A model of grain fragmentation based on lattice curvature

A new model is proposed that aims to capture within a single modelling frame all the main microstructural features of a severe plastic deformation process. These are: evolution of the grain size distribution, misorientation distribution, crystallographic texture and the strain-hardening of the material. The model is based on the lattice curvature that develops in all deformed grains. The basic assumption is that lattice rotation within an individual grain is impeded near the grain boundaries by the constraining effects of the neighbouring grains, which gives rise to lattice curvature. On that basis, a fragmentation scheme is developed which is integrated in the Taylor viscoplastic polycrystal model. Dislocation density evolution is traced for each grain, which includes the contribution of geometrically necessary dislocations associated with lattice curvature. The model is applied to equal-channel angular pressing. The role of texture development is shown to be an important element in the grain fragmentation process. Results of this modelling give fairly precise predictions of grain size and grain misorientation distribution. The crystallographic textures are well reproduced and the strength of the material is also reliably predicted based on the modelling of dislocation density evolution coupled with texture development.

Generalized pseudo-likelihood estimates for markov random fields on lattice

In this paper we generalize Besag's pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag's maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MGPLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.

Measurement of aqueous film thickness between charged mercury and mica surfaces : a direct experimental probe of the Poisson-Boltzmann distribution

A stable aqueous electrolyte film is formed between a mercury drop and a flat mica surface due to electrical double-layer repulsion when a negative potential is applied to the mercury. Film thickness has been measured as a function of applied potential while keeping the film pressure constant. By making measurements in this way, it is possible to map the data directly according to the Poisson-Boltzmann equation. An excellent fit to the data is obtained, providing direct evidence for this classical equation and its use as the basis of the Gouy-Chapman model of the diffuse double layer in electrolyte solutions.

Ordinal Boltzmann machines for collaborative filtering

Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the preference data, that is, it is enough to predict preference of a user on a particular item based on a small subset of other users with similar tastes or of other items with similar properties. More recently, dimensionality reduction techniques have proved to be equally competitive, and these are based on the co-occurrence patterns rather than locality. This paper explores and extends a probabilistic model known as Boltzmann Machine for collaborative filtering tasks. It seamlessly integrates both the similarity and cooccurrence in a principled manner. In particular, we study parameterisation options to deal with the ordinal nature of the preferences, and propose a joint modelling of both the user-based and item-based processes. Experiments on moderate and large-scale movie recommendation show that our framework rivals existing well-known methods.

Mixed-variate restricted Boltzmann machines

Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed- Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous responses, categorical options, multicategorical choices, ordinal assessment and category-ranked preferences. Dependency among variables is modeled using latent binary variables, each of which can be interpreted as a particular hidden aspect of the data. The proposed model, similar to the standard RBMs, allows fast evaluation of the posterior for the latent variables. Hence, it is naturally suitable for many common tasks including, but not limited to, (a) as a pre-processing step to convert complex input data into a more convenient vectorial representation through the latent posteriors, thereby oering a dimensionality reduction capacity, (b) as a classier supporting binary, multiclass, multilabel, and label-ranking outputs, or a regression tool for continuous outputs and (c) as a data completion tool for multimodal and heterogeneous data. We evaluate the proposed model on a large-scale dataset using the world opinion survey results on three tasks: feature extraction and visualization, data completion and prediction.

Learning Boltzmann distance metric for face recognition

We introduce a new method for face recognition using a versatile probabilistic model known as Restricted Boltzmann Machine (RBM). In particular, we propose to regularise the standard data likelihood learning with an information-theoretic distance metric defined on intra-personal images. This results in an effective face representation which captures the regularities in the face space and minimises the intra-personal variations. In addition, our method allows easy incorporation of multiple feature sets with controllable level of sparsity. Our experiments on a high variation dataset show that the proposed method is competitive against other metric learning rivals. We also investigated the RBM method under a variety of settings, including fusing facial parts and utilising localised feature detectors under varying resolutions. In particular, the accuracy is boosted from 71.8% with the standard whole-face pixels to 99.2% with combination of facial parts, localised feature extractors and appropriate resolutions.

Embedded restricted Boltzmann machines for fusion of mixed data types and applications in social measurements analysis

Analysis and fusion of social measurements is important to understand what shapes the public’s opinion and the sustainability of the global development. However, modeling data collected from social responses is challenging as the data is typically complex and heterogeneous, which might take the form of stated facts, subjective assessment, choices, preferences or any combination thereof. Model-wise, these responses are a mixture of data types including binary, categorical, multicategorical, continuous, ordinal, count and rank data. The challenge is therefore to effectively handle mixed data in the a unified fusion framework in order to perform inference and analysis. To that end, this paper introduces eRBM (Embedded Restricted Boltzmann Machine) – a probabilistic latent variable model that can represent mixed data using a layer of hidden variables transparent across different types of data. The proposed model can comfortably support largescale data analysis tasks, including distribution modelling, data completion, prediction and visualisation. We demonstrate these versatile features on several moderate and large-scale publicly available social survey datasets.

Cumulative restricted Boltzmann machines for ordinal matrix data analysis

Ordinal data is omnipresent in almost all multiuser-generated feedback - questionnaires, preferences etc. This paper investigates modelling of ordinal data with Gaussian restricted Boltzmann machines (RBMs). In particular, we present the model architecture, learning and inference procedures for both vector-variate and matrix-variate ordinal data. We show that our model is able to capture latent opinion profile of citizens around the world, and is competitive against state-of-art collaborative filtering techniques on large-scale public datasets. The model thus has the potential to extend application of RBMs to diverse domains such as recommendation systems, product reviews and expert assessments.

