  We introduce a convex approach for mixed linear regression over $d$ features.
This approach is a second-order cone program, based on L1 minimization, which
assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data
point. These estimates can then be clustered using, for example, $k$-means. For
problems with two or more mixture classes, we prove that the convex program
exactly recovers all of the mixture components in the noiseless setting under
technical conditions that include a well-separation assumption on the data.
Under these assumptions, recovery is possible if each class has at least $d$
independent measurements. We also explore an iteratively reweighted least
squares implementation of this method on real and synthetic data.
