| Name | geom-archetypal JSON |
| Version |
1.0.2
JSON |
| download |
| home_page | None |
| Summary | Geometric Archetypal Analysis |
| upload_time | 2024-05-18 10:49:13 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.8 |
| license | Copyright (c) 2024 Demetris Christopoulos Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
| keywords |
geometrical archetypal analysis
convex hull
grid archetypal
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
|
| coveralls test coverage |
No coveralls.
|
# geom_archetypal
## Geometrical Archetypal Analysis
Overview
--------
geom_archetypal is a Python Module for performing Grid Archetypal Analysis (GAA) by using
a properly modified version of the PCHA algorithm.
Basic functions are:
- `fast_archetypal()` Archetypal Analysis (AA) with given data rows as archetypes
- `grid_archetypal` For a data matrix n x d finds the Grid Archetypes and performs AA
- `closer_grid_archetypal` For a data matrix n x d finds the Closer Grid Archetypes and performs AA
- `archetypal_pcha()` Principal Convex Hull Analysis (PCHA)
Installation
------------
On the terminal of your operating system write and press enter:
```python
$ pip install geom_archetypal
```
Usage
-----
```python
# Load Module:
from geom_archetypal import *
# Set seed:
seed=20240518
np.random.seed(seed)
# Create random data
n=100
d=2
df = np.random.random((n, d))
# grid_atrchetypal()
BY, A, B, AM, AMDF, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (
grid_archetypal(df, diag_less = 1e-6, verbose = True))
pd.DataFrame(BY)
AMDF
[SSE, varexpl, fin_iters, time_elapsed, diagsum_final]
Fast Archetypal Analysis:
Compute the compositions when the archetypes are already given
|--------|--------------|--------------|-------------------------|
| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |
|--------|--------------|--------------|-------------------------|
| 1 | 2.626019e+01 | 2.078703e+00 | 11.632968|
| 2 | 2.078703e+00 | 8.176473e-01 | 1.542298|
| 3 | 8.176473e-01 | 1.286832e+00 | 0.364605|
| 4 | 8.176473e-01 | 1.563447e-01 | 4.229772|
| 5 | 1.563447e-01 | 1.204240e-01 | 0.298286|
| 6 | 1.204240e-01 | 1.948338e-01 | 0.381914|
| 7 | 1.204240e-01 | 1.339817e-02 | 7.988091|
| 8 | 1.339817e-02 | 6.356475e-03 | 1.107799|
|--------|--------------|--------------|-------------------------|
Time for the 8 A updates was 0 secs
|----------|------------|--------------|-------------------|--------------|
| Iter | VarExpl | SSE | SSE_8 / SSE_0 | muA |
|----------|------------|--------------|-------------------|--------------|
| 8 | 0.999903 | 6.356475e-03 | 0.000242 | 7.4650e-01|
|----------|------------|--------------|-------------------|--------------|
The sum of diagonal elements for the sub-matrix of closer grid points is 4.0
The ideal sum would be 4
