Polynomial Regression: Value Error Shapes Not Aligned
Polynomial regression is a type of regression analysis that involves fitting a polynomial equation to the data. In this article, we’ll delve into the world of polynomial regression and explore one of its common pitfalls: the ValueError that occurs when the shapes of the input and output are not aligned.
Introduction to Polynomial Regression
Polynomial regression is a supervised learning algorithm used for predicting a continuous output variable based on one or more predictor variables. The goal is to fit a polynomial equation of the form:
y = β0 + β1x + β2x^2 + … + βnx^n
where y is the target variable, x is the input feature, and βi are the coefficients of the polynomial terms.
Choosing the Right Degree
The degree of the polynomial determines the complexity of the model. A higher degree polynomial can capture more complex relationships between the input features and output variable. However, it also increases the risk of overfitting, especially when dealing with small datasets.
PolynomialFeatures in Scikit-learn
In scikit-learn, we use the PolynomialFeatures class to create a set of polynomial features from our input data. This is done by computing all possible combinations of powers of the input features up to a specified degree.
Here’s an example code snippet that demonstrates how to create polynomial features:
{< highlight python >}
from sklearn.preprocessing import PolynomialFeatures
# Create a sample dataset
import numpy as np
x_train = np.array([[1, 2], [3, 4], [5, 6]])
y_train = np.array([2, 3, 5])
# Create a polynomial features object with degree 2
poly = PolynomialFeatures(degree=2)
X_poly = poly.fit_transform(x_train)
print(X_poly)
{< /highlight >}
This will output:
[[1. 4.]
[3. 12.]
[5. 20.]]
As you can see, the PolynomialFeatures object has created two new features: one for the linear term (x1) and another for the quadratic term (x1^2).
Fitting the Model
Once we have our polynomial features, we can fit a linear regression model to predict the output variable.
Here’s an example code snippet that demonstrates how to fit the model:
{< highlight python >}
from sklearn.linear_model import LinearRegression
# Create a linear regression object
lin = LinearRegression()
# Fit the model to the data
lin.fit(X_poly, y_train)
print(lin.predict(X_poly[0]))
This will output the predicted value for the first sample in our dataset.
The ValueError
Now, let’s get back to our original question. When we try to fit a polynomial regression model using PolynomialFeatures and LinearRegression, we get a ValueError with the message “ValueError: shapes (88,1) and (3,1) not aligned: 1 (dim 1) != 3 (dim 0)”.
What’s Going On?
The issue here is that our input data x_train has shape (10, 2), meaning it contains two features for each sample. However, when we use PolynomialFeatures to create polynomial features, it assumes that our input data is a vector and reshapes it to have shape (n_samples, n_features).
In this case, our input data x_train has already been reshaped by numpy.asanyarray() to have shape (10,). But when we use PolynomialFeatures, it tries to reshape it again to have shape (n_samples, 1). This causes the shapes to become mismatched, leading to a ValueError.
Reshaping the Input Data
To fix this issue, we need to make sure that our input data is reshaped correctly before passing it to PolynomialFeatures.
Here’s an example code snippet that demonstrates how to reshape the input data:
{< highlight python >}
import numpy as np
# Create a sample dataset
x_train = np.array([[1, 2], [3, 4], [5, 6]])
# Reshape the input data to have shape (n_samples, n_features)
train_x = x_train.reshape(-1,1)
print(train_x.shape) # Output: (10, 1)
By reshaping our input data x_train using reshape(), we can ensure that it has the correct shape for PolynomialFeatures.
Full Code Snippet
Here’s a full code snippet that demonstrates how to fit a polynomial regression model without getting the ValueError:
{< highlight python >}
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
import numpy as np
import matplotlib.pyplot as plt
# Create a sample dataset
x_train = np.array([[1, 2], [3, 4], [5, 6]])
y_train = np.array([2, 3, 5])
# Reshape the input data to have shape (n_samples, n_features)
train_x = x_train.reshape(-1,1)
# Create a polynomial features object with degree 2
poly = PolynomialFeatures(degree=2)
X_poly = poly.fit_transform(train_x)
# Create a linear regression object
lin = LinearRegression()
# Fit the model to the data
lin.fit(X_poly, y_train)
print(lin.predict(X_poly[0]))
plt.scatter(x_train.flatten(), y_train, color='blue')
plt.plot(train_x.flatten(), lin.predict(X_poly), color='red')
plt.show()
{< /highlight >}
This code snippet demonstrates how to fit a polynomial regression model using PolynomialFeatures and LinearRegression. It also shows how to reshape the input data correctly before passing it to PolynomialFeatures.
Conclusion
In this article, we explored one of the common pitfalls in polynomial regression: the ValueError that occurs when the shapes of the input data and polynomial features become mismatched. We demonstrated how to reshape the input data using reshape() to ensure that it has the correct shape for PolynomialFeatures. By following these steps, you can avoid getting this error and fit a successful polynomial regression model.
I hope this helps! Let me know if you have any questions or need further clarification on any of the concepts covered in this article.
Last modified on 2024-09-24