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Clustering high-dimensional data is the cluster analysis of data with anywhere from a few dozen to many thousands of dimensions.Such high-dimensional spaces of data are often encountered in areas such as medicine, where DNA microarray technology can produce many measurements at once, and the clustering of text documents, where, if a word-frequency vector is used, the number of dimensions ...
This led to new clustering algorithms for high-dimensional data that focus on subspace clustering (where only some attributes are used, and cluster models include the relevant attributes for the cluster) and correlation clustering that also looks for arbitrary rotated ("correlated") subspace clusters that can be modeled by giving a correlation ...
Various extensions to the DBSCAN algorithm have been proposed, including methods for parallelization, parameter estimation, and support for uncertain data. The basic idea has been extended to hierarchical clustering by the OPTICS algorithm. DBSCAN is also used as part of subspace clustering algorithms like PreDeCon and SUBCLU.
Biclustering, block clustering, [1] [2] Co-clustering or two-mode clustering [3] [4] [5] is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix. The term was first introduced by Boris Mirkin [ 6 ] to name a technique introduced many years earlier, [ 6 ] in 1972, by John A. Hartigan .
A number of approaches have been provided which include Principle Angles Configuration (PAC) [19] and Sparse Subspace Clustering (SSC) [20] methods. These work well in two or three motion cases. These algorithms are also robust to noise with a tradeoff with speed, i.e. they are less sensitive to noise but slow in computation.
In machine learning, Vidal has made many contributions to subspace clustering, [16] including his work on Generalized Principal Component Analysis (GPCA), [17] Sparse Subspace Clustering (SSC) [2] and Low Rank Subspace Clustering (LRSC). [18] Much of his work in machine learning is summarized in his book Generalized Principal Component Analysis ...
The outcome of the Rayleigh–Ritz method is determined by the subspace spanned by all columns of matrices ,, and , where a basis of the subspace can theoretically be arbitrary. However, in inexact computer arithmetic the Rayleigh–Ritz method becomes numerically unstable if some of the basis vectors are approximately linearly dependent.
In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data.