#closer_grid_archetypal(
BY, A, B, ADF, imins, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (
closer_grid_archetypal(df, diag_less = 1e-6, verbose = True))
pd.DataFrame(BY)
ADF
[SSE, varexpl, fin_iters, time_elapsed, diagsum_final]
Fast Archetypal Analysis:
Compute the compositions when the archetypes are already given
|--------|--------------|--------------|-------------------------|
| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |
|--------|--------------|--------------|-------------------------|
| 1 | 2.339832e+01 | 2.111296e+00 | 10.082445|
| 2 | 2.111296e+00 | 5.136190e-01 | 3.110626|
| 3 | 5.136190e-01 | 6.213599e-01 | 0.173395|
| 4 | 5.136190e-01 | 1.098227e-01 | 3.676804|
| 5 | 1.098227e-01 | 6.322219e-02 | 0.737090|
| 6 | 6.322219e-02 | 8.338054e-02 | 0.241763|
| 7 | 6.322219e-02 | 1.851679e-02 | 2.414316|
| 8 | 1.851679e-02 | 1.440165e-02 | 0.285741|
| 9 | 1.440165e-02 | 1.325812e-02 | 0.086251|
| 10 | 1.325812e-02 | 1.334901e-02 | 0.006809|
| 11 | 1.325812e-02 | 1.243129e-02 | 0.066512|
|--------|--------------|--------------|-------------------------|
Time for the 11 A updates was 0 secs
|----------|------------|--------------|-------------------|--------------|
| Iter | VarExpl | SSE | SSE_11 / SSE_0 | muA |
|----------|------------|--------------|-------------------|--------------|
| 11 | 0.999799 | 1.243129e-02 | 0.000531 | 5.3748e-01|
|----------|------------|--------------|-------------------|--------------|
The sum of diagonal elements for the sub-matrix of closer grid points is 4.0
The ideal sum would be 4
# fast_archetypal(): we use the imins from closer_grid_archetypal() above
BY, A, B, irows, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (
fast_archetypal(df, irows = imins, verbose = True, diag_less = 1e-6))
pd.DataFrame(BY)
[SSE,varexpl,fin_iters, time_elapsed, diagsum_final]
Fast Archetypal Analysis:
Compute the compositions when the archetypes are already given
|--------|--------------|--------------|-------------------------|
| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |
|--------|--------------|--------------|-------------------------|
| 1 | 2.240585e+01 | 1.936972e+00 | 10.567465|
| 2 | 1.936972e+00 | 5.236400e-01 | 2.699052|
| 3 | 5.236400e-01 | 5.861317e-01 | 0.106617|
| 4 | 5.236400e-01 | 1.122365e-01 | 3.665504|
| 5 | 1.122365e-01 | 7.476762e-02 | 0.501138|
| 6 | 7.476762e-02 | 8.903380e-02 | 0.160233|
| 7 | 7.476762e-02 | 1.994893e-02 | 2.747951|
| 8 | 1.994893e-02 | 1.549558e-02 | 0.287395|
| 9 | 1.549558e-02 | 1.457414e-02 | 0.063225|
|--------|--------------|--------------|-------------------------|
Time for the 9 A updates was 0 secs
|----------|------------|--------------|-------------------|--------------|
| Iter | VarExpl | SSE | SSE_9 / SSE_0 | muA |
