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Medoids
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 wo ... [...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] |
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] |
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). 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 itself is not one specific algorithm, but the general task to be solved. 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 particular statistical distributions. Clustering can therefore be formulated as a multi-object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hierarchical Clustering
In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: * Agglomerative: This is a " bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. * Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy. In general, the merges and splits are determined in a greedy manner. The results of hierarchical clustering are usually presented in a dendrogram. The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of \mathcal(n^3) and requires \Omega(n^2) memory, which makes it too slow for even medium data sets. However, for some special cases, optimal efficient agglomerative methods (of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Set
A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question. The data set lists values for each of the variables, such as for example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files. In the open data discipline, data set is the unit to measure the information released in a public open data repository. The European data.europa.eu portal aggregates more than a million data sets. Some other issues ( real-time data sources, non-relational data sets, etc.) increases the difficulty to reach a consensus about it. Properties Several characteristics define a data set's structure and properties. These include the number and types of the attributes or variables, and various statistical measures applic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric (mathematics)
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Eppstein
David Arthur Eppstein (born 1963) is an American computer scientist and mathematician. He is a Distinguished Professor of computer science at the University of California, Irvine. He is known for his work in computational geometry, graph algorithms, and recreational mathematics. In 2011, he was named an ACM Fellow. Biography Born in Windsor, England, in 1963, Eppstein received a B.S. in Mathematics from Stanford University in 1984, and later an M.S. (1985) and Ph.D. (1989) in computer science from Columbia University, after which he took a postdoctoral position at Xerox's Palo Alto Research Center. He joined the UC Irvine faculty in 1990, and was co-chair of the Computer Science Department there from 2002 to 2005. In 2014, he was named a Chancellor's Professor. In October 2017, Eppstein was one of 396 members elected as fellows of the American Association for the Advancement of Science. Eppstein is also an amateur digital photographer. Research interests In computer science, E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Antony Richard Hoare
Sir Charles Antony Richard Hoare (Tony Hoare or C. A. R. Hoare) (born 11 January 1934) is a British computer scientist who has made foundational contributions to programming languages, algorithms, operating systems, formal verification, and concurrent computing. His work earned him the Turing Award, usually regarded as the highest distinction in computer science, in 1980. Hoare developed the sorting algorithm quicksort in 1959–1960. He developed Hoare logic, an axiomatic basis for verifying program correctness. In the semantics of concurrency, he introduced the formal language communicating sequential processes (CSP) to specify the interactions of concurrent processes, and along with Edsger Dijkstra, formulated the dining philosophers problem. He is also credited with development (and later criticism) of the null pointer, having introduced it in the ALGOL family of languages. Since 1977, he has held positions at the University of Oxford and Microsoft Research in Cambridge. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Tse
David Tse is the Thomas Kailath and Guanghan Xu Professor of Engineering at Stanford University. Education Tse earned a B.S. in systems design engineering from University of Waterloo in 1989, an M.S. in electrical engineering from the Massachusetts Institute of Technology in 1991, and a Ph.D. in electrical engineering from MIT in 1994. As a postdoctoral student he was a staff member at AT&T Bell Laboratories. Career Tse's research at Stanford focuses on information theory and its applications in fields such as wireless communication, machine learning, energy and computational biology. He has designed assembly software to handle DNA and RNA sequencing data and was an inventor of the proportional-fair scheduling algorithm for cellular wireless systems. He received the 2017 Claude E. Shannon Award. In 2018, he was elected to the National Academy of Engineering. Honors * Early Faculty National Science Foundation CAREER Award, 1998 * Frederick Emmons Terman Award from the American S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric
Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathematics, metric may refer to one of two related, but distinct concepts: * A function which measures distance between two points in a metric space * A metric tensor, in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold Natural sciences * Metric tensor (general relativity), the fundamental object of study in general relativity, similar to the gravitational field in Newtonian physics * Senses related to measurement: ** Metric system, an internationally adopted decimal system of measurement ** Metric units, units related to a metric system ** International System of Units, or ''Système International'' (SI), the most widely used metric system * METRIC, a model that uses Landsat satellite data to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Median
In geometry, the geometric median of a discrete set of sample points 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 for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the ''L''1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation. The special case of the problem for three points in the plane (that is, = 3 and = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the Euclidean norm, or 2-norm, which may also be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a ''seminormed vector space''. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality "\,\leq\," in the homogeneity axiom. It can also re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
