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K-medians Clustering
In statistics, ''k''-medians clusteringP. S. Bradley, O. L. Mangasarian, and W. N. Street, "Clustering via Concave Minimization," in Advances in Neural Information Processing Systems, vol. 9, M. C. Mozer, M. I. Jordan, and T. Petsche, Eds. Cambridge, Massachusetts: MIT Press, 1997, pp. 368–374. is a cluster analysis algorithm. It is a variation of ''k''-means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median. This has the effect of minimizing error over all clusters with respect to the 1-norm distance metric, as opposed to the squared 2-norm distance metric (which ''k''-means does.) This relates directly to the ''k''-median problem with respect to the 1-norm, which is the problem of finding ''k'' centers such that the clusters formed by them are the most compact. Formally, given a set of data points ''x'', the ''k'' centers ''c''''i'' are to be chosen so as to minimize the sum of the distances fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "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.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied. In some applications in statistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medoid
Medoids are representative objects of a data set or a cluster within a data set whose sum of dissimilarities to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined, such as graphs. They are also used in contexts where the centroid is not representative of the dataset like in images and 3-D trajectories and gene expression (where while the data is sparse the medoid need not be). These are also of interest while wanting to find a representative using some distance other than squared euclidean distance (for instance in movie-ratings). For some data sets there may be more than one medoid, as with medians. A common application of the medoid is the k-medoids clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-means
''k''-means clustering is a method of vector quantization, originally from signal processing, that aims to partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. ''k''-means clustering minimizes within-cluster variances ( squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances. For instance, better Euclidean solutions can be found using k-medians and k-medoids. The problem is computationally difficult (NP-hard); however, efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the expectation-maximization algorithm for mixtures of Gaussian distributions via an iterative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stata
Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fields, including biomedicine, epidemiology, sociology and science. Stata was initially developed by Computing Resource Center in California and the first version was released in 1985. In 1993, the company moved to College Station, TX and was renamed Stata Corporation, now known as StataCorp. A major release in 2003 included a new graphics system and dialog boxes for all commands. Since then, a new version has been released once every two years. The current version is Stata 17, released in April 2021. Technical overview and terminology User interface From its creation, Stata has always employed an integrated command-line interface. Starting with version 8.0, Stata has included a graphical user interface based on Qt framework which uses m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU R
R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled executables are provided for various operating systems. R ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ELKI
ELKI (for ''Environment for DeveLoping KDD-Applications Supported by Index-Structures'') is a data mining (KDD, knowledge discovery in databases) software framework developed for use in research and teaching. It was originally at the database systems research unit of Professor Hans-Peter Kriegel at the Ludwig Maximilian University of Munich, Germany, and now continued at the Technical University of Dortmund, Germany. It aims at allowing the development and evaluation of advanced data mining algorithms and their interaction with database index structures. Description The ELKI framework is written in Java and built around a modular architecture. Most currently included algorithms belong to clustering, outlier detection and database indexes. The object-oriented architecture allows the combination of arbitrary algorithms, data types, distance functions, indexes, and evaluation measures. The Java just-in-time compiler optimizes all combinations to a similar extent, making benc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-medoids
The -medoids problem is a clustering problem similar to -means. The name was coined by Leonard Kaufman and Peter J. Rousseeuw with their PAM algorithm. Both the -means and -medoids algorithms are partitional (breaking the dataset up into groups) and attempt to minimize the distance between points labeled to be in a cluster and a point designated as the center of that cluster. In contrast to the -means algorithm, -medoids chooses actual data points as centers (medoids or exemplars), and thereby allows for greater interpretability of the cluster centers than in -means, where the center of a cluster is not necessarily one of the input data points (it is the average between the points in the cluster). Furthermore, -medoids can be used with arbitrary dissimilarity measures, whereas -means generally requires Euclidean distance for efficient solutions. Because -medoids minimizes a sum of pairwise dissimilarities instead of a sum of squared Euclidean distances, it is more robust to nois ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Data
Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including ''bit'' (binary digit) in computer science, ''truth value'' in mathematical logic and related domains and ''binary variable'' in statistics. Mathematical and combinatoric foundations A discrete variable that can take only one state contains zero information, and is the next natural number after 1. That is why the bit, a variable with only two possible values, is a standard primary unit of information. A collection of bits may have states: see binary number for details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states of each variable. Ten bits have more () states than three decimal digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anil K
Anil or Anıl may refer to: People * Anil (given name), an Indian given name (including a list of persons with the name) * Anıl (given name), a Turkish given name (including a list of persons with the name) * Anil (director), active in the Malayalam film industry since 1989 Other uses * Anil, Rio de Janeiro, Brazil, a neighborhood * Anıl, Hani, Turkey * Anil (plant) (''Indigofera suffruticosa''), a species of flowering plant in the legume family * Anil (chemistry), a type of imine * Anila Anila or Anil (Sanskrit: अनिल ' "wind") is one of the Vasus in Hinduism, gods of the elements of the cosmos. He is equated with the wind god Vāyu Vayu (, sa, वायु, ), also known as Vata and Pavana, is the Hindu god of the ... or Anil, a Vedic and Hindu deity See also * Añil * Anila (other) * Anneal (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manhattan Distance
A taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or Metric (mathematics), metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, ''L''1 distance, ''L''1 distance or \ell_1 norm (see Lp space, ''Lp'' space), Snake (video game), snake distance, city block distance, Manhattan distance or Manhattan length. The latter names refer to the rectilinear street layout on the island of Manhattan, where the shortest path a taxi travels between two points is the sum of the absolute values of distances that it travels on avenues and on streets. The geometry has been used in regression analysis since the 18th century, and is often referred to as Lasso (statistics), LASSO. The geometric interpretation dates to non-Euclidean geometry of the 19th century and is due to Hermann Minkowski. In \mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
