An evolutionary Pentagon Support Vector (PSV) finder method

• Please Cite:

• Mousavi, Seyed Muhammad Hossein, Vincent Charles, and Tatiana Gherman. "An Evolutionary Pentagon Support Vector Finder Method." Expert Systems with Applications 150 (2020): 113284.

• Link to the paper:

• https://www.sciencedirect.com/science/article/pii/S0957417420301093

This method is designed to improve classification tasks by reducing data size, removing outliers, and identifying support vectors using evolutionary algorithms and geometric computations. Below is a detailed explanation of the method's steps.

Methodology:

1. Load the Dataset:

   • Begin with a dataset that contains features and labels.
   • Split the dataset into training and testing subsets to evaluate the method on unseen data.

2. Evolutionary Clustering (ABC + FCM):

   • Use Artificial Bee Colony (ABC) for optimization. Bees simulate data points in the clustering process.
   • Fuzzy C Means (FCM) is used for soft clustering, assigning probabilities to data points belonging to clusters.
   • Replace Euclidean distance in FCM with Manhattan distance to improve clustering performance.

3. Label Clusters with K-Nearest Neighbors (K-NN):

   • After clustering, the data points in each cluster need to be labeled for classification.
   • Use K-NN to assign labels to clusters based on the proximity of their centers to the original training data.

4. Outlier Removal Using Pentagon Area and Angles:

   • Identify outliers by constructing a pentagon:
     • Select one sample from the current class and four samples from other classes.
     • Compute the area of the pentagon using the coordinates of its vertices.
     • Calculate the internal angles of the pentagon.
   • Apply thresholds:
     • If the pentagon's area exceeds a threshold, the sample is considered an outlier.
     • If any angle of the pentagon is outside the allowed range, the sample is also considered an outlier.

5. Final Classification:

   • Use Support Vector Machine (SVM) for classification.
   • Train the SVM on the reduced dataset (after clustering and outlier removal).
   • Compare the classification performance on:
     • The original dataset.
     • The reduced dataset (processed by the PSV method).

6. Validation:

   • Perform classification on benchmark datasets like Iris, Wine, and EEG Eye State.
   • Compare metrics such as accuracy, precision, recall, and runtime.
   • Analyze improvements in classification speed and accuracy.

Key Advantages:

• Reduces computational load by removing unnecessary data points (outliers).
• Retains classification accuracy or improves it on certain datasets.
• Incorporates geometrical and evolutionary computations for robust data processing.

• Link:

• http://nectar.northampton.ac.uk/13190/1/Mousavi_Seyed_etal_Elsevier_2020_An_Evolutionary_Pentagon_Support_Vector_Finder_Method.pdf