Table 3.

Components of Symphony query.

${\mathbf{G}}_{\mathbf{q}}\in {\mathbb{R}}^{g\times m}$	Input query gene expression matrix, prior to scaling.
${\mathbf{X}}_{\mathbf{q}}\in {\left\{0,1\right\}}^{c\times m}$	Design matrix assigning query cells (cols) to query batches (rows).
${\mathbf{Z}}_{\mathbf{q}}\in {\mathbb{R}}^{d\times m}$	Query cell locations in original (pre-harmonized) PC embedding.
${\widehat{\mathbf{Z}}}_{\mathbf{q}}\in {\mathbb{R}}^{d\times m}$	Approximate query cell locations in integrated embedding (hPC space).
${\mathbf{R}}_{\mathbf{q}}\in {\left[0,1\right]}^{k\times m}$	Soft cluster assignment of query cells (cols) to clusters (rows). Each column is a probability distribution that sums to 1.
${\mathbf{B}}_{\mathbf{q}}\in {\mathbb{R}}^{k\times \left(1+c\right)\times d}$	3D tensor of the estimated parameters (betas and intercepts) of the linear mixture model for each of k clusters.