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K-medians Clustering
K-medians clustering is a partitioning technique used in cluster analysis. It groups data into ''k'' clusters by minimizing the sum of distances—typically using the Manhattan (L1) distance—between data points and the median of their assigned clusters. This method is especially robust to outliers and is well-suited for discrete or categorical data. It is a generalization of the geometric median or 1-median algorithm, defined for a single cluster. ''k''-medians 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 2- norm distance metric, as opposed to the squared 2-norm distance metric (which ''k''-means does). This relates directly to the ''k''-median problem which is the problem of finding ''k'' centers such that the clusters formed by them are the most compact with respect to the 2-norm. Formally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anil K
Anil or Anıl may refer to: People * Anil (given name), an Indian and Nepalese 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 or Anil, a Vedic and Hindu deity See also * Añil * Anal (other) * Anila (other) * Anneal (other) {{disambiguation ... [...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 the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's ''Elements'', distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. 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 b ... [...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, 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 work ... [...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 of a set, partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster (statistics), 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 clustering, ''k''-medians and k-medoids, ''k''-medoids. The problem is computationally difficult (NP-hardness, NP-hard); however, efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Stata
Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose Statistics, statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fields, including biomedicine, economics, epidemiology, and sociology. 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, Texas 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 19, released in April 2025. 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 which uses Menu ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU R
R is a programming language for statistical computing and data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of software packages, which contain reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C, Fortran, and R itself. Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a native command line interface. In addition, multiple third-party applications are available as graphical user interfaces; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ELKI
ELKI (''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 created by the database systems research unit at the Ludwig Maximilian University of Munich, Germany, led by Professor Hans-Peter Kriegel. The project has 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 perform 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 simila ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-medoids
-medoids is a classical partitioning technique of clustering that splits the data set of objects into clusters, where the number of clusters assumed known ''a priori'' (which implies that the programmer must specify k before the execution of a -medoids algorithm). The "goodness" of the given value of can be assessed with methods such as the silhouette method. The name of the clustering method was coined by Leonard Kaufman and Peter J. Rousseeuw with their PAM (Partitioning Around Medoids) algorithm. The medoid of a cluster is defined as the object in the cluster whose sum (and, equivalently, the average) of dissimilarities to all the objects in the cluster is minimal, that is, it is a most centrally located point in the cluster. Unlike certain objects used by other algorithms, the medoid is an actual point in the cluster. Algorithms In general, the -medoids problem is NP-hard to solve exactly. As such, multiple heuristics to optimize this problem exist. Partitioning Arou ... [...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 dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Median
In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances or absolute differences for one-dimensional data. It is also known as the spatial median, Euclidean minisum point, Torricelli point, or 1-median. It provides a measure of central tendency in higher dimensions and it is a standard problem in facility location, i.e., locating a facility to minimize the cost of transportation. The geometric median is an important estimator of location in statistics, because it minimizes the sum of the ''L''2 distances of the samples. It is to be compared to the mean, which minimizes the sum of the ''squared'' ''L''2 distances; and to the coordinate-wise median which minimizes the sum of the ''L''1 distances. The more general ''k''-median problem asks for the location of ''k'' cluster centers minimizing the sum o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
