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A linear, or axial, color gradient. In color science, a color gradient (also known as a color ramp or a color progression) specifies a range of position-dependent colors, usually used to fill a region. In assigning colors to a set of values, a gradient is a continuous colormap, a type of color scheme.
In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
Gradient descent can also be used to solve a system of nonlinear equations. Below is an example that shows how to use the gradient descent to solve for three unknown variables, x 1, x 2, and x 3. This example shows one iteration of the gradient descent. Consider the nonlinear system of equations
The minimization of the Kullback–Leibler divergence with respect to the points is performed using gradient descent. The result of this optimization is a map that reflects the similarities between the high-dimensional inputs.
LightGBM, short for Light Gradient-Boosting Machine, is a free and open-source distributed gradient-boosting framework for machine learning, originally developed by Microsoft. [ 4 ] [ 5 ] It is based on decision tree algorithms and used for ranking , classification and other machine learning tasks.
Reverse accumulation traverses the chain rule from outside to inside, or in the case of the computational graph in Figure 3, from top to bottom. The example function is scalar-valued, and thus there is only one seed for the derivative computation, and only one sweep of the computational graph is needed to calculate the (two-component) gradient.
The pixels with the largest gradient values in the direction of the gradient become edge pixels, and edges may be traced in the direction perpendicular to the gradient direction. One example of an edge detection algorithm that uses gradients is the Canny edge detector. Image gradients can also be used for robust feature and texture matching.