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Saul Kilian Q Weinberger Fei Sha Jihun Ham Daniel D Lee How can we search for low dimensional structure in high dimensional data If the data is mainly con64257ned to a low dimensional subspace then simple linear methods can be used to discover the s. Stoica R Moses Spectral analysis of signals available online at httpuserituuse psSASnewpdf 2 14 brPage 3br Deterministic signals Power spectral density de64257nitions Power spectral density properties Power spectral estimation Goal Given a 64257ni . local. image . descriptors. . into. . compact. . codes. Authors. :. Hervé. . Jegou. Florent. . Perroonnin. Matthijs. . Douze. Jorge. . Sánchez. Patrick . Pérez. Cordelia. Schmidt. Presented. Dimensionality Reduction. Author: . Christoph. . Eick. The material is mostly based on the . Shlens. PCA. Tutorial . http://www2.cs.uh.edu/~. ceick/ML/pca.pdf. . and . to a lesser extend based on material . Computer Graphics Course. June 2013. What is high dimensional data?. Images. Videos. Documents. Most data, actually!. What is high dimensional data?. Images – dimension 3·X·Y. Videos – dimension of image * number of frames.  .  . 2. Adams spectral sequence.  .  . -Many differentials. -. differentials go back by 1 and up by . r. .  . 3. Adams spectral sequence.  .  . -Many differentials. -. differentials go back by 1 and up by . From: The Handbook of Spatial Statistics. (Plus Extra). Dr. Montserrat Fuentes and Dr. Brian Reich. Prepared by: Amanda . Muyskens. Outline. Background. Mathematical Considerations. Estimation Details. PRODUCTS. INTRODUCTION. 111 Highland Drive, Putnam, CT 06260, USA (East Office). 2659A Pan American Freeway NE, Albuquerque, NM 87107, USA (West Office). www.spectralproducts.com. SPECTRAL PRODUCTS 2015. Principle Component Analysis. Why Dimensionality Reduction?. It becomes more difficult to extract meaningful conclusions from a data set as data dimensionality increases--------D. L. . Donoho. Curse of dimensionality. One of these things is not like the other…. spectral clustering (a la Ng-Jordan-Weiss). data. similarity graph. edges have weights . w. (. i. ,. j. ). e.g.. the . Laplacian. diagonal matrix . D. Normalized . biotissues. D.A. Loginova. 1,2. , E.A. Sergeeva. 1. , P.D. Agrba. 2. , . and M. Yu. Kirillin. 1. 1 . Institute of Applied Physics RAS, Nizhny Novgorod, Russia. 2 . Lobachevsky. State University of Nizhny Novgorod, Nizhny Novgorod, Russia. Devansh Arpit. Motivation. Abundance of data. Required storage space explodes!. Images. Documents. Videos. Motivation. Speedup Algorithms. Motivation. Dimensionality reduction for noise filtering. Vector Representation. Aayush Mudgal [12008]. Sheallika Singh [12665]. What is Dimensionality Reduction ?. Mapping . of data to lower dimension such . that:. . uninformative variance is . discarded,. . or a subspace where data lives is . John A. Lee, Michel Verleysen, . Chapter4 . 1. Distance Preservation. دانشگاه صنعتي اميرکبير. (. پلي تکنيک تهران). 2. The motivation behind distance preservation is that any . Steven L. Bressler. Cognitive . Neurodynamics. Laboratory. Center for Complex Systems & Brain Sciences. Department of Psychology. Florida . Atantic. University. Overview. Fourier Analysis. Spectral Analysis of the EEG.