  In this paper, we explore the role of matrix scaling on a matrix of counts
when building a topic model using non-negative matrix factorization. We present
a scaling inspired by the normalized Laplacian (NL) for graphs that can greatly
improve the quality of a non-negative matrix factorization. The results
parallel those in the spectral graph clustering work of \cite{Priebe:2019},
where the authors proved adjacency spectral embedding (ASE) spectral clustering
was more likely to discover core-periphery partitions and Laplacian Spectral
Embedding (LSE) was more likely to discover affinity partitions. In text
analysis non-negative matrix factorization (NMF) is typically used on a matrix
of co-occurrence ``contexts'' and ``terms" counts. The matrix scaling inspired
by LSE gives significant improvement for text topic models in a variety of
datasets. We illustrate the dramatic difference a matrix scalings in NMF can
greatly improve the quality of a topic model on three datasets where human
annotation is available. Using the adjusted Rand index (ARI), a measure cluster
similarity we see an increase of 50\% for Twitter data and over 200\% for a
newsgroup dataset versus using counts, which is the analogue of ASE. For clean
data, such as those from the Document Understanding Conference, NL gives over
40\% improvement over ASE. We conclude with some analysis of this phenomenon
and some connections of this scaling with other matrix scaling methods.

Machine Learning