Abstract
Nonnegative Matrix Factorization (NMF) which was originally designed for dimensionality reduction has received throughout the years a tremendous amount of attention for clustering purposes in several fields such as image processing or text mining. However, despite its mathematical elegance and simplicity, NMF has exposed a main issue which is its strong sensitivity to starting points, resulting in NMF struggling to converge toward an optimal solution. On another hand, we came to explore and discovered that even after providing a meaningful initialization, selecting the solution with the best local minimum was not always leading to the one having the best clustering quality, but somehow a better clustering could be obtained with a solution slightly off in terms of criterion. Therefore in this paper, we undertake to study the clustering characteristics and quality of a set of NMF best solutions and provide a method delivering a better partition using a consensus made of the best NMF solutions.
Highlights
When dealing with text data, document clustering techniques allow to divide a set of documents into groups so that documents assigned to the same group are more similar to each other than to documents assigned to other groups [12,18,21,22]
This hypothesis can be used at different stages in the information retrieval process, the two most notable being: cluster-based retrieval to speed up search, and search result clustering to help users navigate and understand what is in the search results
By using cluster ensembles, we have proposed a simple method to obtain a better clustering for the scope of Nonnegative Matrix Factorization (NMF) algorithms on text data
Summary
When dealing with text data, document clustering techniques allow to divide a set of documents into groups so that documents assigned to the same group are more similar to each other than to documents assigned to other groups [12,18,21,22]. On real data already labeled, many papers evaluate the performance of clustering algorithms by relying on indices such as Accuracy (ACC), Normalized Mutual Information (NMI) [25] and Adjusted Rand Index (ARI) [14]. Are iterative and require several initializations; the resulting partition is the one optimizing the objective function Sometimes in these works, we observe comparative studies between methods on the basis of maximum ACC/NMI/ARI measures obtained after several initializations and not optimizing the criterion used in the algorithm. This remark leads us to consider an ensemble method that is widely used in supervised learning [11,24] but a little less in unsupervised learning [25] If this approach, referred to as consensus clustering, is often used in the context of comparing partitions obtained with different algorithms, it is less studied considering the same algorithm.
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