|----------|------------|--------------|-------------------|--------------|
| 9 | 0.999764 | 1.457414e-02 | 0.000650 | 8.9580e-01|
|----------|------------|--------------|-------------------|--------------|
# archetypal_pcha()
BY, A, B, SSE, varexpl, BY0, converges, iterations, total_time = (
archetypal_pcha(df, kappas = 3, conv_crit=1E-6, maxiter=2000, verbose=True))
pd.DataFrame(BY0)
pd.DataFrame(BY)
[SSE, varexpl, converges, iterations, total_time]
PCHA Archetypal Analysis:
Principal Convex Hull Analysis / Archetypal Analysis
The mumber of Archetypes will be kappas = 3
To stop algorithm press control C
|----------|------------|------------|-------------|------------|------------|------------|------------|
Iter | VarExpl | SSE | |dSSE|/SSE | muC | mualpha | muS | Time(s)
|----------|------------|------------|-------------|------------|------------|------------|------------|
| 1 | 0.969057 | 1.9137e+00 | 7.0437e-01 | 1.548e+00 | 1.000e+00 | 1.154e+00 | 0.004 |
| 2 | 0.973296 | 1.6515e+00 | 1.5874e-01 | 2.396e+00 | 1.000e+00 | 8.929e-01 | 0.004 |
| 3 | 0.974737 | 1.5623e+00 | 5.7068e-02 | 7.418e+00 | 1.000e+00 | 1.382e+00 | 0.003 |
| 4 | 0.975468 | 1.5171e+00 | 2.9789e-02 | 1.148e+01 | 1.000e+00 | 1.070e+00 | 0.004 |
| 5 | 0.975934 | 1.4883e+00 | 1.9357e-02 | 1.777e+01 | 1.000e+00 | 1.656e+00 | 0.003 |
| 6 | 0.976253 | 1.4686e+00 | 1.3440e-02 | 1.376e+01 | 1.000e+00 | 1.282e+00 | 0.004 |
| 7 | 0.976555 | 1.4499e+00 | 1.2862e-02 | 2.129e+01 | 1.000e+00 | 1.984e+00 | 0.002 |
| 8 | 0.976821 | 1.4335e+00 | 1.1475e-02 | 3.296e+01 | 1.000e+00 | 1.535e+00 | 0.002 |
| 9 | 0.977052 | 1.4192e+00 | 1.0097e-02 | 2.551e+01 | 1.000e+00 | 1.188e+00 | 0.002 |
| 10 | 0.977240 | 1.4075e+00 | 8.2598e-03 | 1.975e+01 | 1.000e+00 | 9.197e-01 | 0.002 |
| 11 | 0.977397 | 1.3978e+00 | 6.9319e-03 | 1.528e+01 | 1.000e+00 | 1.424e+00 | 0.002 |
| 12 | 0.977546 | 1.3886e+00 | 6.6443e-03 | 5.914e+00 | 1.000e+00 | 2.204e+00 | 0.002 |
| 13 | 0.977713 | 1.3783e+00 | 7.4633e-03 | 4.577e+00 | 1.000e+00 | 8.528e-01 | 0.002 |
| 14 | 0.977873 | 1.3684e+00 | 7.2652e-03 | 7.085e+00 | 1.000e+00 | 1.320e+00 | 0.002 |
| 15 | 0.978040 | 1.3581e+00 | 7.6022e-03 | 5.484e+00 | 1.000e+00 | 1.022e+00 | 0.002 |
| 16 | 0.978221 | 1.3469e+00 | 8.2898e-03 | 4.244e+00 | 1.000e+00 | 1.582e+00 | 0.002 |
| 17 | 0.978424 | 1.3344e+00 | 9.4027e-03 | 6.570e+00 | 1.000e+00 | 1.224e+00 | 0.002 |
| 18 | 0.978628 | 1.3217e+00 | 9.5674e-03 | 5.085e+00 | 1.000e+00 | 9.474e-01 | 0.002 |
| 19 | 0.978841 | 1.3086e+00 | 1.0053e-02 | 3.935e+00 | 1.000e+00 | 1.467e+00 | 0.002 |
| 20 | 0.979046 | 1.2959e+00 | 9.7856e-03 | 6.092e+00 | 1.000e+00 | 5.675e-01 | 0.002 |
| 21 | 0.979247 | 1.2835e+00 | 9.6734e-03 | 4.715e+00 | 1.000e+00 | 8.785e-01 | 0.002 |
| 22 | 0.979447 | 1.2710e+00 | 9.7607e-03 | 7.298e+00 | 1.000e+00 | 1.360e+00 | 0.002 |
