Context aware nonnegative matrix factorization clustering

Abstract

In this article we propose a method to refine the clustering results obtained with the nonnegative matrix factorization (NMF) technique, imposing consistency constraints on the final labeling of the data. The research community focused its effort on the initialization and on the optimization part of this method, without paying attention to the final cluster assignments. We propose a game theoretic framework in which each object to be clustered is represented as a player, which has to choose its cluster membership. The information obtained with NMF is used to initialize the strategy space of the players and a weighted graph is used to model the interactions among the players. These interactions allow the players to choose a cluster which is coherent with the clusters chosen by similar players, a property which is not guaranteed by NMF, since it produces a soft clustering of the data. The results on common benchmarks show that our model is able to improve the performances of many NMF formulations

Integrative inference of brain cell similarities and differences from single-cell genomics

“…This approach is synergistic with iNMF, which reconstructs each dataset separately, accurately preserving the structure of individual datasets. A recent paper used a related idea to refine cluster assignments from NMF by taking into account the neighborhood of each data point (Tripodi, 2016). Additionally, our graph construction greatly reduces the chances of spurious matches across datasets, because even if a cell type spuriously loads on the same factor as a different cell type in another dataset, they are unlikely to have the same factor neighborhoods.…”

Unsupervised Domain Adaptation using Graph Transduction Games

“…where f i , f j are the features of observations i and j respectively, d(f i , f j ) is the cosine distance between features f i and f j . Here, motivated by [24] and [5], we set the scaling parameter σ i automatically, considering the local statistics of the neighborhood of each point. Accordingly to [24], the value of σ i is set to the distance of the 7-th nearest neighbour of observation i. d) Affinity sparsification: The sparsification of the graph plays an important role in the performances of the algorithm.…”

Expert Opinion and Coherence Based Topic Modeling

“…However, the topic assignment part of the algorithm received a smaller attention from the research community [3]. This is because the assessment of how well the topic assignment being done is subjective.…”

“…This is usually the final step of topic modeling and is the step that we focus on in this paper. Although NMF and LDA themselves are carefully studied and there are multiple algorithms to solve them, this final step of assigning topics receives less attention from the research community [3]. The assessment of this step is usually done by considering the top words (words with high frequency) of each topic and decided by eyeballing to see if they naturally make sense.…”

“…[3] mainly studies topic assignment on NMF and uses game theory and game dynamics to adjust the topics with the method Game Theoretic NMF (GTNMF), and test the algorithm on different datasets. This is what we expect to improve by allowing the approach to a more general topic modeling methods.…”