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# dm5part5 - University of Florida CISE department Clustering...

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University of Florida CISE department Gator Engineering Clustering Part 5 Dr. Sanjay Ranka Professor Computer and Information Science and Engineering University of Florida, Gainesville

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University of Florida CISE department Gator Engineering Data Mining Sanjay Ranka Fall 2011 SNN Approach to Clustering • Ordinary distance measures have problems – Euclidean distance is less appropriate in high dimensions •Presences are more important than absences – Cosine and Jaccard measure take in to account presences, but do not satisfy the triangle inequality • SNN distance is more appropriate in these cases
University of Florida CISE department Gator Engineering Data Mining Sanjay Ranka Fall 2011 Shared Near Neighbor Graph In the SNN graph, the strength of a link is the number of shared neighbors between documents given that the documents are connected i j i j 4

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University of Florida CISE department Gator Engineering Data Mining Sanjay Ranka Fall 2011 SNN Approach: Density Ordinary density measures have problems Typical Euclidean density is number of points per unit volume As dimensionality increases, density goes to 0 Can estimate the relative density, i.e., probability density, in a region Look at the distance to the k th nearest neighbor, or Look at the number of points within a fixed radius However, since distances become uniform in high dimensions, this does not work well either If we use SNN similarity then we can obtain a more robust definition of density Relatively insensitive to variations in normal density Relatively insensitive to high dimensionality Uniform regions are dense, gradients are not
University of Florida CISE department Gator Engineering Data Mining Sanjay Ranka Fall 2011 SNN Density can identify Core, Border and Noise points • Assume a DBSCAN definition of density Number of points within Eps • Example a) All Points Density b) High SNN Density c) Medium SNN Density d) Low SNN Density

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University of Florida CISE department Gator Engineering Data Mining Sanjay Ranka Fall 2011 ROCK ROCK (RObust Clustering using linKs ) Clustering algorithm for data with categorical and boolean attributes It redefines the distances between points to be the number of shared neighbors whose strength is greater than a given threshold Then uses a hierarchical clustering scheme to cluster the data 1. Obtain a sample of points from the data set 2. Compute the link value for each set of points, i.e., transform the original similarities (computed by the Jaccard coefficient) into similarities that reflect the number of shared neighbors between points 3. Perform an agglomerative hierarchical clustering on the data using the “number of shared neighbors” similarities and the “maximize the shared neighbors” objective function 4. Assign the remaining points to the clusters that have been found
University of Florida CISE department Gator Engineering Data Mining Sanjay Ranka Fall 2011 Creating the SNN Graph 5 Near neighbor graph Shared near neighbor graph

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