# Support vector machine

Support vector machine |
---|

See also |

**Support Vector Machine** (SVM) is a supervised machine learning algorithm used for classification and regression problems. It works by mapping data to a high-dimensional feature space, then constructing a hyperplane (or line) that best divides the data. In this way, SVM can accurately classify and predict the outcome of a given data set. From the management point of view, SVM can be used to create complex decision boundaries, identify patterns, and predict outcomes. It can also be used to identify outliers and improve the accuracy of predictions by reducing errors and overfitting. As such, it can be a powerful tool for effectively managing large datasets and making accurate predictions.

## Example of support vector machine

- Support Vector Machine (SVM) is often used in text classification tasks, such as sentiment analysis or natural language processing. In these tasks, SVM creates a hyperplane in the vector space, with each dimension corresponding to a word in the corpus. Then, it maps each document to the vector space and classifies it based on which side of the hyperplane the document falls on.
- SVM can also be used for medical research, where it is used to classify different types of cancer or identify genes that are related to a certain disease. For example, SVM can be used to create a model that can accurately predict whether a patient is likely to develop cancer based on the genes they possess.
- SVM is also used in image recognition tasks, such as facial recognition or object detection. In this case, SVM creates a hyperplane to divide the image into two classes: objects and non-objects. Then, it maps each pixel to the vector space and classifies it according to which side of the hyperplane it falls on.
- Finally, SVM can be used in financial analysis tasks, such as stock market predictions or credit risk assessment. In this case, SVM creates a hyperplane in the vector space, with each dimension corresponding to a financial indicator or feature. Then, it maps each stock or loan to the vector space and classifies it based on which side of the hyperplane it falls on.

## Formula of support vector machine

The support vector machine (SVM) is a supervised learning algorithm that is used for classification and regression problems. It works by mapping data to a high-dimensional feature space and then constructing a hyperplane (or line) that best divides the data. The equation for the hyperplane is given by:

$$\begin{equation} w^{T}x + b = 0 \end{equation}$$

where (w) is a vector of weights, (x) is a vector of features, and (b) is a bias term. The goal is to find the optimal set of weights and bias term that will best separate the data points into two classes.

To find the optimal set of weights and bias term, the SVM algorithm minimizes a cost function, also known as the objective function. This cost function is a measure of how well the model is performing and is typically denoted as $$(J(\theta))$$. The cost function for the SVM is given by:

$$\begin{equation} J(\theta) = \frac{1}{2}||w||^{2} + C \sum_{i=1}^{n} \zeta_{i} \end{equation}$$

where $$(||w||^{2})$$ is the squared norm of the weight vector and (C) is a regularization parameter. The term $$(\zeta_{i})$$ is a penalty term that is used to penalize points that are on the wrong side of the hyperplane. The penalty term is given by:

$$\begin{equation} \zeta_{i} = \max(0, 1-y_{i}(w^{T}x_{i} + b)) \end{equation}$$

where $$(y_{i})$$ is the label of the $$(i^{th})$$ feature vector, $$(x_{i})$$ is the $$(i^{th})$$ feature vector, and (b) is the bias term.

The cost function is minimized using an iterative optimization technique such as gradient descent. The goal is to find the optimal set of weights and bias term that minimizes the cost function while allowing the data points to be accurately classified.

## When to use support vector machine

Support Vector Machine (SVM) is a powerful supervised machine learning algorithm that can be used to solve both classification and regression problems. It is particularly useful when the dataset is large or contains complex patterns. Here are some of the most common applications for SVM:

**Classification of text documents or images**: SVM can be used to classify documents or images based on their contents.**Regression problems**: SVM can be used to predict the value of a continuous variable (e.g. stock prices).**Anomaly detection**: SVM can be used to identify outliers from a dataset and help to reduce errors and overfitting.**Support vector clustering**: SVM can be used for unsupervised learning to identify clusters in a dataset.**Feature selection**: SVM can be used to select the most important features of a dataset, which can then be used to build a predictive model.

