Related papers: Info-Clustering: A Mathematical Theory for Data Cl…
A recent article proposed reduced mutual information for evaluation of clustering, classification and community detection. The motivation is that the standard normalized mutual information (NMI) may give counter-intuitive answers under…
This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…
Shannon's mathematical theory of communication defines fundamental limits on how much information can be transmitted between the different components of any man-made or biological system. This paper is an informal but rigorous introduction…
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
Matrix-variate distributions are a recent addition to the model-based clustering field, thereby making it possible to analyze data in matrix form with complex structure such as images and time series. Due to its recent appearance, there is…
The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through…
Mutual information is a widely-used information theoretic measure to quantify the amount of association between variables. It is used extensively in many applications such as image registration, diagnosis of failures in electrical machines,…
This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…
We propose data thinning, an approach for splitting an observation into two or more independent parts that sum to the original observation, and that follow the same distribution as the original observation, up to a (known) scaling of a…
In the collaborative clustering framework, the hope is that by combining several clustering solutions, each one with its own bias and imperfections, one will get a better overall solution. The goal is that each local computation, quite…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
Finite mixture models have become a popular tool for clustering. Amongst other uses, they have been applied for clustering longitudinal data and clustering high-dimensional data. In the latter case, a latent Gaussian mixture model is…
We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…
This technical report provides the supplementary material for a paper entitled "Information based clustering", to appear shortly in Proceedings of the National Academy of Sciences (USA). In Section I we present in detail the iterative…
Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been proposed that such a decomposition should satisfy, leading to…
Analysis of data without labels is commonly subject to scrutiny by unsupervised machine learning techniques. Such techniques provide more meaningful representations, useful for better understanding of a problem at hand, than by looking only…
We propose a data reduction technique for scattered data based on statistical sampling. Our void-and-cluster sampling technique finds a representative subset that is optimally distributed in the spatial domain with respect to the blue noise…
Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
Does semantic communication require a semantic information theory parallel to Shannon's information theory, or can Shannon's work be generalized for semantic communication? This paper advocates for the latter and introduces a semantic…