logistic like curve fitting using machine learning

Question

I asked this question in data science threads, but didn't get an answer. Hence posting here.

I have a set of points of a function k(x). I am trying to do some curve fitting to find the exact k(x) function. It seems that the data points fit to a logistic like curve only a little shifted and stressed.

So far I have tried polynomial regression, but I don't feel the fitting is correct. I have attached a snap of the fitted curve here.

So my question is, is logistic regression only used in classification tasks? Or can it be used for curve fitting?

If not what are the other available techniques to fit a logistic like curve to a set of data points?

EDIT

Following is the code. (x,y) are the datapoints.

import matplotlib.pyplot as plt 
import numpy as np
from sklearn.linear_model import Ridge
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import mean_squared_error
from sklearn.linear_model import LogisticRegression

x = np.array([0.3, 0.4, 0.5, 0.6, 0.65, 0.67, 0.8])
y = np.array([-936, -892, -178.33, -50.7, -65.7, -70.44, -9])

degree = 5

model = make_pipeline(PolynomialFeatures(degree), Ridge(alpha=1E-10, fit_intercept=False))
# model = LogisticRegression(random_state=0, solver='lbfgs')
model.fit(x[:, None], y)
ridge = model.named_steps['ridge']
print(ridge.coef_)
coef = ridge.coef_

poly_mse = mean_squared_error(model.predict(x[:, None]), y)
print 'RMSE', math.sqrt(poly_mse)

predictions = model.predict(np.arange(0.28,0.85,0.0001).reshape(-1, 1))

plt.plot(x, y, 'ro', label='Measurement Data')
plt.plot(np.arange(0.28,0.85,0.0001), predictions, label="Best Fit: %.2f$X^4$ %.2f$X^3$ + %.2f$X^2$ + %.2fX %.2f" % (coef[-1],coef[-2],coef[-3],coef[-4],coef[-5]))
plt.title('K vs Barium Proportion (X) at 10kHz')
plt.xlabel('Barium Proportion (X)')
plt.ylabel('K')
plt.show()

Answer 1

Here is a graphical fitter using your data and a simple three-parameter logistic type equation, the fit seems fairly good to me.

plot

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import warnings

xData = numpy.array([0.3, 0.4, 0.5, 0.6, 0.65, 0.67, 0.8])
yData = numpy.array([-936.0, -892.0, -178.33, -50.7, -65.7, -70.44, -9.0])


def func(x, a, b, c): # Logistic B equation from zunzun.com
    return a / (1.0 + numpy.power(x/b, c))


# these are the same as the scipy defaults
initialParameters = numpy.array([1.0, 1.0, 1.0])

# curve fit the test data, ignoring warning due to initial parameter estimates
warnings.filterwarnings("ignore")
fittedParameters, pcov = curve_fit(func, xData, yData, initialParameters)

modelPredictions = func(xData, *fittedParameters) 

absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))

print('Parameters:', fittedParameters)
print('RMSE:', RMSE)
print('R-squared:', Rsquared)

print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(xData), max(xData))
    yModel = func(xModel, *fittedParameters)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)