SciPy | Curve Fitting
Given a Dataset comprising of a group of points, find the best fit representing the Data.
We often have a dataset comprising of data following a general path, but each data has a standard deviation which makes them scattered across the line of best fit. We can get a single line using curve-fit() function.
Using SciPy :
Scipy is the scientific computing module of Python providing in-built functions on a lot of well-known Mathematical functions. The scipy.optimize package equips us with multiple optimization procedures. A detailed list of all functionalities of Optimize can be found on typing the following in the iPython console:
Among the most used are Least-Square minimization, curve-fitting, minimization of multivariate scalar functions etc.
Curve Fitting Examples –
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As seen in the input, the Dataset seems to be scattered across a sine function in the first case and an exponential function in the second case, Curve-Fit gives legitimacy to the functions and determines the coefficients to provide the line of best fit.
Code showing the generation of the first example –
Sine function coefficients: [ 3.66474998 1.32876756] Covariance of coefficients: [[ 5.43766857e-02 -3.69114170e-05] [ -3.69114170e-05 1.02824503e-04]]
Second example can be achieved by using the numpy exponential function shown as follows:
However, if the coefficients are too large, the curve flattens and fails to provide the best fit. The following code explains this fact:
Sine funcion coefficients: [ 0.70867169 0.7346216 ] Covariance of coefficients: [[ 2.87320136 -0.05245869] [-0.05245869 0.14094361]]
The blue dotted line is undoubtedly the line with best-optimized distances from all points of the dataset, but it fails to provide a sine function with the best fit.
Curve Fitting should not be confused with Regression. They both involve approximating data with functions. But the goal of Curve-fitting is to get the values for a Dataset through which a given set of explanatory variables can actually depict another variable. Regression is a special case of curve fitting but here you just don’t need a curve that fits the training data in the best possible way(which may lead to overfitting) but a model which is able to generalize the learning and thus predict new points efficiently.