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 guality of a clustering method depends on the similarity measure used by the method a its implementation, and Its ability to discover some or all of the hidden patterns 6
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 6
Measure the quality of clustering Dissimilarity/Similarity metric Similarity is expressed in terms of a distance function typically metric: d(,D The definitions of distance functions are usually rather different for interval-scaled boolean categorical ordinal ratio, and vector variables Weights should be associated with different variables based on applications and data semantics Quality of clustering There is usually a separate "quality function that measures the goodness" of a cluster It is hard to define similar enough"or "good enough The answer is typically highly subjective
Measure the Quality of Clustering ◼ Dissimilarity/Similarity metric ◼ Similarity is expressed in terms of a distance function, typically metric: d(i, j) ◼ The definitions of distance functions are usually rather different for interval-scaled, boolean, categorical, ordinal ratio, and vector variables ◼ Weights should be associated with different variables based on applications and data semantics ◼ Quality of clustering: ◼ There is usually a separate “quality” function that measures the “goodness” of a cluster. ◼ It is hard to define “similar enough” or “good enough” ◼ The answer is typically highly subjective 7
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 subspaces(often in high-dimensional clustering 8
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. nonexclusive (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. subspaces (often in high-dimensional clustering) 8
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 the lese 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 Incremental clustering and insensitivity to input order High dimensionalit
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 ◼ Incremental clustering and insensitivity to input order ◼ High dimensionality 9
Major Clustering Approaches o Partitioning approach Construct various partitions and then evaluate them by some criterion, e.g., minimizing the sum of square errors Typical methods: k-means, k-medoids, CLARANS Hierarchical approach Create a hierarchical decomposition of the set of data(or objects using some criterion Typical methods: Diana, Agnes, BIRCH, CAMELEON Density-based approach Based on connectivity and density functions Typical methods: DBSACN, OPTICS, DenClue Grid-based approach based on a multiple- level granularity structure Typical methods: STING, WaveCluster, CLIQUE 10
Major Clustering Approaches (I) ◼ Partitioning approach: ◼ Construct various partitions and then evaluate them by some criterion, e.g., minimizing the sum of square errors ◼ Typical methods: k-means, k-medoids, CLARANS ◼ Hierarchical approach: ◼ Create a hierarchical decomposition of the set of data (or objects) using some criterion ◼ Typical methods: Diana, Agnes, BIRCH, CAMELEON ◼ Density-based approach: ◼ Based on connectivity and density functions ◼ Typical methods: DBSACN, OPTICS, DenClue ◼ Grid-based approach: ◼ based on a multiple-level granularity structure ◼ Typical methods: STING, WaveCluster, CLIQUE 10