| 23 | 0.979640 | 1.2592e+00 | 9.4451e-03 | 5.649e+00 | 1.000e+00 | 1.052e+00 | 0.002 |
| 24 | 0.979829 | 1.2474e+00 | 9.4144e-03 | 8.744e+00 | 1.000e+00 | 8.146e-01 | 0.002 |
| 25 | 0.979933 | 1.2410e+00 | 5.1822e-03 | 6.767e+00 | 1.000e+00 | 1.261e+00 | 0.002 |
| 26 | 0.980005 | 1.2366e+00 | 3.5570e-03 | 1.048e+01 | 1.000e+00 | 1.952e+00 | 0.002 |
| 27 | 0.980053 | 1.2336e+00 | 2.4384e-03 | 1.622e+01 | 1.000e+00 | 7.553e-01 | 0.002 |
| 28 | 0.980086 | 1.2315e+00 | 1.6616e-03 | 1.255e+01 | 1.000e+00 | 1.169e+00 | 0.002 |
| 29 | 0.980109 | 1.2301e+00 | 1.1472e-03 | 1.943e+01 | 1.000e+00 | 9.049e-01 | 0.002 |
| 30 | 0.980124 | 1.2292e+00 | 7.7082e-04 | 1.504e+01 | 1.000e+00 | 1.401e+00 | 0.002 |
| 31 | 0.980135 | 1.2285e+00 | 5.2532e-04 | 2.327e+01 | 1.000e+00 | 1.084e+00 | 0.002 |
| 32 | 0.980142 | 1.2281e+00 | 3.7454e-04 | 1.801e+01 | 1.000e+00 | 1.678e+00 | 0.002 |
| 33 | 0.980147 | 1.2277e+00 | 2.5874e-04 | 1.394e+01 | 1.000e+00 | 1.299e+00 | 0.002 |
| 34 | 0.980151 | 1.2275e+00 | 1.7650e-04 | 1.079e+01 | 1.000e+00 | 2.011e+00 | 0.002 |
| 35 | 0.980154 | 1.2274e+00 | 1.2759e-04 | 1.670e+01 | 1.000e+00 | 1.556e+00 | 0.002 |
| 36 | 0.980155 | 1.2273e+00 | 9.8252e-05 | 1.293e+01 | 1.000e+00 | 1.204e+00 | 0.002 |
| 37 | 0.980157 | 1.2272e+00 | 7.7710e-05 | 1.001e+01 | 1.000e+00 | 9.321e-01 | 0.002 |
| 38 | 0.980158 | 1.2271e+00 | 5.6505e-05 | 1.549e+01 | 1.000e+00 | 1.443e+00 | 0.002 |
| 39 | 0.980159 | 1.2270e+00 | 4.9600e-05 | 1.199e+01 | 1.000e+00 | 1.117e+00 | 0.002 |
| 40 | 0.980160 | 1.2270e+00 | 4.1790e-05 | 9.278e+00 | 1.000e+00 | 1.729e+00 | 0.002 |
| 41 | 0.980161 | 1.2269e+00 | 3.7995e-05 | 1.436e+01 | 1.000e+00 | 1.338e+00 | 0.002 |
| 42 | 0.980161 | 1.2269e+00 | 3.6791e-05 | 1.112e+01 | 1.000e+00 | 2.071e+00 | 0.002 |
| 43 | 0.980162 | 1.2268e+00 | 3.3335e-05 | 1.721e+01 | 1.000e+00 | 1.603e+00 | 0.002 |
| 44 | 0.980163 | 1.2268e+00 | 3.1141e-05 | 1.332e+01 | 1.000e+00 | 1.241e+00 | 0.002 |
| 45 | 0.980163 | 1.2268e+00 | 3.3211e-05 | 1.031e+01 | 1.000e+00 | 9.602e-01 | 0.002 |
| 46 | 0.980164 | 1.2267e+00 | 3.3546e-05 | 7.977e+00 | 1.000e+00 | 1.486e+00 | 0.002 |
| 47 | 0.980165 | 1.2267e+00 | 3.1603e-05 | 1.235e+01 | 1.000e+00 | 1.150e+00 | 0.002 |
| 48 | 0.980165 | 1.2266e+00 | 3.0910e-05 | 1.911e+01 | 1.000e+00 | 1.781e+00 | 0.002 |
| 49 | 0.980166 | 1.2266e+00 | 3.1031e-05 | 1.479e+01 | 1.000e+00 | 1.378e+00 | 0.002 |
| 50 | 0.980167 | 1.2266e+00 | 3.1274e-05 | 1.145e+01 | 1.000e+00 | 1.067e+00 | 0.002 |
| 51 | 0.980167 | 1.2265e+00 | 3.0282e-05 | 1.772e+01 | 1.000e+00 | 1.651e+00 | 0.002 |
| 52 | 0.980168 | 1.2265e+00 | 3.0849e-05 | 1.372e+01 | 1.000e+00 | 1.278e+00 | 0.002 |
| 53 | 0.980168 | 1.2265e+00 | 3.1283e-05 | 1.062e+01 | 1.000e+00 | 9.890e-01 | 0.002 |
