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Cophenetic Correlation
In statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. Although it has been most widely applied in the field of biostatistics (typically to assess cluster-based models of DNA sequences, or other taxonomic models), it can also be used in other fields of inquiry where raw data tend to occur in clumps, or clusters. This coefficient has also been proposed for use as a test for nested clusters. Calculating the cophenetic correlation coefficient Suppose that the original data have been modeled using a cluster method to produce a dendrogram ; that is, a simplified model in which data that are "close" have been grouped into a hierarchical tree. Define the following distance measures. * x(i,j) = , X_i-X_j, , the Euclidean distance between the ''i''th and ''j''th observations. * t(i,j), the dendrogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Biostatistics
Biostatistics (also known as biometry) is a branch of statistics that applies statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results. History Biostatistics and genetics Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools. Gregor Mendel started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism. Francis Galton tried to expand Mendel's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dendrogram
A dendrogram is a diagram representing a Tree (graph theory), tree graph. This diagrammatic representation is frequently used in different contexts: * in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses. * in computational biology, it shows the clustering of genes or samples, sometimes in the margins of heat map, heatmaps. * in phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree. The name ''dendrogram'' derives from the two ancient greek words (), meaning "tree", and (), meaning "drawing, mathematical figure". Clustering example For a clustering example, suppose that five taxa (a to e) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes repre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxonomy (biology)
In biology, taxonomy () is the science, scientific study of naming, defining (Circumscription (taxonomy), circumscribing) and classifying groups of biological organisms based on shared characteristics. Organisms are grouped into taxon, taxa (singular: taxon), and these groups are given a taxonomic rank; groups of a given rank can be aggregated to form a more inclusive group of higher rank, thus creating a taxonomic hierarchy. The principal ranks in modern use are domain (biology), domain, kingdom (biology), kingdom, phylum (''division'' is sometimes used in botany in place of ''phylum''), class (biology), class, order (biology), order, family (biology), family, genus, and species. The Swedish botanist Carl Linnaeus is regarded as the founder of the current system of taxonomy, having developed a ranked system known as Linnaean taxonomy for categorizing organisms. With advances in the theory, data and analytical technology of biological systematics, the Linnaean system has transfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Department Of Energy
The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and energy production, the research and development of nuclear power, the military's nuclear weapons program, nuclear reactor production for the United States Navy, energy-related research, and energy conservation. The DOE was created in 1977 in the aftermath of the 1973 oil crisis. It sponsors more physical science research than any other U.S. federal agency, the majority of which is conducted through its system of National Laboratories. The DOE also directs research in genomics, with the Human Genome Project originating from a DOE initiative. The department is headed by the secretary of energy, who reports directly to the president of the United States and is a member of the Cabinet. The current secretary of energy is Chris Wright, who has served in the position since February 2025. The department's headquarters are in sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, 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 R package, software packages, which contain Reusability, 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 (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SciPy
SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, fast Fourier transform, signal and image processing, ordinary differential equation solvers and other tasks common in science and engineering. SciPy is also a family of conferences for users and developers of these tools: SciPy (in the United States), EuroSciPy (in Europe) and SciPy.in (in India). Enthought originated the SciPy conference in the United States and continues to sponsor many of the international conferences as well as host the SciPy website. The SciPy library is currently distributed under the BSD license, and its development is sponsored and supported by an open community of developers. It is also supported by NumFOCUS, a community foundation for supporting reproducible and accessible science. Components The SciPy package is at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cophenetic
In the clustering of biological information such as data from microarray experiments, the cophenetic similarity or cophenetic distanceSokal, R. R. and F. J. Rohlf. 1962. The comparison of dendrograms by objective methods. Taxon, 11:33-40 of two objects is a measure of how similar those two objects have to be in order to be grouped into the same cluster. The cophenetic distance between two objects is the height of the dendrogram A dendrogram is a diagram representing a Tree (graph theory), tree graph. This diagrammatic representation is frequently used in different contexts: * in hierarchical clustering, it illustrates the arrangement of the clusters produced by ... where the two branches that include the two objects merge into a single branch. Outside the context of a dendrogram, it is the distance between the largest two clusters that contain the two objects individually when they are merged into a single cluster that contains both. See also * Cophenetic correlation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
