Unsupervised Learning Algorithms by M. Emre Celebi & Kemal Aydin

Author:M. Emre Celebi & Kemal Aydin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

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Theorem 7 (Winner Update Rule).

The update of the winning multi-prototype of x i can be realized by

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Similar to [40], in one iteration of competitive learning, each data point x i is assigned to exactly one multi-prototype. Let the index array store the indices of m j q ordered data points assigned to the ω j q -th multi-prototype in one iteration. For instance, if x 1, x 32, x 8, x 20, x 15 are 5 ordered data points assigned to the ω 3 2-th multi-prototype in the t-th iteration, then the index array with and m 3 2 = 5. The following lemma formulates the cumulative update of the ω j q -th multi-prototype based on the index array π j q .

Lemma 2.

In the t-th iteration, the relation between the updated multi-prototype w j q and the old is:

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