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Fuzzy Clustering
Fuzzy clustering (also referred to as soft clustering or soft ''k''-means) is a form of clustering in which each data point can belong to more than one cluster. Clustering or cluster analysis involves assigning data points to clusters such that items in the same cluster are as similar as possible, while items belonging to different clusters are as dissimilar as possible. Clusters are identified via similarity measures. These similarity measures include distance, connectivity, and intensity. Different similarity measures may be chosen based on the data or the application. Comparison to hard clustering In non-fuzzy clustering (also known as hard clustering), data are divided into distinct clusters, where each data point can only belong to exactly one cluster. In fuzzy clustering, data points can potentially belong to multiple clusters. For example, an apple can be red or green (hard clustering), but an apple can also be red AND green (fuzzy clustering). Here, the apple can be red ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Point
In statistics, a unit of observation is the unit described by the data that one analyzes. A study may treat groups as a unit of observation with a country as the unit of analysis, drawing conclusions on group characteristics from data collected at the national level. For example, in a study of the demand for money, the unit of observation might be chosen as the individual, with different observations (data points) for a given point in time differing as to which individual they refer to; or the unit of observation might be the country, with different observations differing only in regard to the country they refer to. Unit of observation vs unit of analysis The unit of observation should not be confused with the unit of analysis. A study may have a differing unit of observation and unit of analysis: for example, in community research, the research design may collect data at the individual level of observation but the level of analysis might be at the neighborhood level, drawing c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Set
In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an ''L''-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of ''L''-relations when ''L'' is the unit interval , 1 In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition—an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval , 1 Fuzzy sets generali ... [...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] |
HCL Color Space
HCL (Hue- Chroma-Luminance) or LCh refers to any of the many cylindrical color space models that are designed to accord with human perception of color with the three parameters. Lch has been adopted by information visualization practitioners to present data without the bias implicit in using varying saturation. They are, in general, designed to have characteristics of both cylindrical translations of the RGB color space, such as HSL and HSV, and the L*a*b* color space. Some conflicting definitions of the terms are: * A name for a cylindrical transformation of CIELuv (CIELChuv) employed by Ihaka (2003) and adopted by Zeileis et al. (2009, 2020). This name appears to be the one most commonly used in information visualization. Ihaka, Zeileis, and co-authors also provide software implementations and web pages to promote its use. * A name for cylindrical CIELab (CIELChab), employed by chroma.js. * "HCL" designed in 2005 by Sarifuddin and Missaou, which is a transformation of whatever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RGB Color Space
An RGB color space is any additive color space based on the RGB color model. An RGB color space is defined by chromaticity coordinates of the red, green, and blue additive primaries, the white point which is usually a standard illuminant, and the transfer function which is also known as the tone response curve (TRC) or gamma. Applying Grassmann's law of light additivity, a colorspace so defined can produce colors which are enclosed within the 2D triangle on the chromaticity diagram defined by those primary coordinates. The TRC and white point further define the possible colors, creating a volume in a 3D shape that never exceeds the triangular bounds. The primary colors are often specified in terms of their xyY chromaticity coordinates, though the uʹ,vʹ coordinates from the UCS chromaticity diagram may be used. Both xyY and uʹ,vʹ are derived from the CIE 1931 color space, a device independent space also known as XYZ which uses the 2° standard observer, an averaging of expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-means Clustering
''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 refine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Segmentation
In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects ( sets of pixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Linda G. Shapiro and George C. Stockman (2001): “Computer Vision”, pp 279–325, New Jersey, Prentice-Hall, Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics. The result of image segmentation is a set of segments that collectively cover the entire image, or a set of contours extracted from the image (see edge detection). Each of the pixels in a region are similar with respect to some characteristic or computed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Clustering Example
Fuzzy or Fuzzies may refer to: Music * Fuzzy (band), a 1990s Boston indie pop band * Fuzzy (composer) (born 1939), Danish composer Jens Vilhelm Pedersen * ''Fuzzy'' (album), 1993 debut album by the Los Angeles rock group Grant Lee Buffalo * "Fuzzy", a song from the 2009 ''Collective Soul'' album by Collective Soul * "Fuzzy", a song by Poppy from ''Poppy.Computer'' Nickname * Faustina Agolley (born 1984), Australian television presenter, host of the Australian television show ''Video Hits'' * Fuzzy Haskins (born 1941), American singer and guitarist with the doo-wop group Parliament-Funkadelic * Fuzzy Hufft (1901−1973), American baseball player * Fuzzy Knight (1901−1976), American actor * Andrew Levane (1920−2012), American National Basketball Association player and coach * Robert Alfred Theobald (1884−1957), United States Navy rear admiral * Fuzzy Thurston (1933-2014), American National Football League player * Fuzzy Vandivier (1903−1983), American high school and colleg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HSL And HSV
HSL (for hue, saturation, lightness) and HSV (for hue, saturation, value; also known as HSB, for hue, saturation, brightness) are alternative representations of the RGB color model, RGB color model, designed in the 1970s by computer graphics researchers to more closely align with the way human vision perceives color-making attributes. In these models, colors of each ''hue'' are arranged in a radial slice, around a central axis of neutral colors which ranges from black at the bottom to white at the top. The HSL representation models the way different paints mix together to create color in the real world, with the ''lightness'' dimension resembling the varying amounts of black or white paint in the mixture (e.g. to create "light red", a red pigment can be mixed with white paint; this white paint corresponds to a high "lightness" value in the HSL representation). Fully saturated colors are placed around a circle at a lightness value of ½, with a lightness value of 0 or 1 correspon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term ''fuzzy logic'' was introduced with the 1965 proposal of fuzzy set theory by Iranian Azerbaijani mathematician Lotfi Zadeh. Fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack ... [...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] |