## Types of support vector machine

Support Vector Machines (SVMs) are a type of supervised machine learning algorithm used for classification and regression problems. There are several types of SVMs, each with its own advantages and disadvantages. These include:

**Linear Support Vector Machines (Linear SVM)**: Linear SVMs are the most basic type of SVM, which creates a hyperplane that best separates two classes. It is suitable for training data with a linear separable pattern.**Nonlinear Support Vector Machines (Nonlinear SVM)**: Nonlinear SVMs are used for training data with a nonlinear separable pattern. They use a combination of kernels, such as polynomial, radial basis function (RBF), and sigmoid, to create a boundary that separates the two classes.**Kernel Support Vector Machines (Kernel SVM)**: Kernel SVMs are used when the data is not linearly separable. The kernel functions are used to transform the data into a higher dimensional space, where it can be separated by a hyperplane.**Support Vector Machines with Cost Sensitive Loss (CSL-SVM)**: CSL-SVMs are used when the data contains imbalanced classes. It uses a cost-sensitive loss function to adjust the model’s decision boundary, and improve its performance on imbalanced datasets.**Support Vector Regression (SVR)**: SVR is used for regression problems. It uses a linear or nonlinear kernel to create a model that predicts an output value for a given input.

## Advantages of support vector machine

One of the main advantages of using Support Vector Machines (SVM) is its ability to create complex decision boundaries, identify patterns, and predict outcomes with high accuracy. Additionally, SVMs provide several other benefits, including:

**Robustness**: SVMs are not sensitive to outliers and are less prone to overfitting than other algorithms.**Flexibility**: SVMs can work with a variety of data types and can be used for both linear and non-linear problems.**Sparse Solutions**: SVMs can produce sparse solutions, which are solutions that only use a small subset of the available data points. This can significantly reduce the computational cost of training and can improve the generalization performance.**Versatility**: SVMs can be used for both classification and regression tasks.**High Accuracy**: SVMs can provide high accuracy and can be tuned to optimize performance.

## Limitations of support vector machine

Support Vector Machine (SVM) is a powerful supervised machine learning algorithm used for classification and regression problems. However, like any other machine learning algorithm, SVM has some drawbacks. Here are some of the limitations of SVM:

- SVMs can be computationally expensive, as the training time increases with the size of the data set.
- SVMs are sensitive to noise and outliers, and can be easily overfitted if the data set is not properly preprocessed.
- The kernel functions used in SVM can be difficult to choose, and the parameters of the kernel functions require careful tuning.
- SVMs are not well-suited for large data sets, as the training time increases exponentially with the number of features.
- SVMs are prone to the “curse of dimensionality”, meaning that they become less effective as the number of features increases.

Other approaches related to Support Vector Machine (SVM) include kernel methods, decision tree learning, and artificial neural networks.

**Kernel Methods**: Kernel methods are similar to SVM in that they map data points to a higher dimensional feature space, but they use different types of kernels to do so. Popular kernels include linear, polynomial, radial basis function (RBF), and sigmoid.**Decision Tree Learning**: Decision tree learning is a supervised machine learning technique used to classify and predict outcomes. The algorithm works by constructing a decision tree based on a given dataset, where each node in the tree represents a feature and each branch represents a decision or rule.**Artificial Neural Networks**: Artificial neural networks are also a supervised machine learning technique. Unlike SVM, which maps data points to a feature space, neural networks are used to approximate nonlinear functions of input data. They consist of interconnected nodes that use weights and bias to classify and predict outcomes.

In summary, Support Vector Machine (SVM) is a supervised machine learning algorithm used for classification and regression problems, but there are also other approaches related to SVM, such as kernel methods, decision tree learning, and artificial neural networks.

## Suggested literature

- Noble, W. S. (2006).
*What is a support vector machine?*. Nature biotechnology, 24(12), 1565-1567. - Hearst, M. A., Dumais, S. T., Osuna, E., Platt, J., & Scholkopf, B. (1998).
*Support vector machines*. IEEE Intelligent Systems and their applications, 13(4), 18-28.