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Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
Eigenvalues and eigenvectors. In linear algebra, it is often important to know which vectors have their directions unchanged by a given linear transformation. An eigenvector ( / ˈaɪɡən -/ EYE-gən-) or characteristic vector is such a vector. Thus an eigenvector of a linear transformation is scaled by a constant factor when the linear ...
Dijkstra's algorithm (/ˈdaɪkstrəz/ DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.[4][5][6] Dijkstra's algorithm finds the shortest path from a ...
Fundamental operation A block diagram of a PID controller in a feedback loop.r(t) is the desired process variable (PV) or setpoint (SP), and y(t) is the measured PV. The distinguishing feature of the PID controller is the ability to use the three control terms of proportional, integral and derivative influence on the controller output to apply accurate and optimal control.
Scope. Matrix calculus refers to a number of different notations that use matrices and vectors to collect the derivative of each component of the dependent variable with respect to each component of the independent variable. In general, the independent variable can be a scalar, a vector, or a matrix while the dependent variable can be any of ...
In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 {\displaystyle 10} of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x ...
Visual comparison of convolution, cross-correlation, and autocorrelation.For the operations involving function , and assuming the height of is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. The symmetry of is the reason and are identical in this example. ...
