Machine learning will definitely be used to design algorithm optimization problems, primarily focusing on implementing the Platt SMO algorithm. The following article discusses the optimization of SVM, with a focus on enhancing the Platt SMO algorithm to build a more efficient SVM model. It also explores the possibility of using a genetic algorithm framework, GAFT, to initialize and optimize the SVM model.
**Heuristic Selection of Variables in SMO**
In the SMO algorithm, we need to select a pair of α values for optimization at each step. By applying heuristic selection, we can identify the most effective variables to optimize, ensuring that the objective function decreases as quickly as possible.
Different heuristics are applied for selecting the first and second α values in Platt SMO.
**Selection of the First Variable**
The selection of the first variable is part of the outer loop. Instead of iterating through the entire α list as before, we now alternate between the full training set and the non-boundary sample set:
- First, we scan the entire training set to check for any violations of the KKT conditions. If an α_i and its corresponding x_i, y_i violate the KKT condition, it needs to be optimized.
- The Karush-Kuhn-Tucker (KKT) conditions are necessary and sufficient for the optimal solution of a positive definite quadratic programming problem. For the SVM dual problem, the KKT conditions are relatively simple.
After scanning the entire training set and optimizing the corresponding α values, we then focus on the non-boundary αs in the next iteration. These are α values that are not equal to 0 or C. Again, these points are checked for KKT violations and optimized if needed.
This process continues by alternating between the two data sets until all αs satisfy the KKT conditions, at which point the algorithm terminates.
To efficiently select α values that result in the largest step size, we cache the error values for all data points. A custom SVMUtil class was created to store important SVM variables and provide auxiliary methods.
A snippet of code for the alternating traversal of the first variable is shown below, with the complete Python implementation available at: [https://github.com/PytLab/MLBox/blob/master/svm/svm_platt_smo.py](https://github.com/PytLab/MLBox/blob/master/svm/svm_platt_smo.py)
**Choice of the Second Variable**
The selection of the second variable in SMO is part of the inner loop. Once the first α1 is chosen, we aim to select the second α2 such that the change after optimization is significant.
From our previous derivation, we know that the new α2 change depends on |E1 - E2|. When E1 is positive, we choose the smallest Ei as E2. The Ei values of each sample are typically cached in a list, and we select the α2 with the maximum |E1 - E2| to achieve the largest step size.
Sometimes, even with this heuristic, the function value may not decrease sufficiently. In such cases, the following steps are taken:
- Select a sample from the non-boundary dataset that causes a sufficient drop in the function value as the second variable.
- If no such sample exists, search the entire dataset.
- If still no suitable candidate is found, reselect the first α1.
Here is the Python implementation for choosing the second variable.
**Allowing Tolerance in KKT Conditions**
In the Platt paper, there is a tolerance allowed for the KKT conditions, meaning that some errors are permitted. This is implemented in Python as follows.
For the complete implementation of Platt SMO, see: [https://github.com/PytLab/MLBox/blob/master/svm/svm_platt_smo.py](https://github.com/PytLab/MLBox/blob/master/svm/svm_platt_smo.py)
Using Platt SMO, we optimized the previous dataset, resulting in the following visualization:
Visualizing the decision boundary and support vectors shows that the support vectors optimized by Platt SMO differ slightly from those obtained using the simplified SMO algorithm.
**Optimizing SVM Using Genetic Algorithms**
Since I recently developed a genetic algorithm framework, I decided to try using it to optimize SVM. Genetic algorithms are powerful heuristic search methods, making them ideal for optimizing complex models like SVM.
By using a genetic algorithm, we can directly optimize the original form of SVM, which is the most intuitive representation:
With the help of my own genetic algorithm framework, GAFT, I was able to optimize SVM with just a few lines of Python code. The key task was writing the fitness function, which calculates the minimum distance from each data point to the decision boundary.
The GAFT project is available at: [https://github.com/PytLab/gaft](https://github.com/PytLab/gaft), with detailed instructions in the README.
I started by creating populations for evolutionary iterations.
**Creating Individuals and Populations**
For two-dimensional data points, we only need to optimize three parameters: [w1, w2] and b. Each individual is defined accordingly.
We created a population of a certain size.
**Creating Genetic Operators and GA Engines**
Nothing special here—just use the built-in operators from the framework.
**Fitness Function**
The fitness function is straightforward, based on the original form of SVM. It takes just a few lines of code.
**Starting the Iteration**
We ran the algorithm for 300 generations.
Visualizing the decision boundary optimized by the genetic algorithm shows the resulting classification curve.
The final segmentation curve is displayed below, showing how the genetic algorithm improved the SVM model.
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