Some computational issues in cluster analysis with no a priori metric

Critical distinction from ScoreQuant

Classical determinant clustering usually minimizes a determinant of pooled within-cluster scatter or an equivalent Gaussian likelihood criterion. ScoreQuant maximizes

$$\det\left( \sum_bW_b\mu_b\mu_b^\top \right),$$

the determinant of retained between-cell score Fisher information. For dimension $d>1$, fixed total scatter $T=W+B$ does not make $\min\det W$ equivalent to $\max\det B$.