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Optimal Matching
Optimal matching is a sequence analysis method used in social science, to assess the dissimilarity of ordered arrays of tokens that usually represent a time-ordered sequence of socio-economic states two individuals have experienced. Once such distances have been calculated for a set of observations (e.g. individuals in a cohort) classical tools (such as cluster analysis) can be used. The method was tailored to social sciences from a technique originally introduced to study molecular biology (protein or genetic) sequences (see sequence alignment). Optimal matching uses the Needleman-Wunsch algorithm. Algorithm Let S = (s_1, s_2, s_3, \ldots s_T) be a sequence of states s_i belonging to a finite set of possible states. Let us denote the sequence space, i.e. the set of all possible sequences of states. Optimal matching algorithms work by defining simple operator algebras that manipulate sequences, i.e. a set of operators a_i: \rightarrow . In the most simple approach, a set com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Cardinality Matching
Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph , and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this problem is equivalent to the task of finding a matching that covers as many vertices as possible. An important special case of the maximum cardinality matching problem is when is a bipartite graph, whose vertices are partitioned between left vertices in and right vertices in , and edges in always connect a left vertex to a right vertex. In this case, the problem can be efficiently solved with simpler algorithms than in the general case. Algorithms for bipartite graphs Flow-based algorithm The simplest way to compute a maximum cardinality matching is to follow the Ford–Fulkerson algorithm. This algorithm solves the more general probl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching (statistics)
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned). The goal of matching is to reduce bias for the estimated treatment effect in an observational-data study, by finding, for every treated unit, one (or more) non-treated unit(s) with similar observable characteristics against which the covariates are balanced out (similar to the K-nearest neighbors algorithm). By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding. Propensity score matching, an early matching technique, was developed as part of the Rubin causal model, but has been shown to increase model dependence, bias, inefficiency, and power and is no longer recommended compared to other matching methods. A si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence Analysis In Social Sciences
In social sciences, sequence analysis (SA) is concerned with the analysis of sets of categorical sequences that typically describe longitudinal data. Analyzed sequences are encoded representations of, for example, individual life trajectories such as family formation, school to work transitions, working careers, but they may also describe daily or weekly time use or represent the evolution of observed or self-reported health, of political behaviors, or the development stages of organizations. Such sequences are chronologically ordered unlike words or DNA sequences for example. SA is a longitudinal analysis approach that is holistic in the sense that it considers each sequence as a whole. SA is essentially exploratory. Broadly, SA provides a comprehensible overall picture of sets of sequences with the objective of characterizing the structure of the set of sequences, finding the salient characteristics of groups, identifying typical paths, comparing groups, and more generally study ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Science
Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the field of sociology, the original "science of society", established in the 18th century. It now encompasses a wide array of additional academic disciplines, including anthropology, archaeology, economics, geography, history, linguistics, management, communication studies, psychology, culturology, and political science. The majority of positivist social scientists use methods resembling those used in the natural sciences as tools for understanding societies, and so define science in its stricter modern sense. Speculative social scientists, otherwise known as interpretivist scientists, by contrast, may use social critique or symbolic interpretation rather than constructing empirically falsifiable theories, and thus treat science in its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cohort (statistics)
In statistics, epidemiology, marketing and demography, a cohort is a group of research subject, subjects who share a defining characteristic (typically subjects who experienced a common event in a selected time period, such as birth or graduation). Comparison with period data Cohort data can oftentimes be more advantageous to Demography, demographers than period data. Because cohort data is honed to a specific time period, it is usually more accurate. It is more accurate because it can be tuned to retrieve custom data for a specific study. In addition, cohort data is not affected by tempo effects, unlike period data. However, cohort data can be disadvantageous in the sense that it can take a long amount of time to collect the data necessary for the cohort study. Another disadvantage of cohort studies is that it can be extremely costly to carry out, since the study will go on for a long period of time, demographers often require sufficient funds to fuel the study. Demography ... [...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] |
Sequence Alignment
In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural biology, structural, or evolutionary relationships between the sequences. Aligned sequences of nucleotide or amino acid residues are typically represented as rows within a matrix (mathematics), matrix. Gaps are inserted between the Residue (chemistry), residues so that identical or similar characters are aligned in successive columns. Sequence alignments are also used for non-biological sequences such as calculating the Edit distance, distance cost between strings in a natural language, or to display financial data. Interpretation If two sequences in an alignment share a common ancestor, mismatches can be interpreted as point mutations and gaps as indels (that is, insertion or deletion mutations) introduced in one or both lineages in the time since they diverged from one another. In sequence ali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebras
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear". The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras where associativity of multiplication is assumed, and non-associative algebras, where associativity is not assumed (but not excluded, either). Given an integer ''n'', the ring of real square matrices of order ''n'' is an example of an associative algebra over the field of real numbers under matrix addition and matrix multiplication since matrix multiplication is associative. Three-dimensional Euclidean space with multiplication given by the vector cross product is an example of a nonassociative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art, and music. The opposite of symmetry is asymmetr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a binary relation on a set (mathematics), set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Every partial order and every equivalence relation is transitive. For example, less than and equality (mathematics), equality among real numbers are both transitive: If and then ; and if and then . Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy is also an ancestor of Carrie. On the other hand, "is the birth mother of" is not a transitive relation, because if Alice is the birth mother of Brenda, and Brenda is the birth mother of Claire, then it does ... [...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] |
