|
Model-based Clustering
In statistics, cluster analysis is the algorithmic grouping of objects into homogeneous groups based on numerical measurements. Model-based clustering based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not belong to any group. Model-based clustering Suppose that for each of n observations we have data on d variables, denoted by y_i = (y_,\ldots,y_) for observation i. Then model-based clustering expresses the probability density function of y_i as a finite mixture, or weighted average of G component probability density functions: :p(y_i) = \sum_^G \tau_g f_g (y_i \mid \theta_g), where f_g is a probability density function with parameter \theta_g, \tau_g is the corresponding mixture probability where \sum_^G \tau_g = 1. Then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Eigendecomposition Of A Matrix
In linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. Fundamental theory of matrix eigenvectors and eigenvalues A (nonzero) vector of dimension is an eigenvector of a square matrix if it satisfies a linear equation of the form \mathbf \mathbf = \lambda \mathbf for some scalar . Then is called the eigenvalue corresponding to . Geometrically speaking, the eigenvectors of are the vectors that merely elongates or shrinks, and the amount that they elongate/shrink by is the eigenvalue. The above equation is called the eigenvalue equation or the eigenvalue problem. This yields an equation for the eigenvalues p\left(\lambda\right) = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cluster Analysis
Cluster analysis or clustering is the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more Similarity measure, 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 statistics, statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Cluster analysis refers to a family of algorithms and tasks rather than one specific algorithm. It 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 Distance function, distances between cluster members, dense areas of the data space, intervals or pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
John H
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Paul Lazarsfeld
Paul Felix Lazarsfeld (February 13, 1901August 30, 1976) was an Austrian-American sociologist and mathematician. The founder of Columbia University's Bureau of Applied Social Research, he exerted influence over the techniques and the organization of social research. "It is not so much that he was an American sociologist," one colleague said of him after his death, "as it was that he determined what American sociology would be." Lazarsfeld said that his goal was "to produce Paul Lazarsfelds". He was a founding figure in 20th-century empirical sociology. Early life Lazarsfeld was born to Jewish parents in Vienna: his mother was the Adlerian therapist Sophie Lazarsfeld, and his father Robert was a lawyer. He attended the University of Vienna, eventually receiving a doctorate in mathematics (his doctoral dissertation dealt with mathematical aspects of Einstein's gravitational theory) in 1925. In the 1920s, he moved in the same circles as the Vienna Circle of philosophers, inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
R Package
R packages are extensions to the R statistical programming language. R packages contain code, data, and documentation in a standardised collection format that can be installed by users of R, typically via a centralised software repository such as CRAN (the Comprehensive R Archive Network). The large number of packages available for R, and the ease of installing and using them, has been cited as a major factor driving the widespread adoption of the language in data science. Compared to libraries in other programming languages, R packages must conform to a relatively strict specification. The ''Writing R Extensions'' manual specifies a standard directory structure for R source code, data, documentation, and package metadata, which enables them to be installed and loaded using R's in-built package management tools. Packages distributed on CRAN must meet additional standards. According to John Chambers, whilst these requirements "impose considerable demands" on package developers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Latent Class Model
In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data. It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent. It is called a latent class model because the class to which each data point belongs is unobserved, or latent. Latent class analysis (LCA) is a subset of structural equation modeling, used to find groups or subtypes of cases in multivariate categorical data. These subtypes are called "latent classes".Lazarsfeld, P.F. and Henry, N.W. (1968) ''Latent structure analysis''. Boston: Houghton Mifflin Confronted with a situation as follows, a researcher might choose to use LCA to understand the data: Imagine that symptoms a-d have been measured in a range of patients with diseases X, Y, and Z, and that disease X is associated with the presence of symptoms a, b, and c, disease Y with symptoms b, c, d, and disease Z with symptoms a, c and d. The LCA will attempt to detect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust statistics, robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Complete-linkage Clustering
Complete-linkage clustering is one of several methods of agglomerative hierarchical clustering. At the beginning of the process, each element is in a cluster of its own. The clusters are then sequentially combined into larger clusters until all elements end up being in the same cluster. The method is also known as farthest neighbour clustering. The result of the clustering can be visualized as a dendrogram, which shows the sequence of cluster fusion and the distance at which each fusion took place. Clustering procedure At each step, the two clusters separated by the shortest distance are combined. The definition of 'shortest distance' is what differentiates between the different agglomerative clustering methods. In complete-linkage clustering, the link between two clusters contains all element pairs, and the distance between clusters equals the distance between those two elements (one in each cluster) that are farthest away from each other. The shortest of these links that rem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Single-linkage Clustering
In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other. This method tends to produce long thin clusters in which nearby elements of the same cluster have small distances, but elements at opposite ends of a cluster may be much farther from each other than two elements of other clusters. For some classes of data, this may lead to difficulties in defining classes that could usefully subdivide the data. However, it is popular in astronomy for analyzing galaxy clusters, which may often involve long strings of matter; in this application, it is also known as the friends-of-friends algorithm. Overview of agglomerative clustering methods In the beginning of the agglomerative clustering process, each element is in a cluster of its own. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
