Clustering
I want to go through the Wikipedia series on Machine Learning and Data mining. Data mining is the process of extracting and discovering patterns in large data sets involving methods at the intersection of machine learning, statistics, and database systems.
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Cluster analysis or clustering is the task of grouping a set of object sin such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters).
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, and machine learning.
Cluster analysis refers to a family of algorithms and tasks rather than one specific algorithm.
Cluster analysis can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The appropriate clustering algorithm and parameter settings depend on the individual data set and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery on interactive multi-objective optimization that involves trial and failure. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.
Typical cluster models include:
- connectivity models: for example, hierarchal clustering builds models based on distance connectivity
- centroid models: for example, the k-means algorithm represents each cluster by a single mean vector
- Distribution models: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the expectation-maximization algorithm
- Density models: for example DBSCAN and OPTICS defines clusters as connected dense regions in the data space
- Subspace models: in biclustering, clusters are modeled with both cluster members and relevant attributes
- Group models: some algorithms do not provide a refined model for their results and just provide the grouping information
- 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 prototypical form of a cluster., 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
- Signed graph models: Every path in signed graph has a sign from the product of the signs on the edges. Under the assumptions of balance theory, edges may change sign and result in a bifurcated graph. The weaker
cluster axiom
yields results with more than two clusters, or subgraphs with only positive edges - Neural models: the most well known unsupervised neural network is the self-organizing map and these models can usually be characterized as similar to one or more of the above models, and including subspace models when neural networks implement principal component analysis or independent component analysis
A clustering
is essentially a set of such clusters, usually containing all objects in the data set. Additionally, it may specify the relationship of the clusters to each other, for example, a hierarchy of clusters embedded in each other. Clustering can be roughly distinguished as:
- Hard clustering: each object belongs to the cluster or not
- Soft clustering: each object belongs to each cluster to a certain degree (for example, a likelihood of belonging to the cluster)
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