Discourse Segmentation. Ling575 Discourse and Dialogue April 20, 2011. Roadmap. Project updates and milestones Automatic Discourse Segmentation Linear Segmentation Unsupervised techniques Supervised techniques Segmentation evaluation Discourse Parsing Discourse R elation Extraction

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Dimensionality reduction. Outline. From distances to points : MultiDimensional Scaling (MDS) Dimensionality Reductions or data projections Random projections Singular Value Decomposition and Principal Component Analysis (PCA). Multi-Dimensional Scaling (MDS).

Dimensionality Reduction. Given N vectors in n dims, find the k most important axes to project them k is user defined ( k < n ) Applications : information retrieval & indexing identify the k most important features or

Dimensionality reduction. Outline. From distances to points : MultiDimensional Scaling (MDS ) FastMap Dimensionality Reductions or data projections Random projections Principal Component Analysis (PCA ). Multi-Dimensional Scaling (MDS).

Dimensionality reduction. Usman Roshan CS 698 Fall 2013. Dimensionality reduction. What is dimensionality reduction? Compress high dimensional data into lower dimensions How do we achieve this?

Dimensionality reduction. Usman Roshan. Dimensionality reduction. What is dimensionality reduction? Compress high dimensional data into lower dimensions How do we achieve this?

Dimensionality Reduction. Multimedia DBs. Many multimedia applications require efficient indexing in high-dimensions (time-series, images and videos, etc) Answering similarity queries in high-dimensions is a difficult problem due to “curse of dimensionality”

Dimensionality Reduction. Random Projections. Johnson-Lindenstrauss lemma For: 0< e < 1/2, any (sufficiently large) set S of M points in R n k = O( e -2 lnM) There exists a linear map f: S R k , such that (1- e ) ||u-v|| 2 ≤ ||f(u)-f(v)|| 2 ≤ (1+ e )||u-v|| 2 for u,v in S

Dimensionality Reduction. Dimensionality Reduction. High-dimensional == many features Find concepts/topics/genres: Documents: Features: Thousands of words, millions of word pairs Surveys – Netflix: 480k users x 177k movies. Dimensionality Reduction. Compress / reduce dimensionality: