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Informally, an algorithm can be said to exhibit a growth rate on the order of a mathematical function if beyond a certain input size n, the function f(n) times a positive constant provides an upper bound or limit for the run-time of that algorithm.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations N as the result of input size n for each function. In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.
For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ. For any non-zero time τ the growth rate is given by the dimensionless positive number b. Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different base.
The order of growth (e.g. linear, logarithmic) of the worst-case complexity is commonly used to compare the efficiency of two algorithms. The worst-case complexity of an algorithm should be contrasted with its average-case complexity, which is an average measure of the amount of resources the algorithm uses on a random input.
In asymptotic analysis in general, one sequence () that converges to a limit is said to asymptotically converge to with a faster order of convergence than another sequence () that converges to in a shared metric space with distance metric | |, such as the real numbers or complex numbers with the ordinary absolute difference metrics, if
The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. [5] The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization ...
Big O notation is an asymptotic measure of function complexity, where () = (()) roughly means the time requirement for an algorithm is proportional to (), omitting lower-order terms that contribute less than () to the growth of the function as grows arbitrarily large.
In data mining and association rule learning, lift is a measure of the performance of a targeting model (association rule) at predicting or classifying cases as having an enhanced response (with respect to the population as a whole), measured against a random choice targeting model.