The equation used to classify new points in Support Vector Machines (SVM) is known as the Support Vector Assertion. SVM is a popular machine learning algorithm used for classification and regression tasks. It is particularly effective in solving complex problems with high-dimensional data.
The Support Vector Assertion is derived from the decision function of SVM. In SVM, the decision function is used to determine the class label of a new data point based on its feature values. The decision function is defined as:
f(x) = sign(w^T x + b)
Here, x represents the feature vector of the new data point, w is the weight vector, and b is the bias term. The sign function returns +1 if the argument is positive or zero, and -1 otherwise. The decision function essentially calculates the signed distance of the new data point from the decision boundary.
The weight vector w and bias term b are learned during the training phase of the SVM algorithm. The goal of SVM is to find the hyperplane that maximally separates the data points of different classes. The hyperplane is defined by the equation:
w^T x + b = 0
The support vectors are the data points that lie closest to the decision boundary. These support vectors play a important role in the classification process. The decision function evaluates the distance of a new data point from the decision boundary using the support vectors. The sign of this distance determines the class label assigned to the new data point.
To classify a new data point using the Support Vector Assertion, we substitute the feature vector x into the decision function. If the result is positive, the data point belongs to one class, and if it is negative, the data point belongs to the other class. The magnitude of the result can also provide a measure of confidence in the classification decision.
For example, let's consider a binary classification problem where we want to classify flowers as either "Iris setosa" or "Iris versicolor" based on their sepal length and width. After training an SVM model on a labeled dataset, we can use the Support Vector Assertion to classify a new flower with sepal length 5.2 and width 3.1. We substitute the feature vector [5.2, 3.1] into the decision function:
f([5.2, 3.1]) = sign(w^T [5.2, 3.1] + b)
If the result is positive, we classify the flower as "Iris setosa," and if it is negative, we classify it as "Iris versicolor."
The equation used to classify new points in SVM is the Support Vector Assertion, which is derived from the decision function of the SVM algorithm. It calculates the signed distance of a new data point from the decision boundary and assigns a class label based on the sign of this distance.
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