I'm trying to replicate the results in this paper. I'm stuck at this part:enter image description here specifically,

calculate Jaccard intersection of pdata1 & pdata2

Is there some neat formula for calculating the Jaccard index of two normal distributions given their parameters?

I found this on Wikipedia, for the generalized Jaccard distance:

Or more simply, is there an easy trick to calculate the intersection and the union of two normal distributions given their parameters

[1]: https://www.researchgate.net/publication/304187762_Human_Activity_Recognition_in_AAL_Environments_Using_Random_Projections

  • $\begingroup$ Please explain what you mean by "Jaccard distance." There is a Jaccard index that is meaningful for two finite datasets, as indicated in the algorithm, but it's unclear how that would generalize to "normal distributions" and it isn't at all evident how it would be applicable to this algorithm anyway. $\endgroup$ – whuber Nov 20 '17 at 23:26
  • $\begingroup$ As a criterion for estimating the mapping, we use the Jaccard distance metric between two probability density estimates of data points representing each class. $\endgroup$ – aksd Nov 20 '17 at 23:55
  • $\begingroup$ The author uses Jaccard distance to mean Jaccard index. They're using random projections for coming up with a kernel density estimation given the data points and then calculating the Jaccard index. I don't see why Jaccard index cannot be applied to continuous distributions, the formula seems general enough. $\endgroup$ – aksd Nov 20 '17 at 23:59
  • $\begingroup$ According to Wikipedia, the Jaccard index "measures similarity between finite sample sets". Please explain in what possible sense a normal distribution could be considered a finite sample set! $\endgroup$ – whuber Nov 21 '17 at 1:23
  • 1
    $\begingroup$ According to Wikipedia, it can be generalized to probability measures. $\endgroup$ – aksd Nov 21 '17 at 17:50

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