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Manifold visualisation techniques are commonly used to visualise high-dimensional datasets in physical sciences. In this paper, we apply a recently introduced manifold visualisation method, slisemap, on datasets from physics and chemistry. slisemap combines manifold visualisation with explainable artificial intelligence. Explainable artificial intelligence investigates the decision processes of black box machine learning models and complex simulators. With slisemap, we find an embedding such that data items with similar local explanations are grouped together. Hence, slisemap gives us an overview of the different behaviours of a black box model, where the patterns in the embedding reflect a target property. In this paper, we show how slisemap can be used and evaluated on physical data and that it is helpful in finding meaningful information on classification and regression models trained on these datasets. [ABSTRACT FROM AUTHOR]

Compositional data, which is data consisting of fractions or probabilities, is common in many fields including ecology, economics, physical science and political science. If these data would otherwise be normally distributed, their spread can be conveniently represented by a multivariate normal distribution truncated to the non-negative space under a unit simplex. Here this distribution is called the simplex-truncated multivariate normal distribution. For calculations on truncated distributions, it is often useful to obtain rapid estimates of their integral, mean and covariance; these quantities characterising the truncated distribution will generally possess different values to the corresponding non-truncated distribution. In this paper, three different approaches that can estimate the integral, mean and covariance of any simplex-truncated multivariate normal distribution are described and compared. These three approaches are (1) naive rejection sampling, (2) a method described by Gessner et al. that unifies subset simulation and the Holmes-Diaconis-Ross algorithm with an analytical version of elliptical slice sampling, and (3) a semi-analytical method that expresses the integral, mean and covariance in terms of integrals of hyperrectangularly-truncated multivariate normal distributions, the latter of which are readily computed in modern mathematical and statistical packages. Strong agreement is demonstrated between all three approaches, but the most computationally efficient approach depends strongly both on implementation details and the dimension of the simplex-truncated multivariate normal distribution. For computations in low-dimensional distributions, the semi-analytical method is fast and thus should be considered. As the dimension increases, the Gessner et al. method becomes the only practically efficient approach of the methods tested here. [ABSTRACT FROM AUTHOR]