Mutual Information is a measure of the statistical dependence between two random variables. It quantifies the amount of information that knowing the value of one variable provides about the other variable. In other words, it measures how much the uncertainty about one variable is reduced when the value of the other variable is known. Mutual information is often denoted by I(X;Y), where X and Y are the two random variables in question.


Deep Co-Clustering

Deep Co-Clustering Co-clustering partitions instances and features simultaneously by leveraging the duality between them and it often yields impressive performance improvement over traditional clustering algorithms. The recent development in learning deep representations has demonstrated the advantage in extracting effective features. However, the research on leveraging deep learning frameworks for co-clustering is limited for two reasons: 1) current deep clustering approaches usually decouple feature learning and cluster assignment as two separate steps, which cannot yield the task-specific feature representation; 2) existing deep clustering approaches cannot learn representations for instances and features simultaneously. In this paper, we propose a deep learning model for co-clustering called DeepCC. DeepCC utilizes the deep autoencoder for dimension reduction, and employs a variant of Gaussian Mixture Model (GMM) to infer the cluster assignments. A mutual information loss is proposed to bridge the training of instances and features. DeepCC jointly optimizes the parameters of the deep autoencoder and the mixture model in an end-to-end fashion on both the instance and the feature spaces, which can help the deep autoencoder escape from local optima and the mixture model circumvent the Expectation-Maximization (EM) algorithm. To the best of our knowledge, DeepCC is the first deep learning model for co-clustering. Experimental results on various dataseis demonstrate the effectiveness of DeepCC.