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Estimating Jaccard Index with Missing Observations: A Matrix Calibration Approach
Wenye Li

Thu Dec 10 08:00 AM -- 12:00 PM (PST) @ 210 C #41 #None

The Jaccard index is a standard statistics for comparing the pairwise similarity between data samples. This paper investigates the problem of estimating a Jaccard index matrix when there are missing observations in data samples. Starting from a Jaccard index matrix approximated from the incomplete data, our method calibrates the matrix to meet the requirement of positive semi-definiteness and other constraints, through a simple alternating projection algorithm. Compared with conventional approaches that estimate the similarity matrix based on the imputed data, our method has a strong advantage in that the calibrated matrix is guaranteed to be closer to the unknown ground truth in the Frobenius norm than the un-calibrated matrix (except in special cases they are identical). We carried out a series of empirical experiments and the results confirmed our theoretical justification. The evaluation also reported significantly improved results in real learning tasks on benchmarked datasets.

Author Information

Wenye Li (Macao Polytechnic Institute)

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