Svm Classification

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What can be the theoretical reason/s for which a support vector machine with linear kernel (implemented with LinearSVC from sklearn) fails miserably in a multi-class (5 classes) classification?

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An SVM assumes that a separating hyperplane classifies your data well. If no separating hyperplane exists, then an SVM will not perform well.

Or, there's a bug in your code.

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A Support Vector Machine only separates binarily. Discriminates between two classes. Or between belonging or not belonging to one class. For more than two classes you will need to be inventive to get it to make sense.