Collaborative Virtual Environments: an introductory review

In Virtual Reality. Research Developments and Applications, Vol 3, 3-15, 1998
Collaborative Virtual Environments: an introductory review
Elizabeth Churchill, Dave Snowdon

A Collaborative Virtual Environment or CVE is a distributed, virtual reality that is designed to support collaborative activities. As such, CVEs provide a potentially infinite, graphically realised digital landscape within which multiple users can interact with each other and with simple or complex data representations.

CVEs are increasingly being used to support collaborative work between geographically separated and between collocated collaborators. CVEs vary in the sophistication of the data and embodiment representations employed and in the level of interactivity supported.

It is clear that systems which are intended to support collaborative activities should be designed with explicit consideration of the tasks to be achieved and the intended users' social and cognitive characteristics.

In this paper, we detail a number of existing systems and applications, but first discuss the nature of collaborative and cooperative work activities and consider the place of virtual reality systems in supporting such collaborative work. Following this, we discuss some future research directions.

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Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.