Читать книгу Artificial Intelligence and Quantum Computing for Advanced Wireless Networks - Savo G. Glisic - Страница 21

Support vector machine (SVM) is a supervised ML algorithm that can be used for both classification and regression challenges [48, 49]. However, it is mostly used in classification problems. In the SVM algorithm, we plot each data item as a point in n‐dimensional space (where n is the number of features) with the value of each feature being the value of a particular coordinate. Then, we perform classification by finding the hyperplane that differentiates the two classes very well, as illustrated in Figure 2.5.

Support vectors are simply the coordinates of individual observations. The SVM classifier is a frontier that best segregates the two classes (hyperplane Figure 2.5 (upper part)/line Figure 2.5 (lower part)). The next question is how we identify the right hyperplane. In general, as a rule of thumb, we select the hyperplane that better segregates the two classes, that is,

 If multiple choices are available, choose the option that maximizes the distances between nearest data point (either class) and the hyperplane. This distance is called the margin.Figure 2.5 Data classification.Figure 2.6 Classification with outliers.

 If the two classes cannot be segregated using a straight line as one of the elements lies in the territory of other class as an outlier (see Figure 2.6), the SVM algorithm has a feature to ignore outliers and find the hyperplane that has the maximum margin. Hence, we can state that SVM classification is robust to outliers.

 In some scenarios, we cannot have a linear hyperplane between the two classes. Linear classifiers are not complex enough sometimes. In such cases, SVM maps data into a richer feature space including nonlinear features, and then constructs a hyperplane in that space so that all other equations are identical (Figure 2.7). Formally, it preprocesses data with: x → Φ(x) and then learns the map from Φ(x) to y as follows:

Figure 2.7 Classifiers with nonlinear transformations.

The e1071 package in R is used to create SVMs.

It has helper functions as well as code for the naive Bayes classifier. The creation of an SVM in R and Python follows similar approaches:

#Import Library require(e1071) #Contains the SVM Train <- read.csv(file.choose()) Test <- read.csv(file.choose()) # there are various options associated with SVM training; like changing kernel, gamma and C value. # create model model <- svm(Target~Predictor1+Predictor2+Predictor3,data=Train,kernel='linear',gamma=0.2,cost=100) #Predict Output preds <- predict(model,Test) table(preds)