Mobius strip

%matplotlib inline

# Not really required
import sys
sys.path.insert(0, '../../..')

from pyLDLE2 import datasets
from pyLDLE2 import buml_, util_

matplotlib.get_backend() =  module://matplotlib_inline.backend_inline

save_dir_root = '../data/pyLDLE2/mobiusstrip3d/'

X, labelsMat, ddX = datasets.Datasets().mobiusstrip3d()

X.shape =  (8280, 3)

# The supplied options would override the default options
buml_obj = buml_.BUML(local_opts={'algo':'LDLE'},
                  intermed_opts={'eta_min': 5},
                  vis_opts={'c': labelsMat[:,0], 'save_dir': save_dir_root},
                  verbose=True, debug=True)

local_opts['k_nn0'] = 700 is created.
Options provided:
local_opts:
{
    "Atilde_method": "LDLE_1",
    "N": 100,
    "U_method": "k_nn",
    "algo": "LDLE",
    "alpha": 1,
    "debug": true,
    "delta": 0.9,
    "gl_type": "unnorm",
    "k": 28,
    "k_nn": 49,
    "k_nn0": 700,
    "k_tune": 7,
    "lambda1_decay": 0.75,
    "lambda1_init": 8,
    "lambda1_min": 0.001,
    "max_iter": 300,
    "max_sparsity": 0.9,
    "metric": "euclidean",
    "n_proc": 32,
    "p": 0.99,
    "power": 5,
    "pp_n_thresh": 32,
    "radius": 0.5,
    "reg": 0.0,
    "scale_by": "gamma",
    "tau": 50,
    "to_postprocess": true,
    "verbose": true
}
intermed_opts:
{
    "algo": "best",
    "debug": true,
    "eta_max": 25,
    "eta_min": 5,
    "len_S_thresh": 256,
    "local_algo": "LDLE",
    "metric": "euclidean",
    "n_proc": 32,
    "n_times": 4,
    "verbose": true
}
global_opts:
{
    "add_dim": false,
    "align_transform": "rigid",
    "align_w_parent_only": true,
    "alpha": 0.3,
    "beta": {
        "align": null,
        "repel": 1
    },
    "color_tear": true,
    "compute_error": false,
    "debug": true,
    "eps": 1e-08,
    "err_tol": 0.0001,
    "far_off_points_type": "reuse_fixed",
    "init_algo_name": "procrustes",
    "k": 28,
    "max_internal_iter": 100,
    "max_iter": 20,
    "metric": "euclidean",
    "n_proc": 32,
    "n_repel": 0,
    "nu": 3,
    "patience": 5,
    "refine_algo_name": "rgd",
    "repel_by": 0.0,
    "to_tear": true,
    "verbose": true,
    "vis_before_init": false
}

buml_obj.fit(X=X)

