Implementation of Probabilistic Neural Network
The Python code provides a simplified illustration of the core functionalities happening within a PNN. It calculates distances between the new data point and training data points, mimicking the pattern station. Then, it roughly simulates the summation station by adding distances for hypothetical classes. While a real PNN would use Bayes’ rule and probability distributions, this code offers a basic understanding of the PNN’s decision-making process.
A true PNN would use kernel functions (e.g., Gaussian) to estimate the probability density functions for each class and then apply Bayes’ rule to make a probabilistic classification.
- Use a Kernel Function: Replace the Euclidean distance with a kernel function (e.g., Gaussian).
- Estimate Probabilities: Calculate the probability density for each class.
- Apply Bayes’ Rule: Use the estimated probabilities to classify the new data point.
import numpy as np
# Example training data (features and labels)
training_data = np.array([
[1.0, 2.0, 0], # [feature1, feature2, class_label]
[1.5, 1.8, 0],
[5.0, 8.0, 1],
[6.0, 9.0, 1]
])
# New data point to classify
new_data = np.array([2.0, 3.0])
# Gaussian kernel function
def gaussian_kernel(distance, sigma=1.0):
return np.exp(-distance**2 / (2 * sigma**2))
# Calculate Gaussian kernel values between new_data and each training point
kernel_values = []
for data_point in training_data:
distance = np.linalg.norm(new_data - data_point[:2])
kernel_value = gaussian_kernel(distance)
kernel_values.append((kernel_value, data_point[2]))
# Separate kernel values by class
class_1_kernels = [kv[0] for kv in kernel_values if kv[1] == 0]
class_2_kernels = [kv[0] for kv in kernel_values if kv[1] == 1]
# Sum kernel values for each class
class_1_sum = sum(class_1_kernels)
class_2_sum = sum(class_2_kernels)
# Predict the class with the highest sum of kernel values (probability)
predicted_class = 0 if class_1_sum > class_2_sum else 1
print(f"Predicted class: {predicted_class}")
Output:
Predicted class: 0
Probabilistic Neural Networks: A Statistical Approach to Robust and Interpretable Classification
Probabilistic Neural Networks (PNNs) are a class of artificial neural networks that leverage statistical principles to perform classification tasks. Introduced by Donald Specht in 1990, PNNs have gained popularity due to their robustness, simplicity, and ability to handle noisy data. This article delves into the intricacies of PNNs, providing a detailed explanation, practical examples, and insights into their applications.
Table of Content
- What is Probabilistic Neural Network (PNN)?
- Bayes’ Rule in Probabilistic Neural Network
- How Does PNNs Work?
- Implementation of Probabilistic Neural Network
- Advantages and Disadvantages of PNNs
- Use-Cases and Applications of PNN