Sum of Squares Function

A Sum of Squares Function is a metric based on the sum operation on square functions.

• Context:
  • It can be represented as [math]\displaystyle{ \sum^N_1 (x^2_i) }[/math].
• Example(s):
  • [math]\displaystyle{ \sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^2 }[/math] where [math]\displaystyle{ \bar{y} }[/math] is the mean (sum of square residuals).
  • …
• Counter-Example(s):
  • Sum of Residuals.
• See: Regression Tree Splitting Criterion, Least Squares, Nonlinear Least Squares, Partition of Sums of Qquares.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/sum_of_squares Retrieved:2017-10-2.
  • In mathematics, statistics and elsewhere, sums of squares occur in a number of contexts:
    • For the "sum of squared deviations", see Least squares.
    • For the "sum of squared differences", see Mean squared error.
    • For the "sum of squared error", see Residual sum of squares.
    • For the "sum of squares due to lack of fit", see Lack-of-fit sum of squares.
    • For sums of squares relating to model predictions, see Explained sum of squares.
    • For sums of squares relating to observations, see Total sum of squares.
    • For sums of squared deviations, see Squared deviations.
    • For modelling involving sums of squares, see Analysis of variance.
    • For modelling involving the multivariate generalisation of sums of squares, see Multivariate analysis of variance

2014

• http://en.wikipedia.org/wiki/Least_squares#Problem_statement
  • The least squares method finds its optimum when the sum, S, of squared residuals :[math]\displaystyle{ S=\sum_{i=1}^{n}{r_i}^2 }[/math]

1994

• (Hagan & Menhaj, 1994) ⇒ Martin T. Hagan, and Mohammad B. Menhaj. (1994). “Training Feedforward Networks with the Marquardt Algorithm.” In: IEEE Transactions on Neural Networks Journal, 5(6). doi:10.1109/72.329697
  • QUOTE: ....If we assume that [math]\displaystyle{ V(\underline{x}) }[/math] is a sum of squares function [math]\displaystyle{ V(\underline{x}) = \sum^N_{i=q} e^2_i(\underline{x}) }[/math] ...

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