Machine learning plays a crucial role in designing algorithm optimization problems, particularly in implementing the Platt SMO algorithm. This article discusses the optimization of Support Vector Machines (SVM) by focusing on the implementation and enhancement of the Platt SMO algorithm. Additionally, it explores the integration of a genetic algorithm framework, GAFT, to further optimize SVM parameters.
**Heuristic Selection of Variables in SMO**
In the SMO algorithm, selecting a pair of α values to optimize at each iteration is essential. Heuristic selection helps identify the most impactful variables, allowing the objective function to decrease as rapidly as possible. The first and second αs are selected using different heuristics.
**Selection of the First Variable**
The selection of the first variable operates in an outer loop. Instead of scanning the entire α list, we alternate between the full training set and the non-boundary samples. Initially, we scan the entire dataset to check for violations of the KKT conditions. If any α_i violates these conditions, it must be optimized.
The Karush-Kuhn-Tucker (KKT) conditions serve as necessary and sufficient conditions for solving positive definite quadratic programming problems. For the SVM dual problem, the KKT conditions are relatively simple. After optimizing the α values based on the KKT conditions, we then focus on non-boundary αs—those that are not equal to 0 or C. These points are also checked and optimized if needed.
This process continues alternating between the two data sets until all αs satisfy the KKT conditions, at which point the algorithm terminates.
To efficiently select αs with the largest step size, we cache the error values for all data points. A custom SVMUtil class was created to store key SVM variables and auxiliary methods.
**Choice of the Second Variable**
The selection of the second variable occurs in an inner loop. Once α1 is chosen, we aim to select α2 such that the optimization leads to a significant change. Based on previous derivations, the new α2 depends on |E1 - E2|. When E1 is positive, we choose the smallest Ei as E2. By maintaining a buffer of Ei values, we can quickly find the maximum step size.
If this heuristic isn’t sufficient, we proceed with additional steps: select a non-boundary sample that causes a large enough drop in the function value, or fall back to the full dataset if necessary. If no suitable candidate is found, we reselect α1.
**Allowing Tolerance in KKT Conditions**
The Platt paper introduces a tolerance in the KKT condition checks, allowing for small errors. This is implemented in Python to ensure robustness during optimization.
For more details, you can refer to the complete implementation of Platt SMO 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).
After applying Platt SMO to our dataset, we observed a clear decision boundary with support vectors. Visualizing the results shows that the support vectors differ slightly from those produced by a simplified version of the SMO algorithm.
**Optimizing SVM Using Genetic Algorithms**
Inspired by my recent work on a genetic algorithm framework, I decided to apply genetic algorithms (GA) to optimize SVM. GA serves as a powerful heuristic search method, making it ideal for this task.
Using GA, we directly optimize the original form of SVM, which involves minimizing the distance from each data point to the decision boundary. With the help of the GAFT framework, only a few lines of code are needed to implement the fitness function. The fitness function calculates the minimum distance from data points to the separating line, which is then used for evolutionary iterations.
The GAFT project can be found at [https://github.com/PytLab/gaft](https://github.com/PytLab/gaft), where you can find detailed documentation.
**Creating Individuals and Populations**
For two-dimensional data, we only need to optimize three parameters: [w1, w2, b]. Each individual in the population represents these parameters, and the population size is determined accordingly.
**Genetic Operators and GA Engine**
We use built-in operators from the GAFT framework to create the genetic engine. This includes crossover, mutation, and selection mechanisms that drive the evolutionary process.
**Fitness Function**
The fitness function is straightforward, involving just a few lines of code that calculate the distance from each data point to the decision boundary.
**Starting the Iteration**
We run the genetic algorithm for 300 generations, allowing the population to evolve toward an optimal solution.
After the iterations, we visualize the decision boundary generated by the genetic algorithm. The resulting segmentation curve demonstrates the effectiveness of the approach.
By combining machine learning techniques like SMO with evolutionary algorithms like GA, we achieve more efficient and accurate SVM models. This hybrid approach opens up new possibilities for optimizing complex machine learning tasks.
HP Envy x360 lcd back cover,L93203-001,HP envy x360 15-ed
S-yuan Electronic Technology Limited , https://www.syuanelectronic.com