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However, this is discontinuous and the scale of $\mathbf{q}$ is unidentifiable. The problem above is recast as   \[ \min f(\mathbf{q}; \hat{\mathbf{Y}}) = \frac{1}{p} \sum_{k=1}^p h_{\mu} (\mathbf{q}^T \hat{\mathbf{y}_k}), \quad s.t. \ \|q\|_2 = 1, \]  where $\hat{\mathbf{Y}}$ is the data after pre-conditioning. The loss function is a special convex function, namely  \[ h_{\mu} (z) = \mu \log \cosh(z / \mu) \mu).  \] Next, we discuss some of the key properties of this problem.