#### Transcript PP140-141

Data Mining Technology Chapter 12 Clustering: Large Databases Written by Farial Shahnaz Presented by Zhao Xinyou 5/29/2008AI Lab @ UEC in Japan Contents Introduction Idea for there major approaches for scalable clustering {Divide-and-Conquer, Incremental, Parallel} There approaches for scalable clustering { BIRCH, DSBCAN, CURE} Application Introduction –Common method PP133 Common method for clustering: visit all data from database and analyze the data, just like: huge, huge number millions Time: Computational Complexities: O(n*n). Memory: Need to load all data to main memory Time/ Memory Data PP134 Motivation—Clustering for large database Time/ Memory Data Method ??? f(x): O(n*n). Time/ Memory Data f(x): O(n). PP134 Requirement—Clustering for large database Time/ Memory No more (preferably less) than one scan of the database. Process each [record] only once With limited memory Data Method ??? f(x): O(n*n). Can suspend, stop, and resume Can update the results when new data inserted or removed Can perform different technology to scan the database During execution, method should provide status and ‘best’ answer. Time/ Memory Data f(x): O(n). PP135 Major approach for scalable clustering Divide-and-Conquer approach Parallel clustering approach Incremental clustering approach Divide-and Conquer approach PP135 9*9 数独 Definition. Divide-and-conquer is a problem-solving approach in which we: divide the problem into sub-problems, recursively conquer or solve each sub-problem, and then combine the sub-problem solutions to obtain a solution to the original problem. Key Assumptions 1.Problem solutions can be constructed using subproblem solutions. 2.Subproblem solutions are independent of one another. Parallel clustering approach PP136-137 Idea: Divide data into small set and then run small set on different machine (Come from Divide-and-Conquer) Explanation about Divide-and-Conquer Divide Pi P1 n/p P0 n/p Divide is some algorithms Conquer is some algorithms n/p Conquer K kp clusters clusters Merging K clusters Record: n Aim: k cluster P0 n/p K clusters n/p Divide Conquer K clusters K Conquer clusters P1 Merging Pi n/p Conquer K clusters kp clusters K clusters Application Sorting: quick-sort and merge sort Fast Fourier transforms Tower of Hanoi puzzle matrix multiplication ….. PP135 CURE- Divide-and-Conquer PP140-141 1.Get the size n of set D and partition D into p group (contain n/p elements) 2.To each group pi, clustered into k groups by using Heap and k-d tree 3.delete some no relationship node in Heap and k-d tree 4. Cluster the partial clusters and get the final cluster Heap PP140-141 PP140-141 k-D Tree Technically, the letter k refers to the number of dimensions 3-dimensional kd-tree K-D Tree PP140-141 CURE- Divide-and-Conquer Nearest Merge Merge Nearest PP140-141 Incremental clustering approach PP135-136 Idea: scan all data in database, Compare with the existing clusters, if find similar cluster, assign it to with cluster, or else, create a new cluster. Go on till no data Steps: 1. S={};//set cluster = NULL 2. do{ 3. read one record d; 4. r = find_simiarity_cluster(d, S); 5. if (r exists) 6. assign d to the cluster r 6. else 7. Add_cluster(d, S); 8. } untill (no record in database); Application--Incremental clustering approach BIRCH Balanced Iterative Reducing and Clustering using Hierarchies DBSCAN Density-Based Spatial Clustering of Application with Noise PP137-138 BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies ) Based on distance measurement, compute the similarity between record and cluster and give the clusters. Inner Cluster Among Cluster PP137-138 BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies ) Inner Cluster Among Cluster Related Definiation Cluster: {xi}, where i = 1, 2, …, N CF(Clustering Feature)：is a triple, (N,LS,SS)，N：number of data；LS：linear sum of N data ； SS：Square sum Related Definiation CF tree = (B,T), B = (CFi, childi), if is internal node in a cluster B = (CFi, prev, next) if is external or leaf node in a cluster. T: threshold for all leaf node, which should satisfy mean distance D < T Algorithm for BIRCH DBSCAN DBSCAN: Density-Based Spatial Clustering of Application with Noise Ex1: We want to class house along with river from one spatial photo Ex2: Definition for DBSCAN Eps-neighborhood of a point The Eps-neighborhood of a point p, denoted by NEps(p), is defined by NEps(p)={q∈D|dist(p,q) ≤ Eps} Minimum Number (MinPts) The MinPts is the minimum number of data points in any cluster. Definition for DBSCAN Directly density-reachable A point p is directly density-reachable from a point q. Eps and MinPts if 1): p ∈ NEps(q); 2): |NEps(q)|≥MinPts; Definition for DBSCAN Density-reachable A point p is density-reachable from a point q. Eps and MinPts if there is a chain of points p1,p2,…,pn,p=p1,q=pn such as pi+1 is directly desity-reachable from pi; Definition for DBSCAN Density-reachable A point p is density-reachable from a point q. Eps and MinPts if there is a chain of points p1,p2,…,pn,p=p1,q=pn such as pi+1 is directly desity-reachable from pi; Algorithm of DBSCAN Input D={t1,t2,…,tn} MinPts Eps Output K=K1,K2,…Kk k = 0; for i =1 to n do if ti is not in a cluster then X={ti| tj is density-reachable from ti} end if if X is a valid cluster then k= k+1; Kk = X; end if end for