Fitting spatial models in the R package: hglm

We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).

Fitting conditional and simultaneous autoregressive spatial models in hglm

We present a new version (> 2.0) of the hglm package for fitting hierarchical generalized linear models (HGLMs) with spatially correlated random effects. CAR() and SAR() families for conditional and simultaneous autoregressive random effects were implemented. Eigen decomposition of the matrix describing the spatial structure (e.g., the neighborhood matrix) was used to transform the CAR/SAR random effects into an independent, but eteroscedastic, Gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR and SAR models. This gives a computationally efficient algorithm for moderately sized problems.

Interpolation of Lipschitz functions

This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.

Research on network anycast

Anycast is defined as a service in IPv6, which provides stateless best effort delivery of an anycast datagram to at least one, and preferably only one host. It is a topic of increasing interest. This paper is an attempt to gather and report on the work done on anycast. There are two main categories at present: network-layer anycast and application-layer anycast. Both involve anycast architectures, routing algorithms, metrics, applications, etc. We also present an efficient algorithm for application-layer anycast, and point out possible research directions based on our research.

Smoothing Lipschitz functions

This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties of f. Depending on the assumptions about the distribution of the random noise, smoothing is reduced to a standard quadratic or a linear programming problem. We discuss an efficient algorithm which eliminates the redundant inequality constraints. Numerical experiments illustrate applicability and efficiency of the method. This approach provides an efficient new tool of multivariate scattered data approximation.

Extended cutting angle method of global optimization

Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.

Dynamic route construction for mobile collectors in wireless sensor networks

Wireless sensor networks with mobile data collectors have been recently proposed for extending the sensor network lifetime. Powerful mobile collectors are deployed to patrol the network and approach the static sensors for collecting their data buffers using single hop communication. The route followed by the mobile collector is very crucial for the data collection operation performed in the network and highly impacts the data collection time. This paper presents a practically efficient algorithm for constructing the mobile collector route. The route is constructed dynamically during the network operational time regardless of the sensors data generation rates. The algorithm acts on minimizing the sleeping time and the number of sensors waiting for the arrival of the mobile collector. Simulation results demonstrate that the presented algorithm can effectively reduce the overall data collection time.

Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue

An efficient algorithm for solving the transient radiative transfer equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. The Runge–Kutta– Fehlberg method is used to solve the intensity. The discrete ordinates method is used to discretize with respect to azimuthal and zenith angles. This method offers the advantages of representing the intensity with a high accuracy using only a few Laguerre polynomials, and straightforward extension to inhomogeneous media. Also, this formulation can be easily extended for solving the 2-D and 3-D transient radiative transfer equations.

Nonnegative shared subspace learning and its application to social media retrieval

Although tagging has become increasingly popular in online image and video sharing systems, tags are known to be noisy, ambiguous, incomplete and subjective. These factors can seriously affect the precision of a social tag-based web retrieval system. Therefore improving the precision performance of these social tag-based web retrieval systems has become an increasingly important research topic. To this end, we propose a shared subspace learning framework to leverage a secondary source to improve retrieval performance from a primary dataset. This is achieved by learning a shared subspace between the two sources under a joint Nonnegative Matrix Factorization in which the level of subspace sharing can be explicitly controlled. We derive an efficient algorithm for learning the factorization, analyze its complexity, and provide proof of convergence. We validate the framework on image and video retrieval tasks in which tags from the LabelMe dataset are used to improve image retrieval performance from a Flickr dataset and video retrieval performance from a YouTube dataset. This has implications for how to exploit and transfer knowledge from readily available auxiliary tagging resources to improve another social web retrieval system. Our shared subspace learning framework is applicable to a range of problems where one needs to exploit the strengths existing among multiple and heterogeneous datasets.

