# Classification of circular data

I have a multi-class classification problem with circular and linear data. For example a feature vector contains 20 circular ($\theta \in [0,2\pi)$) and two linear ($\in (0,1)$) variables. I plan to transform $\theta$ into $(\sin\theta,\cos\theta)$ and apply any traditional classifier (MLP, SVM). In fact my data appear to be linearly separable, so I try Perceptron also. I don't find any specific classifier that handles $\theta$ directly. So, is my planning okay? $\sin\theta$ and $\cos\theta$ seem to be highly correlated. Does that create a problem for a classifier?

I appreciate any help and any reference on this issue.

You could try clustering the observations of each $\theta_j$ feature. If there is a preferred direction, $\theta_j^{(1)}$, then you might consider replacing $\theta_j$ with $\theta_j-\theta_j^{(1)}$.
If you have enough data not to overfit, then you could replace $\theta_j$ with the deltas to each of the $m$ most preferred directions, $\theta_j-\theta_j^{(1)}$ to $\theta_j-\theta_j^{(m)}$.
• Thanks but I don't really get you answer. My feature vector is $\Xi = (\theta_1,\ldots,\theta_{20}, x_1,x_2)$. I have $n$ such feature vectors corresponding to 10 classes. Is it problematic if I convert $\theta_j$ to $(\sin\theta_j,\cos\theta_j)$ and apply MLP or SVM? Can you suggest some article, because I don't find anything. I don't understand "preferred direction" also. Is that the average of $n$ values of $\theta_j$ component ? Sorry, linear separability is an assumption so far. Nov 23, 2015 at 21:49
• I'm sure it's not problematic at all to convert $\theta_j$ to $(\sin\theta_j,\cos\theta_j)$. Try it and see; you may as well try the preferred direction thing as well. Suppose, for example, that $\theta_1$ consists mostly of angles near $\theta_1^{(1)}=55$ degrees and near $\theta_1^{(2)}=355$ degrees; then an angle of $5$ degrees, say, could be represented by feature values $-50$ (=5-55) and $+10$ (=5-355 mod 360). If plotting the data reveals no such clustering, forget the idea. Nov 24, 2015 at 21:08