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24 relations: Adjacency matrix, Affinity propagation, Cluster analysis, Community structure, Condition number, Conductance (graph), Dimensionality reduction, Eigenvalues and eigenvectors, Hierarchical clustering, Image segmentation, Kernel principal component analysis, Lanczos algorithm, Laplacian matrix, LOBPCG, Matrix-free methods, Multivariate statistics, Nonlinear dimensionality reduction, Power iteration, R (programming language), Scikit-learn, Segmentation-based object categorization, Similarity measure, Spectral graph theory, Spectrum of a matrix.
Adjacency matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph.
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Affinity propagation
In statistics and data mining, affinity propagation (AP) is a clustering algorithm based on the concept of "message passing" between data points.
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Cluster analysis
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 sense) to each other than to those in other groups (clusters).
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Community structure
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping) sets of nodes such that each set of nodes is densely connected internally.
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Condition number
In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.
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Conductance (graph)
In graph theory the conductance of a graph G.
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Dimensionality reduction
In statistics, machine learning, and information theory, dimensionality reduction or dimension reduction is the process of reducing the number of random variables under consideration by obtaining a set of principal variables.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Hierarchical clustering
In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters.
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Image segmentation
In computer vision, image segmentation is the process of partitioning a digital image into multiple segments (sets of pixels, also known as super-pixels).
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Kernel principal component analysis
In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods.
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Lanczos algorithm
The Lanczos algorithm is a direct algorithm devised by Cornelius Lanczos that is an adaptation of power methods to find the m most useful eigenvalues and eigenvectors of an n \times n Hermitian matrix, where m is often but not necessarily much smaller than n. Although computationally efficient in principle, the method as initially formulated was not useful, due to its numerical instability.
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Laplacian matrix
In the mathematical field of graph theory, the Laplacian matrix, sometimes called admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph.
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LOBPCG
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem for a given pair (A, B) of complex Hermitian or real symmetric matrices, where the matrix B is also assumed positive-definite.
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Matrix-free methods
In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products.
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Multivariate statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
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Nonlinear dimensionality reduction
High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret.
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Power iteration
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A, the algorithm will produce a number \lambda, which is the greatest (in absolute value) eigenvalue of A, and a nonzero vector v, the corresponding eigenvector of \lambda, such that Av.
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R (programming language)
R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.
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Scikit-learn
Scikit-learn (formerly scikits.learn) is a free software machine learning library for the Python programming language.
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Segmentation-based object categorization
The image segmentation problem is concerned with partitioning an image into multiple regions according to some homogeneity criterion.
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Similarity measure
In statistics and related fields, a similarity measure or similarity function is a real-valued function that quantifies the similarity between two objects.
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Spectral graph theory
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix.
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Spectrum of a matrix
In mathematics, the spectrum of a matrix is the set of its eigenvalues.
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References
[1] https://en.wikipedia.org/wiki/Spectral_clustering
