Data Visualisation and Exploration with Prior Knowledge
نویسندگان
چکیده
Visualising data for exploratory analysis is a major challenge in many applications where there is a need to gain insight into the structure and distribution of the data (e.g. to find common patterns and to identify relationships between samples as well as variables). Typically, visualisationmethods like principal components analysis (PCA) and multi-dimensional scaling (MDS) are employed. These methods are favoured because of their simplicity but it is difficult to incorporate prior knowledge about properties of the variable space into the analysis (particularly important where strong correlations are present) or to cope with missing data. One way to benefit from highly correlated variables is to model them using a block correlation matrix; this reduces the number of free parameters significantly and also captures the structural knowledge. In this way, noise on the correlated variables is modelled with a common parameter. In this paper we show how to utilise on such information by using a modification of a well known non-linear probabilistic visualisation model, Generative Topographic Mapping (GTM). The model has the advantage it can cope with missing data, which is particularly valuable in high-dimensional sparse datasets. In this paper it is shown that by including prior information about the grouping of variables in the covariance structure into the model one can improve both the data visualisation and the model fit. These benefits will be demonstrated on artificial data as well as a real geochemical dataset used for oil exploration, where the modification improved the imputation results by 3 to 13 %.
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تاریخ انتشار 2009