feat: add Radial Basis Function Neural Network (Implements #12322) #13636
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Implements TheAlgorithms#12322 - Add RadialBasisFunctionNetwork class with train() and predict() methods - Use KMeans clustering for RBF center initialization - Implement Gaussian RBF activation functions - Use least-squares fitting for output weight calculation - Include comprehensive doctests and error handling - Add detailed docstrings with mathematical formulas
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| weights: Output layer weights | ||
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| def __init__(self, num_centers: int = 10, gamma: float = 1.0): |
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Please provide return type hint for the function: __init__. If the function does not return a value, please provide the type hint as: def function() -> None:
| self.centers = None | ||
| self.weights = None | ||
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| def _gaussian_rbf(self, x: np.ndarray, center: np.ndarray) -> float: |
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As there is no test file in this pull request nor any test function or class in the file machine_learning/rbf_network.py, please provide doctest for the function _gaussian_rbf
Please provide descriptive name for the parameter: x
| distance_squared = np.sum((x - center) ** 2) | ||
| return np.exp(-self.gamma * distance_squared) | ||
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| def _compute_rbf_activations(self, X: np.ndarray) -> np.ndarray: # noqa: N803 |
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As there is no test file in this pull request nor any test function or class in the file machine_learning/rbf_network.py, please provide doctest for the function _compute_rbf_activations
Please provide descriptive name for the parameter: X
machine_learning/rbf_network.py
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| return activations | ||
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| def train(self, X: np.ndarray, y: np.ndarray) -> None: # noqa: N803 |
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Please provide descriptive name for the parameter: y
machine_learning/rbf_network.py
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| # weights = (A^T A)^-1 A^T y, where A is the activation matrix | ||
| self.weights = np.linalg.lstsq(activations, y, rcond=None)[0] | ||
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| def predict(self, X: np.ndarray) -> np.ndarray: # noqa: N803 |
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Please provide descriptive name for the parameter: X
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Description
Implements #12322
This PR adds a complete implementation of Radial Basis Function Neural Network (RBFNN) to the machine learning algorithms collection.
Implementation Details
Architecture:
Features:
__init__(num_centers, gamma): Initialize network parameterstrain(X, y): Train using KMeans clustering and least-squarespredict(X): Make predictions on new dataTraining Process:
Mathematical Foundation
The Gaussian RBF is defined as:
φ(x) = exp(-γ * ||x - c||²)
Where:
Output is computed as weighted sum:
y = Σ(w_i * φ_i(x))Testing
All doctests pass successfully:
python -m doctest machine_learning/rbf_network.py -v
Test coverage:
Requirements Met
✅ RBFNN class with
num_centersandgammainitialization✅
train(X, y)method with KMeans and least-squares✅
predict(X)method for making predictions✅ Gaussian RBF activation functions
✅ Comprehensive documentation and doctests
Example Usage
import numpy as np
from machine_learning.rbf_network import RadialBasisFunctionNetwork
Generate training data
X_train = np.random.randn(100, 2)
y_train = np.sum(X_train ** 2, axis=1)
Create and train RBFNN
rbfnn = RadialBasisFunctionNetwork(num_centers=10, gamma=1.0)
rbfnn.train(X_train, y_train)
Make predictions
X_test = np.random.randn(20, 2)
predictions = rbfnn.predict(X_test)
References