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Pathfinder Network
A method for pruning dense networks to highlight key links Rationale Relationships among a set of elements are often represented as a square matrix with entries representing the relations between all pairs of the elements. Relations such as distances, dissimilarities, similarities, relatedness, correlations, co-occurrences, conditional probabilities, etc., can be represented by such matrices. Such data can also be represented as networks with weighted links between the elements. Such matrices and networks are extremely dense and are not easily apprehended without some form of data reduction or pruning. A pathfinder network results from applying a pruning method that removes weaker links from a (usually dense) network according to the lengths of alternative paths (see below). It is used as a psychometric scaling method based on graph theory and used in the study of expertise, education, knowledge acquisition, mental models, and knowledge engineering. It is also employed in gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Reduction
Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form. The purpose of data reduction can be two-fold: reduce the number of data records by eliminating invalid data or produce summary data and statistics at different aggregation levels for various applications. Data reduction does not necessarily mean loss of information. When information is derived from instrument readings there may also be a transformation from analog to digital form. When the data are already in digital form the 'reduction' of the data typically involves some editing, scaling, encoding, sorting, collating, and producing tabular summaries. When the observations are discrete but the underlying phenomenon is continuous then smoothing and interpolation are often needed. The data reduction is often undertaken in the presence of reading or measurement errors. Some idea of the nature of these errors is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Clustering
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 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 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 distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Spanning Tree
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components. There are many use cases for minimum spanning trees. One example is a telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would be a graph containing the points (e.g. houses) connected by those paths. Some of the paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Transformation
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if it is either entirely non-decreasing, or entirely non-increasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is termed ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\right), so it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Level Of Measurement
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and has since had a complex history, being adopted and extended in some disciplines and by some scholars, and criticized or rejected by others. Other classifications include those by Mosteller and Tukey, and by Chrisman. Stevens's typology Overview Stevens proposed his typology in a 1946 ''Science'' article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval", and "ratio", unifying both " qualitative" (which are described by his "nominal" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dijkstra's Algorithm
Dijkstra's algorithm ( ) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of edges represent the distances between pairs of cities connected by a direct road, then Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and OSPF (Open Shortest Path First). It is also employed as a subroutine in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floyd–Warshall Algorithm
In computer science, the Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights (but with no negative cycles). See in particular Section 26.2, "The Floyd–Warshall algorithm", pp. 558–565 and Section 26.4, "A general framework for solving path problems in directed graphs", pp. 570–576. A single execution of the algorithm will find the lengths (summed weights) of shortest paths between all pairs of vertices. Although it does not return details of the paths themselves, it is possible to reconstruct the paths with simple modifications to the algorithm. Versions of the algorithm can also be used for finding the transitive closure of a relation R, or (in connection with the Schulze voting system) widest paths between all pairs of vertices in a weighted graph. History and nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Distance
The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the Polish mathematician Hermann Minkowski. Definition The Minkowski distance of order p (where p is an integer) between two points X = (x_1,x_2,\ldots,x_n) \text Y = (y_1,y_2,\ldots,y_n) \in \R^n is defined as: D\left(X,Y\right) = \biggl(\sum_^n , x_i-y_i, ^p\biggr)^. For p \geq 1, the Minkowski distance is a metric as a result of the Minkowski inequality. When p 2, but the point (0, 1) is at a distance 1 from both of these points. Since this violates the triangle inequality, for p < 1 it is not a metric. However, a metric can be obtained for these values by simply removing the exponent of The resulting metric is also an F-norm. Minkowski distance is typically used with < ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multidimensional Scaling
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of n objects in a set into a configuration of n points mapped into an abstract Cartesian space. More technically, MDS refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction. Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, ''N'', an MDS algorithm places each object into ''N''-dimensional space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible. For ''N'' = 1, 2, and 3, the resulting points can be visualized on a scatter plot. Core theoretical contributions to MDS were made by James O. Ramsay of McGill University, who is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Theory
In mathematics, computer science, and network science, network theory is a part of graph theory. It defines networks as Graph (discrete mathematics), graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or directed graph, asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience. Applications of network theory include Logistics, logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.; see List of network theory topics for more examples. Euler's solution of the Seven Bridges of Königsberg, Seven Bridges of Königsberg problem is c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychometric
Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and related activities. Psychometrics is concerned with the objective measurement of Latent variable, latent constructs that cannot be directly observed. Examples of latent constructs include intelligence, introversion, Mental disorder, mental disorders, and Educational measurement, educational achievement. The levels of individuals on nonobservable latent variables are Statistical inference, inferred through mathematical model, mathematical modeling based on what is observed from individuals' responses to items on tests and scales. Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess specific qualifications, such as degrees or certifications, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Visualization
Data and information visualization (data viz/vis or info viz/vis) is the practice of designing and creating Graphics, graphic or visual Representation (arts), representations of a large amount of complex quantitative and qualitative data and information with the help of static, dynamic or interactive visual items. Typically based on data and information collected from a certain domain of expertise, these visualizations are intended for a broader audience to help them visually explore and discover, quickly understand, interpret and gain important insights into otherwise difficult-to-identify structures, relationships, correlations, local and global patterns, trends, variations, constancy, clusters, outliers and unusual groupings within data (''exploratory visualization''). When intended for the general public (mass communication) to convey a concise version of known, specific information in a clear and engaging manner (''presentational'' or ''explanatory visualization''), it is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
