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  2. Cross-correlation matrix - Wikipedia

    en.wikipedia.org/wiki/Cross-correlation_matrix

    The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The cross-correlation matrix is used in various digital signal processing algorithms.

  3. Covariance matrix - Wikipedia

    en.wikipedia.org/wiki/Covariance_matrix

    Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...

  4. Outer product - Wikipedia

    en.wikipedia.org/wiki/Outer_product

    In MATLAB, the function kron (A, B) is used for this product. These often generalize to multi-dimensional arguments, and more than two arguments. In the Python library NumPy, the outer product can be computed with function np.outer(). [8] In contrast, np.kron results in a flat array.

  5. Cross-correlation - Wikipedia

    en.wikipedia.org/wiki/Cross-correlation

    In time series analysis and statistics, the cross-correlation of a pair of random process is the correlation between values of the processes at different times, as a function of the two times. Let ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} be a pair of random processes, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be ...

  6. Cosine similarity - Wikipedia

    en.wikipedia.org/wiki/Cosine_similarity

    The angle between two term frequency vectors cannot be greater than 90°. If the attribute vectors are normalized by subtracting the vector means (e.g., ¯), the measure is called the centered cosine similarity and is equivalent to the Pearson correlation coefficient. For an example of centering,

  7. NumPy - Wikipedia

    en.wikipedia.org/wiki/NumPy

    NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]

  8. Multivariate random variable - Wikipedia

    en.wikipedia.org/wiki/Multivariate_random_variable

    The observations on the dependent variable are stacked into a column vector y; the observations on each independent variable are also stacked into column vectors, and these latter column vectors are combined into a design matrix X (not denoting a random vector in this context) of observations on the independent variables. Then the following ...

  9. Covariance and correlation - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_correlation

    [1] [2] Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways. If X and Y are two random variables, with means (expected values) μ X and μ Y and standard deviations σ X and σ Y, respectively, then their covariance and correlation are as follows: covariance