Discrete Maths Nots for stdents, Summaries of Mathematics

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CLUSTERING

MODULE 4

AMEYAA BIWALKAR

Topics to be Covered

Clustering for Data Understanding and Applications  (^) Biology: taxonomy of living things: kingdom, phylum, class, order, family, genus and species  (^) Information retrieval: document clustering  (^) Land use: Identification of areas of similar land use in an earth observation database  (^) Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs  (^) City-planning: Identifying groups of houses according to their house type, value, and geographical location  (^) Earth-quake studies: Observed earth quake epicenters should be clustered along continent faults  (^) Climate: understanding earth climate, find patterns of atmospheric and ocean  (^) Economic Science: market research

Quality: What Is Good Clustering?  A good clustering method will produce high quality clusters  (^) high intra-class similarity: cohesive within clusters  (^) low inter-class similarity: distinctive between clusters  (^) The quality of a clustering method depends on  (^) the similarity measure used by the method  (^) its implementation, and  (^) Its ability to discover some or all of the hidden patterns

Considerations for Cluster Analysis  (^) Partitioning criteria  (^) Single level vs. hierarchical partitioning (often, multi-level hierarchical partitioning is desirable)  (^) Separation of clusters  (^) Exclusive (e.g., one customer belongs to only one region) vs. non-exclusive (e.g., one document may belong to more than one class)  (^) Similarity measure  (^) Distance-based (e.g., Euclidian, road network, vector) vs. connectivity-based (e.g., density or contiguity)  (^) Clustering space  (^) Full space (often when low dimensional) vs.

Requirements and Challenges  (^) Scalability  (^) Clustering all the data instead of only on samples  (^) Ability to deal with different types of attributes  (^) Numerical, binary, categorical, ordinal, linked, and mixture of these  (^) Constraint-based clustering  User may give inputs on constraints  Use domain knowledge to determine input parameters  (^) Interpretability and usability  (^) Others  (^) Discovery of clusters with arbitrary shape  (^) Ability to deal with noisy data

Major Clustering Approaches (II)  (^) Model-based:  (^) A model is hypothesized for each of the clusters and tries to find the best fit of that model to each other  (^) Typical methods: EM, SOM, COBWEB  (^) Frequent pattern-based:  (^) Based on the analysis of frequent patterns  (^) Typical methods: p-Cluster  (^) User-guided or constraint-based:  (^) Clustering by considering user-specified or application- specific constraints  (^) Typical methods: COD (obstacles), constrained clustering  (^) Link-based clustering:  (^) Objects are often linked together in various ways  (^) Massive links can be used to cluster objects: SimRank,

Partitioning Algorithms: Basic Concept  (^) Partitioning method: Partitioning a database D of n objects into a set of k clusters, such that the sum of squared distances is minimized (where ci is the centroid or medoid of cluster Ci)  (^) Given k , find a partition of k clusters that optimizes the chosen partitioning criterion  (^) Global optimal: exhaustively enumerate all partitions  (^) Heuristic methods: k-means and k-medoids algorithms  (^) k-means : Each cluster is represented by the center of the cluster  (^) k-medoids or PAM (Partition around medoids): Each 2 1 ( ) p C i k i E p c i     

An Example of K-Means Clustering K= Arbitrarily partition objects into k groups Update the cluster centroids Update the cluster centroids Reassign objects Loop if needed The initial data set  (^) Partition objects into k nonempty subsets  (^) Repeat  (^) Compute centroid (i.e., mean point) for each partition  (^) Assign each object to the cluster of its nearest centroid  (^) Until no change

ELBOW METHOD-TO FIND BEST K (SUM OF SQUARED ERROR)