Network component analysis (NCA) is a method to deduce transcription factor (TF) activities and TF-gene regulation control strengths from gene expression data and a TF-gene binding connectivity network. Previously, this method could analyze a maximum number of regulators equal to the total sample size because of the identifiability limit in data decomposition. As such, the total number of source signal components was limited to the total number of experiments rather than the total number of biological regulators. However, networks that have less transcriptome data points than the number of regulators are of interest. Thus it is imperative to develop a theoretical basis that allows realistic source signal extraction based on relatively few data points. On the other hand, such methods would inherently increase numerical challenges leading to multiple solutions. Therefore, solutions to both the problems are needed.