uricohen
commented
9 months ago Dear @sydddl, apologies for the delayed response. The contribution of the paper is in correctly handling correlations between object centers; those correlations can be estimated only when the number of objects is large (such that the centers covariance matrix can be decomposed into a low rank matrix and a diagonal one, see paper). For the case from PRX where you have only a few objects, you can use the following:
[mean_half_width1, mean_argmax_norm1, mean_half_width2, mean_argmax_norm2, effective_dimension, effective_dimension2, alphac_hat, alphac_hat2] = calc_manifold_properties2(tuning_function, center_norm_from_cluster);
where tuning_function is an N x M if you have M samples from features of dimension N. The center_norm_from_cluster argument is the euclidian distance between the object center and the global objects center (e.g., in images there is a non zero global center because all pixel values are positive).
sydddl
I noticed that the example requires a dataset with a large number of classes for manifold analysis，
num class > 30。 I also read the PRX article that proposed the algorithm you implemented, but I didn’t have the relevant mathematical physics background so I didn’t quite understand it. So I would like to ask whether a single specific category can estimate its manifold radius in the model. Thank you so much