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, called Slise, on datasets from physics and chemistry. Slisemap combines manifold visualisation with explainable artificial intelligence. Explainable artificial intelligence is used to investigate 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. This makes Slisemap into a supervised manifold visualisation method, 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 Slisemap is helpful in finding meaningful information on classification and regression models trained on these datasets.

Abstract: Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the regression. The method can result in substantial gains in estimation efficiency and prediction accuracy over traditional maximum likelihood and least squares estimates. While predictor envelopes have been developed and studied for independent data, no work has been done adapting predictor envelopes to spatial data. In this work, the predictor envelope is adapted to a popular spatial model to form the spatial predictor envelope (SPE).

Existing explanation methods for black-box supervised learning models generally work by building local models that explain the models behaviour for a particular data item. It is possible to make global explanations, but the explanations may have low fidelity for complex models. Most of the prior work on explainable models has been focused on classification problems, with less attention on regression. We propose a new manifold visualization method, SLISEMAP, that at the same time finds local explanations for all of the data items and builds a two-dimensional visualization of model space such that the data items explained by the same model are projected nearby. We provide an open source implementation of our methods, implemented by using GPU-optimized PyTorch library. SLISEMAP works both on classification and regression models. We compare SLISEMAP to most popular dimensionality reduction methods and some local explanation methods. We provide mathematical derivation of our problem and show that SLISEMAP provides fast and stable visualizations that can be used to explain and understand black box regression and classification models.