# SVM: What is relationship between the number of features and the number of dimensions?

I have implemented a support vector machine (SVM) in Python. I want to know the relationship between the number of features and the number of dimensions. My dataset contains 5 features, does it mean that my SVM classifier has 5 dimensions? Thanks

Excluding the target variable, if your dataset has $$n$$ columns (predictors, covariates etc.), then your SVM separates the space $$\mathbb{R}^n$$. So, Your SVM operates on $$n$$ dimensional data. The separating hyperplane is in $$\mathbb{R}^{n-1}$$, i.e. $$n-1$$ dimensional by definition, and its equation can be generally written as $$w^Tx+b$$, where $$w,x$$ are $$n$$ dimensional, and $$b$$, bias, is $$1$$ dimensional (i.e. a scalar). So, the hyperplane equation has $$n+1$$ coefficients, including the bias term, which means your parameter space is $$n+1$$ dimensional. I haven't heard a term like SVM dimension, but these are all the dimensionality concerns inside the classifier.