@You are not allowed to view links. Register or Login to view. Thanks for the long response. I'll chew on it and come back when I have time to go through that and the ecology papers properly.
@Stolfi I agree the order depends on the axes on which the data is projected on. If the data follows a sequence-like pattern (like horseshoe) in some direction, then surely that sequence pattern will be apparent in at least 1 PC (PCA1) if using the Euclidean norm, but I think the reciprocal might be true as well: if a horseshoe pattern emerges, where the clusters are sequential in PCA1, then in that axis (PCA1) the data must be sequence-like distributed, and what's more I suspect a partial order may be preserved to some extent between data points.
Of course, interpreting that sequence and its meaning depends on what PCA1 even stands for, and whether we could canonically ascribe it to "time" is a whole different matter. Because the plot is based on pairwise divergence, PCA1 probably measures a pondered "distance" to many folia, as in "It's 20% similar to f33v's glyph transitions, 5% similar to f66r's, 13.5% similar to 107v, ···", which is hard to interpret. On that topic, @npcompl33t Is the PCA data open-sourced? Could we take a peak on the MDS axes and their coordinates to try and interpret that? Sorry if you've mentioned this in your main thread, I'm having a hard time catching up on threads lately.
@Stolfi I agree the order depends on the axes on which the data is projected on. If the data follows a sequence-like pattern (like horseshoe) in some direction, then surely that sequence pattern will be apparent in at least 1 PC (PCA1) if using the Euclidean norm, but I think the reciprocal might be true as well: if a horseshoe pattern emerges, where the clusters are sequential in PCA1, then in that axis (PCA1) the data must be sequence-like distributed, and what's more I suspect a partial order may be preserved to some extent between data points.
Of course, interpreting that sequence and its meaning depends on what PCA1 even stands for, and whether we could canonically ascribe it to "time" is a whole different matter. Because the plot is based on pairwise divergence, PCA1 probably measures a pondered "distance" to many folia, as in "It's 20% similar to f33v's glyph transitions, 5% similar to f66r's, 13.5% similar to 107v, ···", which is hard to interpret. On that topic, @npcompl33t Is the PCA data open-sourced? Could we take a peak on the MDS axes and their coordinates to try and interpret that? Sorry if you've mentioned this in your main thread, I'm having a hard time catching up on threads lately.