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TL;DR: I am looking for datasets of which the attributes can be intuitively visualized (e.g. as a matrix, an image, a diagram, etc.) and are easy to individually select (e.g. by dragging/brushing over the matrix/image). What's more, it should be a dataset with which t-SNE has some difficulty, and of which some conceptual clusters are erroneously merged or separated in the embedding.

I am developing an adaptation of t-SNE that allows users to manipulate embeddings on-the-fly. Imagine one apparent cluster in a t-SNE embedding of which the user suspects or knows it to consist of two or more "actual"/conceptual clusters. t-SNE likely hasn't been able to separate them due to the discriminatory attributes (i.e. the high dimensions on which those conceptual clusters differ the most) being a minority within the dataset's high dimensions. In such a case, the user should be able to select all datapoints in this erroneously merged cluster in the embedding, select the discriminatory attributes in a visualization summarizing the selected datapoints, and let t-SNE adapt the similarities in such a way that:

  • inter-similarities (between datapoints from different conceptual clusters) are reduced by a lot

  • intra-similatities (between datapoints from the same conceptual cluster) are reduced very little

Now, I am looking for datasets with which I can demonstrate this feature. Suitable datasets have attributes that can be intuitively visualized and are individually selectable. Grayscale image datasets are the most obvious example (I'm already aware of these MNIST-like datasets), but it can be any dataset with a natural visualization.

Any suggestions for datasets that exhibit this problem, or directions for where to look, or ideas to go about this, are very much appreciated!

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