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In others words, the sample complexity (,,) defines the rate of consistency of the algorithm: given a desired accuracy and confidence , one needs to sample (,,) data points to guarantee that the risk of the output function is within of the best possible, with probability at least .
Data science is "a concept to unify statistics, data analysis, informatics, and their related methods" to "understand and analyze actual phenomena" with data. [5] It uses techniques and theories drawn from many fields within the context of mathematics , statistics, computer science , information science , and domain knowledge . [ 6 ]
Data mining is a particular data analysis technique that focuses on statistical modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. [4]
The study of these complex linkages at various scales is the main goal of complex systems theory. The intuitive criterion of complexity can be formulated as follows: a system would be more complex if more parts could be distinguished, and if more connections between them existed. [3]
Symbolic data analysis (SDA) is an extension of standard data analysis where symbolic data tables are used as input and symbolic objects are made output as a result. The data units are called symbolic since they are more complex than standard ones, as they not only contain values or categories, but also include internal variation and structure.
The Čech complex and the Vietoris–Rips complex are most natural at first glance; however, their size grows rapidly with the number of data points. The Vietoris–Rips complex is preferred over the Čech complex because its definition is simpler and the Čech complex requires extra effort to define in a general finite metric space.
In information science and ontology, a classification scheme is an arrangement of classes or groups of classes. The activity of developing the schemes bears similarity to taxonomy, but with perhaps a more theoretical bent, as a single classification scheme can be applied over a wide semantic spectrum while taxonomies tend to be devoted to a single topic.
Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near ...