Machine Learning-based Natural Scene Recognition for Mobile Robot Localization in An Unknown Environment by Xiaochun Wang & Xiali Wang & Don Mitchell Wilkes

Author:Xiaochun Wang & Xiali Wang & Don Mitchell Wilkes
Language: eng
Format: epub
ISBN: 9789811392177
Publisher: Springer Singapore

(2)To utilize the above observation, a favorable property of kNN is that the k-th nearest distance to each data point is a monotonic nonincreasing function of the portion of the dataset already explored (Angiulli and Pizzuti 2005; Angiulli et al. 2006; Angiulli and Fassetti 2009).

(3)As shown in Fig. 8.3, when searching for kNN for a data point, say p, it could be more efficient if more than one close data points are searched together, say all the data points no more than r distance away from p, so that the average number of distance computations can be much smaller than that when only one is searched. This is where triangular inequality can be of some help. Suppose that p and q are R distance apart. Data point q could have only one distance computation with p for it to be pruned from its distance computations with all those data points r distance from p, if R > 3r. Further, if R is larger than the sum of 3r plus the current k-th distance (not necessarily k-th nearest distance) of q, the k neighbors of q could be pruned from search as well.

Fig. 8.3Illustration of triangle inequality

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