Visualization by Linear Projections as Information Retrieval

We apply a recent formalization of visualization as information retrieval to linear projections. We introduce a method that optimizes a linear projection for an information retrieval task: retrieving neighbors of input samples based on their low-dimensional visualization coordinates only. The simple linear projection makes the method easy to interpret, while the visualization task is made well-defined by the novel information retrieval criterion. The method has a further advantage: it projects input features, but the input neighborhoods it preserves can be given separately from the input features, e.g. by external data of sample similarities. Thus the visualization can reveal the relationship between data features and complicated data similarities. We further extend the method to kernel-based projections.