Current Slide

• Assess if non-random structure exists in the data by measuring the probability that the data is generated by a uniform data distribution
• Test spatial randomness by statistic test: Hopkins Static
• Given a dataset D regarded as a sample of a random variable o, determine how far away o is from being uniformly distributed in the data space
• Sample n points, p1, …, pn, uniformly from D. For each pi, find its nearest neighbor in D: xi = min{dist (pi, v)} where v in D
• Sample n points, q1, …, qn, uniformly from D. For each qi, find its nearest neighbor in D – {qi}: yi = min{dist (qi, v)} where v in D and v ≠ qi
• Calculate the Hopkins Statistic:

\[H=\frac{\sum_{i=1}^{n}y_{i}}{\sum_{i=1}^{n}x_{i}+\sum_{i=1}^{n}y_{i}}\]

• If D is uniformly distributed, ∑ xi and ∑ yi will be close to each other and H is close to 0.5. If D is clustered, H is close to 1