# Applied Mathematics for Computer Science

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keynote:2011-lesson03

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 keynote:2011-lesson03 [2011/06/26 06:17]11021015 [第三课] keynote:2011-lesson03 [2014/05/22 08:34] Line 1: Line 1: - ====== 第三课 ======= - === Distance and similarity === - * Clustering: unsupervised method to group data points, and find the overall structure. - - * Distance ​ : $L^1$ distance, $L^2$ distance, $L^p$ distance. - - * Distance, Norm and inner procuct. - - * Dimensional aware distances. - - * M-distance: $dist(x,​y;​M)=(x-y)^{T}M^{-1}(x-y)$ - - * More complex methods: PCA, MDS, LLE. - - * Isomap: use the geodesic distances on manifold between all pairs. - * Three step algorithm: ​ - * Using KNN or $\varepsilon$ -radius distance to construct neighborhood graph. - * Using Floyd'​s algorithm to compute the shortest paths between every pair of nodes. - * Minimize the cost function to construct d-dimensional embedding. - * Application:​ - * Texture mapping. - * Face Detection. - - * LLE: locally linear embedding, recovers global nonlinear structure from locally linear fits. - * Main idea: represent each data point as a weight-sum function of its neighbour point. - * Input: D dimension data. - * Output: d​ 本节编撰作者(请大家在这里报到)： ​ - * [[ender.liux@gmail.com|刘霄]] (ID: 11021018)， ​  ​编写了LLE、Isomap以及之前的内容 - * [[yy06@zju.edu.cn|林云胤]] (ID: 11021017)， ​  ​编写了spectral clustering - * [[hlt218@zju.edu.cn|黄龙涛]] (ID: 11021014)， ​  ​编写了K-means clusterging - * [[stel@zju.edu.cn|雷昊]] (ID: 11021015)， ​  ​编写了GMM高斯混合模型 - * [[xxxx@xxx.xxx|AuthorName5]] (ID: xxxxxxxxx)， ​  ​编写了... - * [[xxxx@xxx.xxx|AuthorName6]] (ID: xxxxxxxxx)， ​  ​编写了... - - 浙江大学2008-2010版权所有，如需转载或引用，请与[[zhx@cad.zju.edu.cn | 作者联系]]。 -