We further highlight the relationship between the SAM topology and the HFE by performing principal component analysis (PCA) on all 400 sampled EC curves derived from 40 simulations with precomputed HFE values. The EC curve of each sample is represented as a vector x j ∈ R m where m = 20 is our number of filtration thresholds and the entries of x j are the EC values of the sublevel sets. Each vector is stacked into a matrix