Computing local views using LDLE
Constructing unnorm graph Laplacian + its eigendecomposition.
Done.
##############################
Time elapsed from last time log: 2.7 seconds
Total time elapsed: 2.7 seconds
##############################
Computing Atilde: Inner Prod of Grad of EigFuncs.
FEM for Atilde.
Atilde: 0 points processed...
Atilde: 2070 points processed...
Atilde: 4140 points processed...
Atilde: 6210 points processed...
Atilde: all points processed...
Done.
##############################
Time elapsed from last time log: 0.6 seconds
Total time elapsed: 3.4 seconds
##############################
Computing LDLE.
local_param: all 8280 points processed...
max distortion is 1004.665859
Done.
##############################
Time elapsed from last time log: 1.5 seconds
Total time elapsed: 4.9 seconds
##############################
Posprocessing local parameterizations.
#Param replaced: 7795, max distortion: 10.215162
#Param replaced: 3599, max distortion: 5.101422
#Param replaced: 1207, max distortion: 5.062659
#Param replaced: 311, max distortion: 5.062659
#Param replaced: 65, max distortion: 5.062659
#Param replaced: 16, max distortion: 5.062659
#Param replaced: 1, max distortion: 5.062659
#Param replaced: 0, max distortion: 5.062659
Max local distortion after postprocessing: 5.062659433467454
Done.
##############################
Time elapsed from last time log: 6.3 seconds
Total time elapsed: 11.3 seconds
##############################
Max local distortion = 5.062659433467454
Constructing intermediate views.
eta = 2.
#non-empty views with sz < 2 = 8280
#nodes in views with sz < 2 = 8280
Costs computed when eta = 2.
##############################
Time elapsed from last time log: 6.3 seconds
Total time elapsed: 7.1 seconds
##############################
ctr=6431, total_len_S=42462, avg_len_S=6.603
Remaining #nodes in views with sz < 2 = 0
Done with eta = 2.
##############################
Time elapsed from last time log: 158.4 seconds
Total time elapsed: 165.5 seconds
##############################
eta = 3.
#non-empty views with sz < 3 = 442
#nodes in views with sz < 3 = 884
Costs computed when eta = 3.
##############################
Time elapsed from last time log: 1.5 seconds
Total time elapsed: 167.0 seconds
##############################
ctr=777, total_len_S=14526, avg_len_S=18.695
Remaining #nodes in views with sz < 3 = 0
Done with eta = 3.
##############################
Time elapsed from last time log: 8.2 seconds
Total time elapsed: 175.2 seconds
##############################
eta = 4.
#non-empty views with sz < 4 = 338
#nodes in views with sz < 4 = 1014
Costs computed when eta = 4.
##############################
Time elapsed from last time log: 1.4 seconds
Total time elapsed: 176.6 seconds
##############################
ctr=915, total_len_S=24304, avg_len_S=26.562
Remaining #nodes in views with sz < 4 = 0
Done with eta = 4.
##############################
Time elapsed from last time log: 15.7 seconds
Total time elapsed: 192.4 seconds
##############################
eta = 5.
#non-empty views with sz < 5 = 210
#nodes in views with sz < 5 = 840
Costs computed when eta = 5.
##############################
Time elapsed from last time log: 1.5 seconds
Total time elapsed: 193.8 seconds
##############################
ctr=780, total_len_S=24837, avg_len_S=31.842
Remaining #nodes in views with sz < 5 = 0
Done with eta = 5.
##############################
Time elapsed from last time log: 14.2 seconds
Total time elapsed: 208.0 seconds
##############################
Pruning and cleaning up.
Done.
##############################
Time elapsed from last time log: 0.8 seconds
Total time elapsed: 208.8 seconds
##############################
After clustering, max distortion is 5.170363
Using rigid transforms for alignment.
Computing laterations scores for overlaps b/w intermed views
Done
##############################
Time elapsed from last time log: 1.4 seconds
Total time elapsed: 1.4 seconds
##############################
Computing a lateration.
Seq of intermediate views and their predecessors computed.
No. of connected components = 1
Done.
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 1.4 seconds
##############################
Computing initial embedding using: procrustes algorithm
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 1.4 seconds
##############################
Initial alignment of 242 views completed
Initial alignment of 484 views completed
Initial alignment of 726 views completed
Initial alignment of 968 views completed
Embedding initialized.
##############################
Time elapsed from last time log: 0.9 seconds
Total time elapsed: 2.3 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 0
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 8.8 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.0 seconds
Total time elapsed: 14.8 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 1
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 18.2 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.3 seconds
Total time elapsed: 24.5 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 2
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 27.7 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 7.0 seconds
Total time elapsed: 34.6 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 3
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 38.5 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 10.9 seconds
Total time elapsed: 49.4 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 4
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 52.5 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 11.8 seconds
Total time elapsed: 64.3 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 5
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 67.6 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.7 seconds
Total time elapsed: 74.3 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 6
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 77.1 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.2 seconds
Total time elapsed: 83.3 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 7
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 86.0 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.7 seconds
Total time elapsed: 92.7 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 8
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 95.7 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.6 seconds
Total time elapsed: 102.3 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 9
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 105.3 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.5 seconds
Total time elapsed: 111.9 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 10
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 115.1 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.7 seconds
Total time elapsed: 121.8 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 11
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 124.6 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.5 seconds
Total time elapsed: 131.1 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 12
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 134.0 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.6 seconds
Total time elapsed: 140.6 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 13
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 143.5 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.2 seconds
Total time elapsed: 149.6 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 14
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 152.6 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.5 seconds
Total time elapsed: 159.1 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 15
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 162.0 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 7.0 seconds
Total time elapsed: 169.0 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 16
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 172.3 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 7.2 seconds
Total time elapsed: 179.5 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 17
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 182.6 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.5 seconds
Total time elapsed: 189.1 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 18
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 192.4 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 6.7 seconds
Total time elapsed: 199.1 seconds
##############################

Refining with rgd algorithm for 100 iterations.
Refinement iteration: 19
##############################
Time elapsed from last time log: 0.0 seconds
Total time elapsed: 202.3 seconds
##############################
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Descent starts
Done.
##############################
Time elapsed from last time log: 7.3 seconds
Total time elapsed: 209.6 seconds
##############################
Computing error.
min and max weights: 1.0 1.0
Computing Pseudoinverse of a matrix of L of size 8280 + 970 multiplied with B
Computing svd
Done
Alignment error: 1.234180
##############################
Time elapsed from last time log: 3.4 seconds
Total time elapsed: 213.0 seconds
##############################

array([[0.0915467 , 0.09981265],
       [0.09332139, 0.09977557],
       [0.09698226, 0.09969434],
       ...,
       [0.09658628, 0.11246386],
       [0.09313934, 0.11155664],
       [0.09133735, 0.10783215]])

%matplotlib inline
buml_obj.GlobalViews.vis_embedding(buml_obj.GlobalViews.y_final, buml_obj.vis, buml_obj.vis_opts,
                               buml_obj.GlobalViews.color_of_pts_on_tear_final,
                               title='Final global embedding', )

util_.save(save_dir_root, 'ldle.dat', [X, labelsMat, buml_obj])