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... If we have manifold information, we can perform compressive sensing using significantly fewer measurements. Whitney s Embedding Theorem: ...

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Dimensionality Reduction

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Dimensionality Reduction Multimedia DBs Many multimedia applications require efficient indexing in high-dimensions (time-series, images and videos, etc) Answering ...

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Feature extraction: create new features by combining new ones ... x=(x1,...,xd), d independent Gaussian N(0,1) random variables; y = 1/|x|(x1,...,xd) ...

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GEMINI ... GEMINI framework. PCA ... di(a,b) = sign(di(a,b)) (| di(a,b) |2)1/2. where, di(a,b) = di-1(a,b)2 (xia-xbi)2 ...

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Best performing methods are GPFS and ARD which usually find the optimal subset. However the GPFS method is on average more than three times slower than ARD. ...

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any (sufficiently large) set S of M points in Rn. k = O(e-2lnM) There exists a linear map f:S Rk, such that ... 'Database friendly' RP ...

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Dimensionality Reduction and Embeddings

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Intuition: find the axis that shows the greatest variation, and project all points to this axis ... ATAvi = sivi , viTvi = 1, viTvj = 0 for i j. ...

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SVD decomposition, Discrete Fourier transform, and Discrete Cosine transform. Wavelets ... SVD decomposition - the Karhunen-Loeve transform ...

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FACE RECOGNITION, EXPERIMENTS WITH RANDOM PROJECTION. Navin Goel ... Eccentricity ... subspace of 50-dimension and eccentricity 1,000 is projected onto ...

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Embedding. An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic ...

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( ) Nonlinear Dimensionality Reduction Nonlinear Dimensionality Reduction , John A. Lee, Michel ...

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Dimensionality Reduction for Data Mining - Techniques, Applications and Trends Lei Yu Binghamton University Jieping Ye, Huan Liu Arizona State University

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[3] Misha Belkin and Partha Niyogi, 'Laplacian eigenmaps for dimensionality ... Application: Wireless Motion Detection Sensor Net ...

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E.g., to round max-cut, just pick a random hyperplane ... Pick a random hyperplane. See if it is any good. ... chance a random hyperplane will be a weak ...

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Random Projection for High Dimensional Data Clustering: A Cluster Ensemble Approach Xiaoli Zhang Fern, Carla E. Brodley ICML 2003 Presented by Dehong Liu

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... Dimensionality Reduction with Fuzzy Integral and Applications. Speaker: Wang ... The Choquet integral is based on linear operators to deal ... integral to ...

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Statistical analysis of array data: Dimensionality reduction, ... If clusters centroids are stabile or some other stopping criteria is achieved, stop algorithm. ...

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Data consists of 2,340 documents in 20 Yahoo news categories. ... Revised Yahoo News Categories. 60. Technology. 141. Sports. 114. Politics. 494. Health. 1,389 ...

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We get much better global organization if we use annealing. ... Anneal the perplexity. ... It does not require simulated annealing. ...

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Dimensionality reduction: Some Assumptions High-dimensional data often lies on or near a much lower dimensional, curved manifold. A good way to represent data points ...

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Title: Diffusion Maps and Spectral Clustering Last modified by: Xiang Created Date: 6/1/2006 6:13:16 PM Document presentation format: On-screen Show (4:3)

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Face Recognition Using Dimensionality Reduction. M. Turk, A. Pentland, 'Eigenfaces for ... LDA is then applied to find the most discriminative directions: 44 ...

Dimension Reduction in the Hamming Cube (and its Applications) Rafail Ostrovsky UCLA (joint works with Rabani; and Kushilevitz and Rabani)

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PCA discovered the map of the lab. Problems and limitations. What if very large dimensional data? ... A = U L VT - example: data. inf. retrieval. brain. lung ...

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Data Quality Follow Discussions of Ch. 2 of the Textbook Aggregation Sampling Dimensionality Reduction Feature subset selection Feature creation Discretization and ...

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Jon. Alice. Bob. Eve. Panconesi. Kate. Fred. A.Panconesi ? Geometric formulation ... To estimate hamming distance between X and Y (within (1 e)) with small CC, ...

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Xiaoli Zhang Fern, Carla E. Brodley. ICML'2003. Presented by Dehong Liu. Contents. Motivation ... The presence of irrelevant and noisy features can mislead the ...

