Search results
Results from the WOW.Com Content Network
As for time analysis above, analyze the algorithm, typically using space complexity analysis to get an estimate of the run-time memory needed as a function as the size of the input data. The result is normally expressed using Big O notation .
The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. [ 1 ]
Clustering high-dimensional data is the cluster analysis of data with anywhere from a few dozen to many thousands of dimensions.Such high-dimensional spaces of data are often encountered in areas such as medicine, where DNA microarray technology can produce many measurements at once, and the clustering of text documents, where, if a word-frequency vector is used, the number of dimensions ...
The term Borel space is used for different types of measurable spaces. It can refer to any measurable space, so it is a synonym for a measurable space as defined above [1] a measurable space that is Borel isomorphic to a measurable subset of the real numbers (again with the Borel -algebra) [3]
A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the σ-algebra) and the method that is used for measuring (the measure). One important example of a measure space is a probability space.
Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing , the worst-case execution time is often of particular concern since it is important to know how much time might be needed in ...
The parameter space is the space of all possible parameter values that define a particular mathematical model. It is also sometimes called weight space, and is often a subset of finite-dimensional Euclidean space. In statistics, parameter spaces are particularly useful for describing parametric families of probability distributions.
There is an exponential increase in volume associated with adding extra dimensions to a mathematical space.For example, 10 2 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube) with no more than 10 −2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10 −2 ...