Random Projection Dimensionality Reduction PowerPoint PPT Presentations

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

Dimensionality Reduction

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

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) ...

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 ...

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. ...

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. ...

Dimensionality Reduction and Embeddings

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

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

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

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 ...

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

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 ...

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

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

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

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

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 ...

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

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 ...

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)

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

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, ...

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

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

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

NONLINEAR DATA DRIVEN MODEL REDUCTION TECHNIQUES FOR STOCHASTIC PDE SYSTEMS

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

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 ...

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

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

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

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

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 ...

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

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

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

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

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 ...

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

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

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

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

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

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

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

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

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

Intelligent Data Analysis with different methods such as ... crisp. uncertain. single-valued. set-valued. relational. probabilistic. random sets. possibilistic ...

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

RANSAC (line fitting) Variant of generate-and-test. Pick a small set of points at random. Fit them via least squares. Points 'far' from this line are outliers ...

evdb@research.telcordia.com. An SAIC Company. SRS PI Meeting, ... Anomaly detection systems: Few streams for correlation, suffer from curse of dimensionality ...

Department of Computing Science, University of Glasgow. October, 21th - 2002 ... Qualitative part: Directed Acyclic Graph. G=(V,E): V (Nodes) Random variables, and ...

Vines- Provide useful graphical interpretations of the conditional ... Tim Bedford and Roger Cooke, Vines- A New Graphical Model for Dependent Random Variables, 2002 ...