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University of California, Berkeley. Joint work with Kenji Fukumizu and Francis Bach ... Principal Hessian Directions (pHd, Li 1992) Average Hessian is used ...

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NONLINEAR DATA DRIVEN MODEL REDUCTION TECHNIQUES FOR STOCHASTIC PDE SYSTEMS

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Most of the scientific or industrial data is Multivariate data ... Protein1. Protein 2. Proteins 1 and 2 measured for 200 patients. Motivation. Genes. 1. 22,000 ...

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Random projection theorem: http://citeseer.nj.nec.com/dasgupta99elementary.html. Faster random projection: http://citeseer.nj.nec.com/frieze98fast.html ...

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CS 361A (Advanced Data Structures and Algorithms) Lecture 19 (Dec 5, 2005) Nearest Neighbors: Dimensionality Reduction and Locality-Sensitive Hashing

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How classification accuracy depends on the dimensionality ... Data points: parabola Gaussian noise. 10th-degree polynomial perfectly fits the given data ...

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A NONLINEAR DIMENSION REDUCTION STRATEGY FOR GENERATING DATA DRIVEN STOCHASTIC INPUT MODELS

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[A Global Geometric Framework for Nonlinear Dimensionality Reduction. ... Laplacian Eigenmaps [Belkin 03] many other approaches. self-organizing maps [Kohonen 95] ...

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Generate s in small (logN) space using pseudo-random generators ... Key Intuition: Use randomized linear projections of f() to define random variable X such that ...

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Python full coding from scratch Visualization with Python Statistics - theory and application in business Machine Learning with Python - 6 different algorithms Multiple Linear regression Logistic regression Variable Reduction Technique - Information Value Forecasting - ARIMA Cluster Analysis Decision Tree Random Forest Case studies on Machine Learning (18 case studies) SQL queries(with Python) Business Presentation of Technical Solution in-front of end client. Robotic Automation(with Python) CV Building activities Interview preparation Mock Interview sessions

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Last lecture Statistical sampling and Monte Carlo integration Today Variance reduction Importance sampling Stratified sampling Multidimensional sampling patterns

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Fractal Tours. Winding Curve ... 3 - Travel along a geodesic path between these two projection. 4 - Repeat ... on a fractal tour through a hypercube. Projection ...

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Multiple-walker random walk ... Path replication: store the object along the path of a successful 'walk' ... Multi-walker random walk scales much better than flooding ...

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... perform scenario analysis Develop and deliver analytics in software and systems Develop ... for the cost of ... Carlo variance reduction ...

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Curse of dimensionality width x height x channels. Noise reduction ... Measuring nongaussianity by Kurtosis. Kurtosis : 4th order cumulant of randomvariable ...

The Curse of Dimensionality 1st Aspect. The number of training samples ... Curse of Dimensionality 2nd Aspect. Accuracy and overfitting ...

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'Visual' Properties. 5) Random Field Models. 6) Other Representation. Example Query Input ... visual properties representation ...

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optimization vs. risk measurement, model-simulation approach, random-matrix ... Perron) eigenvalue, with the corresponding eigenvector having all positive components. ...

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Reduction of characteristic dimension - nano-biotechnology, ... charges moving along spiralling path. NANOFIBRES, CDMM2005, Warsaw, Poland. Electro-spinning ...

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Statistical Pattern Recognition: A Review Contents Introduction Statistical Pattern Recognition The Curse of Dimensionality & Peaking Phenomena ...

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Workshop in Bioinformatics. Eran Halperin. The Human Genome Project ' ... Results: Manhattan Plots. The curse of dimensionality corrections of multiple testing ...

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Data Mining Lectures Lecture 5: Dimension Reduction Padhraic Smyth, UC Irvine ... Scree diagrams. Computational complexity of computing PCA ...

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Title: FPGA Power Reduction Using Configurable Dual-Vdd Author: Fei Li Last modified by: EDA Created Date: 12/26/2003 11:10:25 PM Document presentation format

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Random Variables Random Processes (that can be described by a probability ... Preliminary Synopsis on Survey of Curricula on Stochastic Theory in the Nation ...

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Motivation: Noise reduction in nuclear medicine ... Fully 4D reconstruction for dynamic PET using KL (1997) ... Percent correctly classified ...

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The scree test suggests a single component is required, but several additional ... This approach also produces the expected random signature in the scree plot. ...

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