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Cluster 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 specific sense defined by the analyst) to each other than to those in other groups (clusters).
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation [1] [2] is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting ...
Automatic clustering algorithms are algorithms that can perform clustering without prior knowledge of data sets. In contrast with other cluster analysis techniques, automatic clustering algorithms can determine the optimal number of clusters even in the presence of noise and outlier points. [1] [needs context]
The cluster algebra also comes with the extra structure of the seeds of this graph. A cluster algebra is said to be of finite type if it has only a finite number of seeds. Fomin & Zelevinsky (2003) showed that the cluster algebras of finite type can be classified in terms of the Dynkin diagrams of finite-dimensional simple Lie algebras.
The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of () and requires () memory, which makes it too slow for even medium data sets. . However, for some special cases, optimal efficient agglomerative methods (of complexity ()) are known: SLINK [2] for single-linkage and CLINK [3] for complete-linkage clusteri
For example, in Gaussian radial basis function, it determines the dot product of the inputs in a higher-dimensional space, called feature space. It is believed that the data become more linearly separable in the feature space, and hence, linear algorithms can be applied on the data with a higher success.
In the theory of cluster analysis, the nearest-neighbor chain algorithm is an algorithm that can speed up several methods for agglomerative hierarchical clustering.These are methods that take a collection of points as input, and create a hierarchy of clusters of points by repeatedly merging pairs of smaller clusters to form larger clusters.
Ordered linear probing [13] (often referred to as Robin Hood hashing [14]) is a technique for reducing the effects of primary clustering on queries. Ordered linear probing sorts the elements within each run by their hash. Thus, a query can terminate as soon as it encounters any element whose hash is larger than that of the element being queried.