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A cumulative accuracy profile (CAP) is a concept utilized in data science to visualize discrimination power.The CAP of a model represents the cumulative number of positive outcomes along the y-axis versus the corresponding cumulative number of a classifying parameter along the x-axis.
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
Consistent with the example illustrated above, a grading curve allows academic institutions to ensure the distribution of students across certain grade point average (GPA) thresholds. As many professors establish the curve to target a course average of a C, [ clarification needed ] the corresponding grade point average equivalent would be a 2.0 ...
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
This is particularly used in optimization, where a knee point is the optimum point for some decision, for example when there is an increasing function and a trade-off between the benefit (vertical y axis) and the cost (horizontal x axis): the knee is where the benefit is no longer increasing rapidly, and is no longer worth the cost of further ...
Example of the typical "elbow" pattern used for choosing the number of clusters even emerging on uniform data. Even on uniform random data (with no meaningful clusters) the curve follows approximately the ratio 1/k where k is the number of clusters parameter, causing users to see an "elbow" to mistakenly choose some "optimal" number of clusters.
The best-fit curve is often assumed to be that which minimizes the sum of squared residuals. This is the ordinary least squares (OLS) approach. However, in cases where the dependent variable does not have constant variance, or there are some outliers, a sum of weighted squared residuals may be minimized; see weighted least squares .
Here we discuss de Boor's algorithm, an efficient and numerically stable scheme to evaluate a spline curve () at position . The curve is built from a sum of B-spline functions B i , p ( x ) {\displaystyle B_{i,p}(x)} multiplied with potentially vector-valued constants c i {\displaystyle \mathbf {c} _{i}} , called control points, S ( x ) = ∑ i ...