This paper introduces a Support Vector Machine (SVM) learning method for structured and interdependent output spaces. The approach generalizes multiclass SVMs to handle complex outputs such as sequences, strings, trees, and graphs. The method uses a joint feature representation of inputs and outputs to learn a function $ f: X \to Y $ that maps inputs to outputs. The optimization problem is solved efficiently using a cutting plane algorithm that exploits the sparseness and structural decomposition of the problem. The method is demonstrated on tasks such as supervised grammar learning, named-entity recognition, taxonomic text classification, and sequence alignment. The paper proposes a framework for learning structured outputs by defining discriminant functions that exploit the structure and dependencies within the output space. It introduces loss functions that quantify the error between predicted and true outputs, and proposes two approaches to incorporate these losses into the SVM formulation: re-scaling the slack variables based on the loss incurred and re-scaling the margin based on the loss function. These approaches allow the method to handle arbitrary loss functions and improve performance on tasks with complex output structures. The paper also presents an algorithm for solving the resulting optimization problems. The algorithm exploits the special structure of the maximum-margin problem to reduce the number of constraints that need to be explicitly examined. It is based on the dual program formulation, which allows the use of kernel functions and supports efficient optimization. The algorithm is shown to converge in polynomial time for a wide range of problems, even when the output space is large or infinite. The method is evaluated on several tasks, including multiclass classification, classification with taxonomies, label sequence learning, sequence alignment, and natural language parsing. The results show that the method achieves high accuracy and outperforms conventional approaches in many cases. The paper concludes that the proposed method is effective for learning structured outputs and can be applied to a wide range of tasks.This paper introduces a Support Vector Machine (SVM) learning method for structured and interdependent output spaces. The approach generalizes multiclass SVMs to handle complex outputs such as sequences, strings, trees, and graphs. The method uses a joint feature representation of inputs and outputs to learn a function $ f: X \to Y $ that maps inputs to outputs. The optimization problem is solved efficiently using a cutting plane algorithm that exploits the sparseness and structural decomposition of the problem. The method is demonstrated on tasks such as supervised grammar learning, named-entity recognition, taxonomic text classification, and sequence alignment. The paper proposes a framework for learning structured outputs by defining discriminant functions that exploit the structure and dependencies within the output space. It introduces loss functions that quantify the error between predicted and true outputs, and proposes two approaches to incorporate these losses into the SVM formulation: re-scaling the slack variables based on the loss incurred and re-scaling the margin based on the loss function. These approaches allow the method to handle arbitrary loss functions and improve performance on tasks with complex output structures. The paper also presents an algorithm for solving the resulting optimization problems. The algorithm exploits the special structure of the maximum-margin problem to reduce the number of constraints that need to be explicitly examined. It is based on the dual program formulation, which allows the use of kernel functions and supports efficient optimization. The algorithm is shown to converge in polynomial time for a wide range of problems, even when the output space is large or infinite. The method is evaluated on several tasks, including multiclass classification, classification with taxonomies, label sequence learning, sequence alignment, and natural language parsing. The results show that the method achieves high accuracy and outperforms conventional approaches in many cases. The paper concludes that the proposed method is effective for learning structured outputs and can be applied to a wide range of tasks.