by Connor, Harry, and Jake

I ran the stream with the following parameters:

N = 10,000 (number of points)

n = 50 (number of landmark points)

maxDistance = 0.1

I ran the algorithm on each dimension 3 times and got the Betti profile correct every time.

For k=5, I had to reduce N to 5,000 for computational efficiency. Even with that reduction, there were on average 250,000 simpleces. I correctly recovered the betti profile each time.

For k=6, I had to reduce N to 1,000 for the program to run (resulting in on average 250,000) simpleces. I could not recover the Betti profile, instead having plots like this:

We found $b_5$ to be very large but $b_6=0$, which is incorrect.

Thus the biggest boundary seems to be just in computational power. If I had more processing power, I could use more than 1,000 points in 6 dimensions, and accurately recover the profile.