Soft SVM - Soft Support Vector Machine - Machine Learning

☕ https://buymeacoffee.com/pankajkporwal ☕ Soft Support Vector Machine ( Soft SVM ) – Soft Maximum Margin Classifier – Machine Learning Given (xi, yi), I = 1, 2, …, n, where xi – input, predictor variable, covariate, independent variable yi – output, predicted variable, label (target), dependent variable, response Our objective is to learn a function y = f(x) called classifier. For a new x this function gives us its class. Support Vector Machine classifier assumes that the data is linearly separable. Linear Separability : Linear Separability of data means that there exists a hyperplane such that all the data belonging to a particular class lie on one side of the hyperplane. Hyperplane is generalization of what is line in 2D space or plane in 3D space. If data is linearly separable then there will be infinitely many hyperplanes that will partition data into two classes. Support Vector Machine learns the best hyperplane, the one that is lying in the middle of the separation between the data, by maximizing the margin. This is why SVM is also called a maximum margin classifier. Margin of a hyperplane with respect to a dataset is the distance of the hyperplane from the point which is closest to it. Support Vectors is the set of points that determined / fix / or support the maximum margin separator. These vectors restrict the movement of the optimal hyperplane with respect to the data. Support vectors also determine the boundary of the classes. SVM assumes that the data is linearly separable. This is a rather strong ( Hard, No Relaxation) constrain to satisfy for data. ( Soft SVM ) Soft Support Vector Machine Algorithm relaxes the linear separability constraint by introducing slack variable. The slack variables measure the extent of relaxation in the linear separability constraint for individual data points in both the classes. The object function is also modified by adding the average of slack variables to it. The hard SVM objective function is also multiplied by a hyperparameter lambda to control the importance given to hard svm objective function as compared to the average of the slack. Large value of lambda gives more importance to hard svm part and thus we are less strict with the average slack. Whereas small value of lambda gives more importance of the average slack and thus we are more strict with the average slack. What is Soft SVM ? What is slack variable ? Why do we need to relax linear separability constraint ? What is the importance of slack variable in soft SVM ? How does the slack variable relax the linear separability constraint in soft SVM ? How the soft SVM different from hard SVM ? What is the difference between soft SVM and hard SVM ? What is the difference between soft SVM constraint and hard SVM constraint ? How the soft SVM constraint different from hard SVM constraint ? What is the meaning of objective function in soft SVM ? What is Soft Support Vector Machine ? What is slack variable ? Why do we need to relax linear separability constraint ? What is the importance of slack variable in soft Support Vector Machine ? How does the slack variable relax the linear separability constraint in soft Support Vector Machine ? How the soft Support Vector Machine different from hard Support Vector Machine ? What is the difference between soft Support Vector Machine and hard Support Vector Machine ? What is the difference between soft Support Vector Machine constraint and hard Support Vector Machine constraint ? How the soft Support Vector Machine constraint different from hard Support Vector Machine constraint ? What is the meaning of objective function in soft Support Vector Machine ? What is the meaning of objective functions in SVM algorithm ? Why do we use class labels -1 and +1 in SVM instead of 0 and 1 ? How SVM solves classification problem ? Why Support Vector Machine is called Support Vector Machine ? What is Support Vector in SVM algorithm ? What is the meaning of linear separability in SVM algorithm ? What is the meaning of objective functions in Support Vector Machine algorithm ? Why do we use class labels -1 and +1 in Support Vector Machine instead of 0 and 1 ? How Support Vector Machine solves classification problem ? Why Support Vector Machine is called Support Vector Machine ? What is Support Vector in Support Vector Machine algorithm ? What is the meaning of linear separability in Support Vector Machine algorithm ? #ArtificialIntelligence #MachineLearning #LearningFromData #LearningParadigms #SupervisedLearning #NewData #Prediction #Classifier #Classification #Dimensions #Feature #ConditionallyIndependent #LabelledTrainingDataset #InputVariable #OutputVariable #IndependentVariable #DependentVariable #Class #Label #Target #SupportVectorMachine #SVM #SupportVector #Margin #Maximum #MaximumMargin