Lect5-6_MDS_LLE

Lect5-6_MDS_LLE - Lecture 5-6: MDS, LLE, Intrinsic...

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1 Lecture 5-6: MDS, LLE, Intrinsic dimensions MDS is a technique motivated by 2-problems in understanding data in high dimensional spaces. Its objective is to project an ensemble of data points into 1 2 or dimensional spaces so that Multi-dimensional scaling Its objective is to project an ensemble of data points into 1, 2, or 3-dimensional spaces so that the spatial distance of these data points are preserved. Thus, MDS is used for two purposes: 1). Visualize the structures and properties of data, so that we may select proper models for them. 2). Verify some distance (metric) measure on some unknown dataset. With a good distance measure, the data clusters should correspond to meaningful set, Lecture note for Stat 231-CS276A © S.C. Zhu e.g., in image database retrieval, or art authentication. Example I: distance visualization Lecture note for Stat 231-CS276A © S.C. Zhu
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2 Reconstructed 2D Map One computes the (x,y) coordinates for the 10 cities that best preserve the distance matrix. Lecture note for Stat 231-CS276A © S.C. Zhu Example II: color mapping Another example is to map various colors in a 2D matrix so that some perceptual distances are preserved. I am sorry that we cannot print out color, but the pdf file will be in color. One can calculate a perceptual color distance by psychology experiments then obtain One can calculate a perceptual color distance by psychology experiments, then obtains a distance matrix, like the city matrix, then we can map colors in 2D Lecture note for Stat 231-CS276A © S.C. Zhu
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3 Example III: image query From Rubner, Tomasi, and Guibus, 00 Lecture note for Stat 231-CS276A © S.C. Zhu Example III: 2D mapping of images Each image is treated as a vector point and some distance is defined between
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Lect5-6_MDS_LLE - Lecture 5-6: MDS, LLE, Intrinsic...

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