From 3f0394ebe3acb76d3073b88b9cccb9f7d40968a5 Mon Sep 17 00:00:00 2001
From: Andru Liu <90433630+WallabyLester@users.noreply.github.com>
Date: Mon, 7 Oct 2024 17:06:46 -0700
Subject: [PATCH] Initial port to open-source. Creation of RBF class using
 numpy.

---
 RBF_numpy.py | 87 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 87 insertions(+)
 create mode 100644 RBF_numpy.py

diff --git a/RBF_numpy.py b/RBF_numpy.py
new file mode 100644
index 0000000..e2c77cb
--- /dev/null
+++ b/RBF_numpy.py
@@ -0,0 +1,87 @@
+import numpy as np
+
+class RBFNetwork:
+    """ Basic radial basis function (RBF) neural network class, numpy implementation. 
+
+    Contains input layer, one hidden layer with RBF activation, and linear output layer. 
+    RBF activation is a Gaussian.
+
+    ...
+
+    Attributes
+    ----------
+    input_dim : int
+        The dimension of the RBF centers. 
+    n_centers : int
+        The number of RBF centers.
+
+    Methods
+    -------
+    gaussian(x, center):
+        Forms the gaussian given the center and input.
+    predict(x, center):
+        Predicts from the model using the gaussian and saved weights.
+    train(x, target):
+        Train the RBF model on stored data. 
+    """
+    def __init__(self, input_dim, n_centers):
+        """ Constructs distribution parameters and initializes weights.
+
+        Parameters
+        ----------
+            input_dim : int
+                The dimension of the RBF centers.
+            n_centers : int
+                The number of RBF centers.
+        """
+        self.input_dim = input_dim
+        self.n_centers = n_centers
+        self.centers = np.random.rand(n_centers, input_dim)     # expected value
+        self.sigma = 1.0                                        # variance
+        self.weights = np.random.rand(n_centers)
+
+    def gaussian(self, x, center):
+        """ Find likelihood of x under Gaussian distribution centered at center with 
+        standard deviation sigma. 
+
+        Parameters
+        ----------
+            x : ndarray[Any, dtype[float64]]
+                The point in space to evaluate the Gaussian.
+            center : ndarray[Any, dtype[float64]]
+                Mean/center of Gaussian distribution.
+
+        Returns
+        -------
+        Height of Gaussian curve at x. 
+
+        """
+        return np.exp(-np.linalg.norm(x - center) ** 2 / (2 * self.sigma ** 2))
+
+    def predict(self, x):
+        """ Prediction function of form dot(Activations, Weights).
+
+        Parameters
+        ----------
+            x : ndarray[Any, dtype[float64]]
+                The point in space to evaluate the Gaussian.
+
+        Returns
+        -------
+        Approximation of the target function. 
+        """
+        activations = np.array([self.gaussian(x, center) for center in self.centers])
+        return np.dot(activations, self.weights)
+
+    def train(self, x, target):
+        """ Training function to adapt weights to known datapoints.
+
+        Parameters
+        ----------
+            x : ndarray[Any, dtype[float64]]
+                The point in space to evaluate the Gaussian.
+            target : float64
+                Target data point.
+        """
+        activations = np.array([self.gaussian(x, center) for center in self.centers])
+        self.weights += 0.01 * (target - np.dot(activations, self.weights)) * activations
\ No newline at end of file