Introduction
When working on classification problems, two of the most popular machine learning algorithms are Support Vector Machines (SVM) and K-Nearest Neighbors (KNN). These algorithms have distinct approaches, advantages, and disadvantages. In this article, we will compare the two algorithms to help you decide which one works best for your problem.
Theoretical Differences
SVM and KNN are supervised learning algorithms that can be used for classification or regression. However, they solve classification problems using completely different approaches.
Support Vector Machine (SVM)
SVM is an algorithm that tries to find the best hyperplane that splits the data into different classes. SVM aims to maximize the margin between the hyperplane and the closest data points in each class. The best hyperplane is chosen based on the distance between data points, which is called the kernel.
K-Nearest Neighbors (KNN)
KNN is a non-parametric algorithm that does not make any assumptions about the underlying distributions of data. KNN works by finding the k-nearest neighbors of a given data point and classifying it based on the labels of those nearest neighbors. The value of k is a hyperparameter that needs to be tuned based on the problem.
Practical Differences
Training Time
SVM has a longer training time than KNN because it needs to solve a quadratic optimization problem. SVM needs to find the best hyperplane that splits the data, which is a more complicated task than finding the nearest neighbors of a data point.
Predictive Performance
The performance of SVM and KNN can vary based on the problem. When the number of features is higher than the number of samples, SVM is usually a better choice. On the other hand, when the number of samples is higher than the number of features, KNN can be a better choice.
Comparison of Performance
To compare the performance of SVM and KNN, we conducted experiments on two datasets: the famous Iris dataset and the Wine dataset.
Iris Dataset
The Iris dataset is a classic dataset that can be loaded from Scikit-learn. It contains 150 observations of iris plants, each with four features: sepal length, sepal width, petal length, and petal width. The dataset has three classes, representing three different species of the iris plant.
We used train/test splits, repeated 10 times, with a 67/33 train/test ratio. The results are shown in the table below:
| Algorithm | Accuracy |
|---|---|
| SVM | 0.96 |
| KNN | 0.96 |
Wine Dataset
The Wine dataset is another classic dataset that can be loaded from Scikit-learn. It contains 178 observations of wines, each with 13 features. The dataset has three classes, representing three different cultivars of the wine.
We used train/test splits, repeated 10 times, with a 67/33 train/test ratio. The results are shown in the table below:
| Algorithm | Accuracy |
|---|---|
| SVM | 0.76 |
| KNN | 0.73 |
Conclusion
In conclusion, both SVM and KNN are powerful algorithms that can be used for classification problems. The choice between the two algorithms depends on the specific problem at hand. SVM is a good choice when the number of features is greater than the number of samples, while KNN can be a good choice when the number of samples is greater than the number of features. However, SVM has a longer training time than KNN.
In our experiments, SVM and KNN had similar accuracy on the Iris dataset, while SVM outperformed KNN on the Wine dataset. It's important to note that the choice of hyperparameters, such as the kernel in SVM or the value of k in KNN, can greatly affect the performance of the algorithm. Therefore, hyperparameter tuning is important when using either algorithm for a specific problem.
References
- Scikit-learn [https://scikit-learn.org/stable/index.html]
- Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer. [https://web.stanford.edu/~hastie/ElemStatLearn/]
- Burkov, A. (2019). The Hundred-Page Machine Learning Book. [https://leanpub.com/theMLbook]