Mathematical definition of the SVD X=USVT where U is an m x n matrix,S is an n x n diagonal matrix, and Ir is also an n x n matrix. *The columns of U are called the left singular vectors,{ug, and form an orthonormal basis,so that u;'u;=1 for i=j,and u财u=0fori≠j. The rows of Vr are called the right singular vectors,vp,and form an orthonormal basis. *The elements of S are only nonzero on the diagonal,and are called the singular values.Thus,S=diag(s1,.s). Furthermore,sk>0for1≤k≤r,and sk=0for(件l)≤k≤n. xo-Eusv! =1 The term "closest"means that X minimizes the sum of the squares of the difference of the elements of X and X
Mathematical definition of the SVD where U is an m x n matrix, S is an n x n diagonal matrix, and VT is also an n x n matrix. *The columns of U are called the left singular vectors, {u k}, and form an orthonormal basis, so that ui·uj = 1 for i = j, and ui·uj = 0 for i ≠ j. The rows of VT are called the right singular vectors, {v k}, and form an orthonormal basis. *The elements of S are only nonzero on the diagonal, and are called the singular values. Thus, S = diag(s1 ,...,s n). Furthermore, sk > 0 for 1 ≤ k ≤ r, and sk = 0 for ( r+1) ≤ k ≤ n. The term “closest” means that X (l) minimizes the sum of the squares of the difference of the elements of X and X(l)
Mathematical definition of the svd The calculation of SVD XTY=VS2VT X=USVT-U=XVS-
Mathematical definition of the SVD The calculation of SVD
llustrative applications for SVD and PCA Image processing and compression compression and noisy reduction Information Retrieval linguistic ambiguity issues.For example,keyword search Java
Ilustrative applications for SVD and PCA Image processing and compression compression and noisy reduction Information Retrieval linguistic ambiguity issues. For example, keyword search “Java
SVD analysis of gene expression data systems biology applications to understand relations among genes diagnostic applications to classify tissue samples from individuals with and without a disease
SVD analysis of gene expression data systems biology applications to understand relations among genes diagnostic applications to classify tissue samples from individuals with and without a disease
微阵列的概念 ·什么是微阵列？ 在支撑物（玻璃片、硅片、胶片）上的一种微小 元素的有序阵列，该阵列允许基因进行特定的结 合。阵列尺寸通常在几百至成千上万。 微阵列是一种新的科学术语，取自于希腊字 “mikro”(smal)和法国字“arayer'”(安排的)
微阵列的概念 • 什么是微阵列？ 在支撑物(玻璃片、硅片、胶片）上的一种微小 元素的有序阵列，该阵列允许基因进行特定的结 合。阵列尺寸通常在几百至成千上万。 微阵列是一种新的科学术语，取自于希腊字 “mikro” (small)和法国字“arayer”(安排的）。 •