Latent patient profile modelling and applications with mixed-variate restricted Boltzmann machine

Efficient management of chronic diseases is critical in modern health care. We consider diabetes mellitus, and our ongoing goal is to examine how machine learning can deliver information for clinical efficiency. The challenge is to aggregate highly heterogeneous sources including demographics, diagnoses, pathologies and treatments, and extract similar groups so that care plans can be designed. To this end, we extend our recent model, the mixed-variate restricted Boltzmann machine (MV.RBM), as it seamlessly integrates multiple data types for each patient aggregated over time and outputs a homogeneous representation called "latent profile" that can be used for patient clustering, visualisation, disease correlation analysis and prediction. We demonstrate that the method outperforms all baselines on these tasks - the primary characteristics of patients in the same groups are able to be identified and the good result can be achieved for the diagnosis codes prediction.

Graph-induced restricted Boltzmann machines for document modeling

Discovering knowledge from unstructured texts is a central theme in data mining and machine learning. We focus on fast discovery of thematic structures from a corpus. Our approach is based on a versatile probabilistic formulation – the restricted Boltzmann machine (RBM) –where the underlying graphical model is an undirected bipartite graph. Inference is efficient document representation can be computed with a single matrix projection, making RBMs suitable for massive text corpora available today. Standard RBMs, however, operate on bag-of-words assumption, ignoring the inherent underlying relational structures among words. This results in less coherent word thematic grouping. We introduce graph-based regularization schemes that exploit the linguistic structures, which in turn can be constructed from either corpus statistics or domain knowledge. We demonstrate that the proposed technique improves the group coherence, facilitates visualization, provides means for estimation of intrinsic dimensionality, reduces overfitting, and possibly leads to better classification accuracy.

Tensor-variate restricted Boltzmann machines

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-order interaction structures. This paper introduces Tensor-variate Restricted Boltzmann Machines (TvRBMs) which generalize RBMs to capture the multiplicative interaction between data modes and the latent variables. TvRBMs are highly compact in that the number of free parameters grows only linear with the number of modes. We demonstrate the capacity of TvRBMs on three real-world applications: handwritten digit classification, face recognition and EEG-based alcoholic diagnosis. The learnt features of the model are more discriminative than the rivals, resulting in better classification performance.

Learning vector representation of medical objects via EMR-driven nonnegative restricted Boltzmann machines (eNRBM)

Electronic medical record (EMR) offers promises for novel analytics. However, manual feature engineering from EMR is labor intensive because EMR is complex - it contains temporal, mixed-type and multimodal data packed in irregular episodes. We present a computational framework to harness EMR with minimal human supervision via restricted Boltzmann machine (RBM). The framework derives a new representation of medical objects by embedding them in a low-dimensional vector space. This new representation facilitates algebraic and statistical manipulations such as projection onto 2D plane (thereby offering intuitive visualization), object grouping (hence enabling automated phenotyping), and risk stratification. To enhance model interpretability, we introduced two constraints into model parameters: (a) nonnegative coefficients, and (b) structural smoothness. These result in a novel model called eNRBM (EMR-driven nonnegative RBM). We demonstrate the capability of the eNRBM on a cohort of 7578 mental health patients under suicide risk assessment. The derived representation not only shows clinically meaningful feature grouping but also facilitates short-term risk stratification. The F-scores, 0.21 for moderate-risk and 0.36 for high-risk, are significantly higher than those obtained by clinicians and competitive with the results obtained by support vector machines.

Learning entry profiles of children with autism from multivariate treatment information using restricted boltzmann machines

Entry profiles can be generated before children with Autism Spectrum Disorders (ASD) begin to traverse an intervention program. They can help evaluate the progress of each child on the dedicated syllabus in addition to enabling narrowing down the best intervention course over time. However, the traits of ASD are expressed in different ways in every individual affected. The resulting spectrum nature of the disorder makes it challenging to discover profiles of children with ASD. Using data from 491 children, traversing the syllabus of a comprehensive intervention program on iPad called TOBY Playpad, we learn the entry profiles of the children based on their age, sex and performance on their first skills of the syllabus. Mixed-variate restricted Boltzmann machines allow us to integrate the heterogeneous data into one model making it a suitable technique. The data based discovery of entry profiles may assist in developing systems that can automatically suggest best suitable paths through the syllabus by clustering the children based on the characteristics they present at the beginning of the program. This may open the pathway for personalised intervention.

Thurstonian Boltzmann machines: learning from multiple inequalities

We introduce Thurstonian Boltzmann Machines (TBM), a unified architecture that can naturally incorporate a wide range of data inputs at the same time. Our motivation rests in the Thurstonian view that many discrete data types can be considered as being generated from a subset of underlying latent continuous variables, and in the observation that each realisation of a discrete type imposes certain inequalities on those variables. Thus learning and inference in TBM reduce to making sense of a set of inequalities. Our proposed TBM naturally supports the following types: Gaussian, intervals, censored, binary, categorical, muticategorical, ordinal, (in)-complete rank with and without ties. We demonstrate the versatility and capacity of the proposed model on three applications of very different natures; namely handwritten digit recognition, collaborative filtering and complex social survey analysis. Copyright 2013 by the author(s).