Abstract
Similarity measures are central to many machine learning algorithms. There are many different similarity measures, each catering for different applications and data requirements. Most similarity measures used with numerical data assume that the attributes are interval scale. In the interval scale, it is assumed that a unit difference has the same meaning irrespective of the magnitudes of the values separated. When this assumption is violated, accuracy may be reduced. Our experiments show that removing the interval scale assumption by transforming data to ranks can improve the accuracy of distance-based similarity measures on some tasks. However the rank transform has high time and storage overheads. In this paper, we introduce an efficient similarity measure which does not consider the magnitudes of inter-instance distances. We compare the new similarity measure with popular similarity measures in two applications: DBScan clustering and content based multimedia information retrieval with real world datasets and different transform functions. The results show that the proposed similarity measure provides good performance on a range of tasks and is invariant to violations of the interval scale assumption.
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Notes
A monotonic transform, \(f:{\mathbb {R}} \rightarrow {\mathbb {R}}\) is either \(\forall x > y \Leftrightarrow f(x) \ge f(y)\) or \(\forall x > y \Leftrightarrow f(x) \le f(y)\). Such a transform can produce ambiguities in the order. A strictly monotonic transform is either \(\forall x > y \Leftrightarrow f(x) > f(y)\) or \(\forall x > y \Leftrightarrow f(x) < f(y)\). Hence, a strictly monotonic transform can guarantee either order preservation or order reversal.
Datasets are generally subjected to min-max normalization. As a result, linear order preserving transforms do not alter the similarity scores.
Only the top k instances are important to the user in information retrieval.
ReFeat works only with imbalanced trees. Sample size 2 can only produce balanced trees.
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Acknowledgments
We are grateful to Francois Petitjean for valuable feedback and suggestions. This research has been supported by the Australian Research Council under Grant DP140100087.
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Fernando, T.L., Webb, G.I. SimUSF: an efficient and effective similarity measure that is invariant to violations of the interval scale assumption. Data Min Knowl Disc 31, 264–286 (2017). https://doi.org/10.1007/s10618-016-0463-0
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DOI: https://doi.org/10.1007/s10618-016-0463-0