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Under the assumptions of balance theory, edges may change sign and result in a bifurcated graph.

Signed graph models: Every path in a signed graph has a sign from the product of the signs on the edges.

Relaxations of the complete connectivity requirement (a fraction of the edges can be missing) are known as quasi-cliques, as in the HCS clustering algorithm.

Graph-based models: a clique, that is, a subset of nodes in a graph such that every two nodes in the subset are connected by an edge can be considered as a prototypical form of cluster.Group models: some algorithms do not provide a refined model for their results and just provide the grouping information.Subspace models: in biclustering (also known as co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes.Density models: for example, DBSCAN and OPTICS defines clusters as connected dense regions in the data space.Distribution models: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the expectation-maximization algorithm.Centroid models: for example, the k-means algorithm represents each cluster by a single mean vector.Connectivity models: for example, hierarchical clustering builds models based on distance connectivity.Understanding these "cluster models" is key to understanding the differences between the various algorithms.

The notion of a cluster, as found by different algorithms, varies significantly in its properties. However, different researchers employ different cluster models, and for each of these cluster models again different algorithms can be given. There is a common denominator: a group of data objects. The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms.

5.2 Techniques used in cluster analysis.

5.1 Specialized types of cluster analysis.

4.1 Biology, computational biology and bioinformatics.

2.1 Connectivity-based clustering (hierarchical clustering).

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The subtle differences are often in the use of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest.Ĭluster analysis was originated in anthropology by Driver and Kroeber in 1932 and introduced to psychology by Joseph Zubin in 1938 and Robert Tryon in 1939 and famously used by Cattell beginning in 1943 for trait theory classification in personality psychology. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.īesides the term clustering, there are a number of terms with similar meanings, including automatic classification, numerical taxonomy, botryology (from Greek βότρυς "grape"), typological analysis, and community detection.

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Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery or interactive multi-objective optimization that involves trial and failure. The appropriate clustering algorithm and parameter settings (including parameters such as the distance function to use, a density threshold or the number of expected clusters) depend on the individual data set and intended use of the results. Clustering can therefore be formulated as a multi-objective optimization problem. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions.

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It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning.Ĭluster analysis itself is not one specific algorithm, but the general task to be solved. The result of a cluster analysis shown as the coloring of the squares into three clusters.Ĭluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters).