There has been a rapid uptake in the use of non-linear dimensionality reduction (NLDR) methods such as t-distributed stochastic neighbour embedding (t-SNE) in the natural sciences as part of cluster orientation and dimension reduction workflows. The appropriate use of these methods is made difficult by their complex parameterisations and the multitude of decisions required to balance the preservation of local and global structure in the resulting visualisation. We present visual diagnostics for the pragmatic usage of NLDR methods by combining them with a technique called the tour.
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Tensor decompositions are used for pattern recognition, exploratory data analysis, dimension reduction, and visualization of tensor-valued data. In this talk, I will review the theory, computation and visualization of the Higher-Order Orthogonal Iteration (HOOI), which is a higher-order generalization of the matrix-valued SVD. I will use a sample of resting state fMRI, and the ggbrain R package to help visualize the decomposition.
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Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for visualising data with concavities, or non-linear structure. It is associated with conditional distributions in statistics, and also linked brushing between plots in interactive data visualisation. This talk will describe the simple approach for slicing in the orthogonal space of projections obtained when running a tour, thus presenting the viewer with an interpolated sequence of sliced projections.
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