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The windows that classical DTW uses to constrain alignments introduce a step function. Any warping of the path is allowed within the window and none beyond it. In contrast, ADTW employs an additive penalty that is incurred each time that the path is warped. Any amount of warping is allowed, but each warping action incurs a direct penalty.
The area size between adjacent warping paths is proportional to the number of edges cut among cross edges. This minimization problem can be reformulated into a minimum cut problem on a special graph termed GTW graph, where the minimum cut and the warping paths are equivalent. [1] The formulation could be described as:
In a learning problem, the goal is to develop a function () that predicts output values for each input datum . The subscript n {\displaystyle n} indicates that the function f n {\displaystyle f_{n}} is developed based on a data set of n {\displaystyle n} data points.
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without explicit instructions. [1]
Wolpert had previously derived no free lunch theorems for machine learning (statistical inference). [3] Before Wolpert's article was published, Cullen Schaffer independently proved a restricted version of one of Wolpert's theorems and used it to critique the current state of machine learning research on the problem of induction. [4]
The learning problem with the least squares loss function and Tikhonov regularization can be solved analytically. Written in matrix form, the optimal w {\displaystyle w} is the one for which the gradient of the loss function with respect to w {\displaystyle w} is 0.
A popular window function, the Hann window. Most popular window functions are similar bell-shaped curves. In signal processing and statistics, a window function (also known as an apodization function or tapering function [1]) is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are ...
Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims to find a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves.