Doubly Aligned Incomplete Multi-View Clustering Algorithm (DAIMC)
Nowadays, multi-view clustering has attracted more and more attention. To date, almost all the previous studies assume that views are complete. However, in reality, it is often the case that each view may contain some missing instances. Such incompleteness makes it impossible to directly use traditional multi-view clustering methods. In this paper, we propose a Doubly Aligned Incomplete Multi-view Clustering algorithm (DAIMC) based on weighted semi-nonnegative matrix factorization (semi-NMF). Specifically, on the one hand, DAIMC utilizes the given instance alignment information to learn a common latent feature matrix for all the views. On the other hand, DAIMC establishes a consensus basis matrix with the help of $L_{2,1}$-Norm regularized regression for reducing the influence of missing instances. Consequently, compared with existing methods, besides inheriting the strength of semi-NMF with ability to handle negative entries, DAIMC has two unique advantages: 1) solving the incomplete view problem by introducing a respective weight matrix for each view, making it able to easily adapt to the case with more than two views; 2) reducing the influence of view incompleteness on clustering by enforcing the basis matrices of individual views being aligned with the help of regression. Experiments on four real-world datasets demonstrate its advantages. …

Rubin Causal Model (RCM)
The Rubin causal model (RCM), also known as the Neyman-Rubin causal model, is an approach to the statistical analysis of cause and effect based on the framework of potential outcomes, named after Donald Rubin. The name ‘Rubin causal model’ was first coined by Rubin’s graduate school colleague, Paul W. Holland. The potential outcomes framework was first proposed by Jerzy Neyman in his 1923 Master’s thesis, though he discussed it only in the context of completely randomized experiments. Rubin, together with other contemporary statisticians, extended it into a general framework for thinking about causation in both observational and experimental studies. …

Metropolis-Hastings Algorithm
In statistics and in statistical physics, the Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult. This sequence can be used to approximate the distribution (i.e., to generate a histogram), or to compute an integral (such as an expected value). Metropolis-Hastings and other MCMC algorithms are generally used for sampling from multi-dimensional distributions, especially when the number of dimensions is high. For single-dimensional distributions, other methods are usually available (e.g. adaptive rejection sampling) that can directly return independent samples from the distribution, and are free from the problem of auto-correlated samples that is inherent in MCMC methods.
http://…/1504.01896 …

Conditionally Autoregressive Hidden Markov Model (CarHMM)
One of the central interests of animal movement ecology is relating movement characteristics to behavioural characteristics. The traditional discrete-time statistical tool for inferring unobserved behaviours from movement data is the hidden Markov model (HMM). While the HMM is an important and powerful tool, sometimes it is not flexible enough to appropriately fit the data. Data for marine animals often exhibit conditional autocorrelation, self-dependence of the step length process which cannot be explained solely by the behavioural state, which violates one of the main assumptions of the HMM. Using a grey seal track as an example, along with multiple simulation scenarios, we motivate and develop the conditionally autoregressive hidden Markov model (CarHMM), which is a generalization of the HMM designed specifically to handle conditional autocorrelation. In addition to introducing and examining the new CarHMM, we provide guidelines for all stages of an analysis using either an HMM or CarHMM. These include guidelines for pre-processing location data to obtain deflection angles and step lengths, model selection, and model checking. In addition to these practical guidelines, we link estimated model parameters to biologically meaningful quantities such as activity budget and residency time. We also provide interpretations of traditional ‘foraging’ and ‘transiting’ behaviours in the context of the new CarHMM parameters. …