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The primal problem and the dual problem in SVM arise from th…

The primal problem and the dual problem in SVM arise from the optimization approach used to find the max-margin hyperplane. Here is a brief explanation of each: The primal problem in SVM seeks to directly minimize the norm of the weight vector ww while ensuring that all data points are classified correctly. For linearly separable data, the primal optimization problem is formulated as: min⁡w,b 12∥w∥2 subject to: yi(wTxi+b)≥1∀i Here, ww is the normal vector to the hyperplane, xix_i are the feature vectors, yiy_i are the class labels, and bb is the bias term. The dual problem is derived from the primal problem using Lagrange multipliers. The dual formulation allows the SVM to be expressed in terms of the dot products between data points, which enables the use of kernel functions to handle non-linear data. The dual problem is written as: max⁡α∑i=1nαi−12∑i=1n∑j=1nαiαjyiyj(xiTxj) subject to: 0≤αi≤C and∑i=1nαiyi=0 Here, αi\alpha_i are the Lagrange multipliers. The dual formulation is particularly useful because it allows for the use of kernel functions to handle non-linearly separable data by mapping it into a higher-dimensional space. Which of the following statements about the primal-dual problem in Support Vector Machines (SVM) is true?