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Proportional data (normalized histograms) have been frequently occurring in various areas, and they could be mathematically abstracted as points residing in a geometric simplex. A proper distance metric on this simplex is of importance in many applications including classification and information re ...

In multiple instance learning (MIL), how the instances determine the bag-labels is an essential issue, both algorithmically and intrinsically. In this paper, we show that the mechanism of how the instances determine the bag-labels is different for different application domains, and does not necessar ...

We consider feature extraction (dimensionality reduction) for compositional data, where the data vectors are constrained to be positive and constant-sum. In real-world problems, the data components (variables) usually have complicated "correlations" while their total number is huge. Such scenario de ...