Frontiers of Multimedia Research by Shih-Fu Chang

Author:Shih-Fu Chang
Language: eng
Format: epub
Publisher: Association for Computing Machinery and Morgan & Claypool Publishers
Published: 2018-03-14T16:00:00+00:00

Expected number of events in a cluster of offspring.The branching factor n* indicates whether the number of offspring associated with each immigrant is finite (n* < 1) or infinite (n* > 1). When n* < 1 a more accurate estimate of the size of each cluster can be obtained. Let Ai be the expected number of events in Generationi, and A0 = 1 (as each cluster has only one immigrant). The expected number of total events in the cluster, N∞, is defined as:

To compute Ai, i ≥ 1, we notice that each of the Ai−1 events in the previous generation has on average n* children events. This leads to an inductive relationship Ai = Ai−1n*. Knowing that A0 = 1, we derive:

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