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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 ...
These clusters then could be visualized as a two-dimensional "map" such that observations in proximal clusters have more similar values than observations in distal clusters. This can make high-dimensional data easier to visualize and analyze.
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of objects in a set into a configuration of points mapped into an abstract Cartesian space. [1]
It is based on Stochastic Neighbor Embedding originally developed by Geoffrey Hinton and Sam Roweis, [1] where Laurens van der Maaten and Hinton proposed the t-distributed variant. [2] It is a nonlinear dimensionality reduction technique for embedding high-dimensional data for visualization in a low-dimensional space of two or three dimensions ...
which represents the inner product space (see Gramian matrix) of the otherwise intractable feature space. The dual form that arises in the creation of a kernel allows us to mathematically formulate a version of PCA in which we never actually solve the eigenvectors and eigenvalues of the covariance matrix in the Φ ( x ) {\displaystyle \Phi ...
For a clustering example, suppose that five taxa (to ) have been clustered by UPGMA based on a matrix of genetic distances.The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity).
Cubes is a light-weight open source multidimensional modelling and OLAP toolkit for development reporting applications and browsing of aggregated data written in Python programming language released under the MIT License.
An OLAP cube is a multi-dimensional array of data. [1] Online analytical processing (OLAP) [ 2 ] is a computer-based technique of analyzing data to look for insights. The term cube here refers to a multi-dimensional dataset, which is also sometimes called a hypercube if the number of dimensions is greater than three.