Usually, in monitoring a proportion p < /em>, the binary observations are considered independent; however, in many real cases, there is a continuous stream of autocorrelated binary observations in which a two-state Markov chain model is applied with first-order dependence. On the other hand, the Bernoulli CUSUM control chart which is not robust to autocorrelation can be applied two-sided co...

Clustering is an unsupervised learning technique that seeks “natural” groupings in data. One form of data that has not been widely studied in the context of clustering is binary data. A rich statistical framework for clustering binary data is the Bernoulli mixture model for which there exists both Bayesian and non-Bayesian approaches. This paper reviews the development and application of Bernou...

A commonly used paradigm in diverse application areas is to assume that an observed set of individual binary features is generated from a Bernoulli distribution with probabilities varying according to a Beta distribution. In this paper, we present our nonparametric variational inference algorithm for the Beta-Bernoulli observation model. Our primary focus is clustering discrete binary data usin...

Mixture modelling is a hot area in pattern recognition. This paper focuses on the use of Bernoulli mixtures for binary data and, in particular, for binary images. More specifically, six EM initialisation techniques are described and empirically compared on a classification task of handwritten Indian digits. Somehow surprisingly, we have found that a relatively good initialisation for Bernoulli ...

The mixture of Bernoulli distributions [6] is a technique that is frequently used for the modeling of binary random vectors. They differ from (restricted) Boltzmann Machines in that they do not model the marginal distribution over the binary data space X as a product of (conditional) Bernoulli distributions, but as a weighted sum of Bernoulli distributions. Despite the non-identifiability of th...

This article reports on the use of Hidden Markov Models to improve the results of Localization within a sequence of Sensor Views. Local image features (SIFT) and multiple types of features from a 2D laser range scan are all converted into binary form and integrated into a single, binary, Feature Incidence Matrix (FIM). To reduce the large dimensionality of the binary data, it is modeled in term...

Dasgupta and Shulman [1] showed that a two-round variant of the EM algorithm can learn mixture of Gaussian distributions with near optimal precision with high probability if the Gaussian distributions are well separated and if the dimension is sufficiently high. In this paper, we generalize their theory to learning mixture of high-dimensional Bernoulli templates. Each template is a binary vecto...

We present a unified statistical framework for quantifying a collection of stroke lesion images that have been segmented in diffusion weighted images. Although Bernoulli models are often used in modeling a collection of binary images, the Bernoulli models actually break down for testing statistical significance of common overlap. To remedy the limitation of the Bernoulli models, we propose to a...

Current data processing tasks often involve manipulation of multi-dimensional objects tensors. In many real world applications such as gait recognition, document analysis or graph mining (with graphs represented by adjacency tensors), the tensors can be constrained to binary values only. To the best of our knowledge at present there is no principled systematic framework for decomposition of bin...

ABSTRACT: This paper begins by using the Haar wavelet to analyze the cumulative distribution function of a stream of two-valued Bernoulli trials. We find that this function maps binary numbers in [0,1] into non-uniform binary numbers in [0,1]. More generally, for r-valued Bernoulli trials, the distribution function likewise maps usual base-r numbers into non-uniform base-r numbers. We also find...