Finding the optimal temporal partitioning of video sequences

The existing techniques for shot partitioning either process each shot boundary independently or proceed sequentially. The sequential process assumes the last shot boundary is correctly detected and utilizes the shot length distribution to adapt the threshold for detecting the next boundary. These techniques are only locally optimal and suffer from the strong assumption about the correct detection of the last boundary. Addressing these fundamental issues, in this paper, we aim to find the global optimal shot partitioning by utilizing Bayesian principles to model the probability of a particular video partition being the shot partition. A computationally efficient algorithm based on Dynamic Programming is then formulated. The experimental results on a large movie set show that our algorithm performs consistently better than the best adaptive-thresholding technique commonly used for the task.

A Bayesian framework for learning shared and individual subspaces from multiple data sources

This paper presents a novel Bayesian formulation to exploit shared structures across multiple data sources, constructing foundations for effective mining and retrieval across disparate domains. We jointly analyze diverse data sources using a unifying piece of metadata (textual tags). We propose a method based on Bayesian Probabilistic Matrix Factorization (BPMF) which is able to explicitly model the partial knowledge common to the datasets using shared subspaces and the knowledge specific to each dataset using individual subspaces. For the proposed model, we derive an efficient algorithm for learning the joint factorization based on Gibbs sampling. The effectiveness of the model is demonstrated by social media retrieval tasks across single and multiple media. The proposed solution is applicable to a wider context, providing a formal framework suitable for exploiting individual as well as mutual knowledge present across heterogeneous data sources of many kinds.

Hierarchical semi-markov conditional random fields for recursive sequential data

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms for learning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.

A matrix factorization framework for jointly analyzing multiple nonnegative data source

Nonnegative matrix factorization based methods provide one of the simplest and most effective approaches to text mining. However, their applicability is mainly limited to analyzing a single data source. In this paper, we propose a novel joint matrix factorization framework which can jointly analyze multiple data sources by exploiting their shared and individual structures. The proposed framework is flexible to handle any arbitrary sharing configurations encountered in real world data. We derive an efficient algorithm for learning the factorization and show that its convergence is theoretically guaranteed. We demonstrate the utility and effectiveness of the proposed framework in two real-world applications–improving social media retrieval using auxiliary sources and cross-social media retrieval. Representing each social media source using their textual tags, for both applications, we show that retrieval performance exceeds the existing state-of-the-art techniques. The proposed solution provides a generic framework and can be applicable to a wider context in data mining wherever one needs to exploit mutual and individual knowledge present across multiple data sources.

eLearning content authentication using bipartite matching

Content authenticity and correctness is one of the important challenges in eLearning as there can be many solutions for one specific problem in the cyber space. Therefore, we feel the necessity of mapping problem to solutions using graph partition and weighted bipartite matching. This paper presents a novel architecture and methodology for a personal eLearning system called PELS that is developed by us. We also present an efficient algorithm to partition question-answer (QA) space and explore best possible solution to a particular problem. Our approach can be efficiently applied to social eLearning space where there is one-to-many and many-to-many relationship with a level of bonding. The main advantage of our approach is that we use QA ranking by adjusted edge weights provided by subject matter experts (SME) or expert database. Finally, we use statistical methods called confidence interval and hypothesis test on the data to check the reliability and dependability of the quality of results.

A hybrid approach for multiple particle tracking microrheology

Geometric object detection has many applications, such as in tracking. Particle tracking microrheology is a technique for studying mechanical properties by accurately tracking the motion of the immersed particles undergoing Brownian motion. Since particles are carried along by these random undulations of the medium, they can move in and out of the microscope's depth of focus, which results in halos (lower intensity). Two-point particle tracking microrheology (TPM) uses a threshold to find those particles with peak, which leads to the broken trajectory of the particles. The halos of those particles which are out of focus are circles and the centres can be accurately tracked in most cases. When the particles are sparse, TPM will lose certain useful information. Thus, it may cause inaccurate microrheology. An efficient algorithm to detect the centre of those particles will increase the accuracy of the Brownian motion. In this paper, a hybrid approach is proposed which combines the steps of TPM for particles in focus with a circle detection step using circular Hough transform for particles with halos. As a consequence, it not only detects more particles in each frame but also dramatically extends the trajectories with satisfactory accuracy. Experiments over a video microscope data set of polystyrene spheres suspended in water undergoing Brownian motion confirmed the efficiency of the algorithm.