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In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point z i is replaced with the transformed value y i = f(z i), where f is a function. Transforms are usually applied so that the data appear to more closely meet the assumptions of a statistical ...
For example, suppose that the values x are realizations from different Poisson distributions: i.e. the distributions each have different mean values μ. Then, because for the Poisson distribution the variance is identical to the mean, the variance varies with the mean. However, if the simple variance-stabilizing transformation
A reflection about a line or plane that does not go through the origin is not a linear transformation — it is an affine transformation — as a 4×4 affine transformation matrix, it can be expressed as follows (assuming the normal is a unit vector): [′ ′ ′] = [] [] where = for some point on the plane, or equivalently, + + + =.
When data is convolved with a function with wide support, such as for downsampling by a large sampling ratio, because of the Convolution theorem and the FFT algorithm, it may be faster to transform it, multiply pointwise by the transform of the filter and then reverse transform it. Alternatively, a good filter is obtained by simply truncating ...
A training data set is a data set of examples used during the learning process and is used to fit the parameters (e.g., weights) of, for example, a classifier. [9] [10]For classification tasks, a supervised learning algorithm looks at the training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model. [11]
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
a smooth function, an analytic function, if the multivariate function that represents it on some basis—and thus on every basis—has the same property. This is specially useful in the theory of manifolds, as this allows extending the concepts of continuous, differentiable, smooth and analytic functions to functions that are defined on a manifold.
Bateman transform; Fourier transform. Short-time Fourier transform; Gabor transform; Hankel transform; Hartley transform; Hermite transform; Hilbert transform. Hilbert–Schmidt integral operator; Jacobi transform; Laguerre transform; Laplace transform. Inverse Laplace transform; Two-sided Laplace transform; Inverse two-sided Laplace transform ...