝑗 𝑧 𝑖 Original Space New (Low-dim) Space Find a set of 𝑧 𝑖 minimizing Keep 𝑤𝑖𝑗 unchanged 𝑖 𝑧 𝑖 − 𝑗 𝑤𝑖𝑗𝑧 𝑗 2
LLE xt,xi Wij 在地領為連理校 在天顧作出墨焉 Wij Source of image: http://feetsprint.blogspot.tw/2016 /02/blog-post_29.html
LLE Source of image: http://feetsprint.blogspot.tw/2016 /02/blog-post_29.html 𝑧 𝑖 ,𝑧 𝑗 𝑤𝑖𝑗 𝑤𝑖𝑗 𝑥 𝑖 ,𝑥 𝑗