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Cluster Analysis: Basic Concepts and Algorithms,[object Object]
What is Cluster Analysis?,[object Object],Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups,[object Object]
Applications of Cluster Analysis ,[object Object],Understanding,[object Object],Group genes and proteins that have similar functionality, or group stocks with similar price fluctuations,[object Object],Summarization,[object Object],Reduce the size of large data sets ,[object Object]
Types of Clustering ,[object Object],A clustering is a set of clusters ,[object Object],     Important distinction between hierarchical and partitional sets of clusters ,[object Object], Partitional Clustering ,[object Object], A division data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset ,[object Object], Hierarchical clustering ,[object Object], A set of nested clusters organized as a hierarchical tree ,[object Object]
Clustering Algorithms,[object Object],K-means ,[object Object],Hierarchical clustering ,[object Object],Graph based clustering ,[object Object]
K-means Clustering ,[object Object],Partitional clustering approach ,[object Object],Each cluster is associated with a centroid (center point) ,[object Object],Each point is assigned to the cluster with the closest centroid,[object Object],Number of clusters, K, must be specified ,[object Object],The basic algorithm is very simple ,[object Object]
K-means Clustering – Details ,[object Object],Initial centroids are often chosen randomly. ,[object Object],Clusters produced vary from one run to another. ,[object Object],The centroid is (typically) the mean of the points in the cluster. ,[object Object],‘Closeness’ is measured by Euclidean distance, cosine similarity, correlation, etc. ,[object Object],K-means will converge for common similarity measures mentioned above,[object Object]
K-means Clustering – Details ,[object Object],Most of the convergence happens in the first few iterations. ,[object Object],Often the stopping condition is changed to ‘Until relatively few points change clusters’ ,[object Object],Complexity is O( n * K * I * d ) ,[object Object],n = number of points, K = number of clusters,  I = number of iterations, d = number of attributes ,[object Object]
Two different K-means Clusterings ,[object Object],Sub-optimal Clustering ,[object Object],Optimal Clustering ,[object Object]
Problems with Selecting Initial Points ,[object Object],If there are K ‘real’ clusters then the chance of selecting one centroid from each cluster is small. ,[object Object],Chance is relatively small when K is large ,[object Object],If clusters are the same size, n, then For example, if K = 10, then probability = 10!/1010 = 0.00036 ,[object Object],Sometimes the initial centroids will readjust themselves in ‘right’ way, and sometimes they don’t ,[object Object],Consider an example of five pairs of clusters ,[object Object]
Solutions to Initial Centroids Problem,[object Object],Multiple runs ,[object Object],Helps, but probability is not on your side ,[object Object], Sample and use hierarchical clustering to determine initial centroids,[object Object], Select more than k initial centroids and then select among these initial centroids,[object Object],Select most widely separated ,[object Object], Bisecting K-means ,[object Object],Not as susceptible to initialization issues ,[object Object]
Evaluating K-means Clusters ,[object Object],Most common measure is Sum of Squared Error (SSE) ,[object Object],For each point, the error is the distance to the nearest cluster ,[object Object],To get SSE, we square these errors and sum them. ,[object Object], x is a data point in cluster Ciand mi is the representative point for cluster Ci,[object Object],can show that micorresponds to the center (mean) of the cluster ,[object Object]
Evaluating K-means Clusters ,[object Object],Given two clusters, we can choose the one with the smaller error ,[object Object],One easy way to reduce SSE is to increase K, the number of clusters ,[object Object],A good clustering with smaller K can have a lower SSE than a poor clustering with higher K ,[object Object]
Limitations of K-means ,[object Object],K-means has problems when clusters are of differing ,[object Object],Sizes ,[object Object],Densities ,[object Object],Non-globular shapes ,[object Object], K-means has problems when the data contains outliers. ,[object Object], The number of clusters (K) is difficult to determine. ,[object Object]
Hierarchical Clustering  ,[object Object],Produces a set of nested clusters organized as a hierarchical tree ,[object Object],Can be visualized as a dendrogram,[object Object],A tree like diagram that records the sequences of merges or splits ,[object Object]
Strengths of Hierarchical Clustering ,[object Object],Do not have to assume any particular number of clusters ,[object Object],Any desired number of clusters can be obtained by ‘cutting’ the dendogram at the proper level ,[object Object], They may correspond to meaningful taxonomies ,[object Object],Example in biological sciences (e.g., animal kingdom, phylogeny reconstruction, …) ,[object Object]
Hierarchical Clustering ,[object Object],Two main types of hierarchical clustering ,[object Object],Agglomerative: ,[object Object],Start with the points as individual clusters ,[object Object],At each step, merge the closest pair of clusters until only one cluster (or k clusters) left ,[object Object],Divisive: ,[object Object],Start with one, all-inclusive cluster ,[object Object],At each step, split a cluster until each cluster contains a point (or there are k clusters) ,[object Object]
Agglomerative Clustering Algorithm ,[object Object],More popular hierarchical clustering technique ,[object Object],Basic algorithm is straightforward ,[object Object],Compute the proximity matrix ,[object Object],Let each data point be a cluster,[object Object],Repeat ,[object Object], Merge the two closest clusters ,[object Object], Update the proximity matrix ,[object Object],Until only a single cluster remains ,[object Object]
Hierarchical Clustering: Group Average ,[object Object],Compromise between Single and Complete Link ,[object Object], Strengths ,[object Object],Less susceptible to noise and outliers ,[object Object], Limitations ,[object Object],Biased towards globular clusters ,[object Object]
Hierarchical Clustering: Time and Space requirements ,[object Object],O(N2) space since it uses the proximity matrix. ,[object Object],N is the number of points. ,[object Object], O(N3) time in many cases ,[object Object],There are N steps and at each step the size, N2, proximity matrix must be updated and searched ,[object Object],Complexity can be reduced to O(N2 log(N) ) time for some approaches ,[object Object]
Hierarchical Clustering: Problems and Limitations ,[object Object],Once a decision is made to combine two clusters, it cannot be undone No objective function is directly minimized ,[object Object],Different schemes have problems with one or more of the following: ,[object Object],Sensitivity to noise and outliers (MIN) ,[object Object],Difficulty handling different sized clusters and non-convex shapes (Group average, MAX) ,[object Object],Breaking large clusters (MAX) ,[object Object]
conclusion,[object Object],The purpose of clustering in data mining and its types are discussed.,[object Object],The k-means and hierarchical algorithm are explained in detail and their pros and cons are analyzed.,[object Object]
Visit more self help tutorials,[object Object],Pick a tutorial of your choice and browse through it at your own pace.,[object Object],The tutorials section is free, self-guiding and will not involve any additional support.,[object Object],Visit us at www.dataminingtools.net,[object Object]

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