| 54 | 0.980169 | 1.2264e+00 | 3.0494e-05 | 1.643e+01 | 1.000e+00 | 1.531e+00 | 0.002 |
| 55 | 0.980170 | 1.2264e+00 | 3.1566e-05 | 1.272e+01 | 1.000e+00 | 1.185e+00 | 0.002 |
| 56 | 0.980170 | 1.2263e+00 | 3.0652e-05 | 9.844e+00 | 1.000e+00 | 1.834e+00 | 0.002 |
| 57 | 0.980171 | 1.2263e+00 | 2.6192e-05 | 3.048e+01 | 1.000e+00 | 1.420e+00 | 0.002 |
| 58 | 0.980171 | 1.2263e+00 | 1.1450e-05 | 2.359e+01 | 1.000e+00 | 1.099e+00 | 0.002 |
| 59 | 0.980171 | 1.2263e+00 | 9.3466e-06 | 1.826e+01 | 1.000e+00 | 1.701e+00 | 0.002 |
| 60 | 0.980171 | 1.2263e+00 | 8.4407e-06 | 2.826e+01 | 1.000e+00 | 1.316e+00 | 0.002 |
| 61 | 0.980171 | 1.2263e+00 | 8.4114e-06 | 2.187e+01 | 1.000e+00 | 1.019e+00 | 0.002 |
| 62 | 0.980172 | 1.2263e+00 | 9.1324e-06 | 1.693e+01 | 1.000e+00 | 1.577e+00 | 0.002 |
| 63 | 0.980172 | 1.2262e+00 | 8.8070e-06 | 1.310e+01 | 1.000e+00 | 1.221e+00 | 0.002 |
| 64 | 0.980172 | 1.2262e+00 | 8.6021e-06 | 2.028e+01 | 1.000e+00 | 9.447e-01 | 0.002 |
| 65 | 0.980172 | 1.2262e+00 | 8.4549e-06 | 1.570e+01 | 1.000e+00 | 1.462e+00 | 0.002 |
| 66 | 0.980172 | 1.2262e+00 | 8.9234e-06 | 1.215e+01 | 1.000e+00 | 1.132e+00 | 0.002 |
| 67 | 0.980172 | 1.2262e+00 | 8.7704e-06 | 1.881e+01 | 1.000e+00 | 8.759e-01 | 0.002 |
| 68 | 0.980173 | 1.2262e+00 | 8.6715e-06 | 1.455e+01 | 1.000e+00 | 1.356e+00 | 0.002 |
| 69 | 0.980173 | 1.2262e+00 | 8.0681e-06 | 2.253e+01 | 1.000e+00 | 1.049e+00 | 0.002 |
| 70 | 0.980173 | 1.2262e+00 | 8.8384e-06 | 1.744e+01 | 1.000e+00 | 1.624e+00 | 0.002 |
| 71 | 0.980173 | 1.2262e+00 | 8.6672e-06 | 2.699e+01 | 1.000e+00 | 1.257e+00 | 0.002 |
| 72 | 0.980173 | 1.2261e+00 | 8.1818e-06 | 2.089e+01 | 1.000e+00 | 9.731e-01 | 0.002 |
| 73 | 0.980174 | 1.2261e+00 | 8.9279e-06 | 1.617e+01 | 1.000e+00 | 1.506e+00 | 0.002 |
| 74 | 0.980174 | 1.2261e+00 | 8.5495e-06 | 2.503e+01 | 1.000e+00 | 1.166e+00 | 0.002 |
| 75 | 0.980174 | 1.2261e+00 | 8.5998e-06 | 1.937e+01 | 1.000e+00 | 9.023e-01 | 0.002 |
| 76 | 0.980174 | 1.2261e+00 | 8.6971e-06 | 1.499e+01 | 1.000e+00 | 1.397e+00 | 0.002 |
| 77 | 0.980174 | 1.2261e+00 | 8.5365e-06 | 2.321e+01 | 1.000e+00 | 1.081e+00 | 0.002 |
| 78 | 0.980174 | 1.2261e+00 | 8.5858e-06 | 1.796e+01 | 1.000e+00 | 1.673e+00 | 0.002 |
| 79 | 0.980175 | 1.2261e+00 | 8.4775e-06 | 2.780e+01 | 1.000e+00 | 1.295e+00 | 0.002 |
| 80 | 0.980175 | 1.2261e+00 | 8.5313e-06 | 2.152e+01 | 1.000e+00 | 1.002e+00 | 0.002 |
| 81 | 0.980175 | 1.2261e+00 | 8.6361e-06 | 1.665e+01 | 1.000e+00 | 1.552e+00 | 0.002 |
| 82 | 0.980175 | 1.2260e+00 | 8.1931e-06 | 2.578e+01 | 1.000e+00 | 1.201e+00 | 0.002 |
| 83 | 0.980175 | 1.2260e+00 | 8.6973e-06 | 1.995e+01 | 1.000e+00 | 9.294e-01 | 0.002 |
| 84 | 0.980175 | 1.2260e+00 | 8.5786e-06 | 1.544e+01 | 1.000e+00 | 1.439e+00 | 0.002 |
| 85 | 0.980176 | 1.2260e+00 | 8.3171e-06 | 2.391e+01 | 1.000e+00 | 1.114e+00 | 0.002 |
| 86 | 0.980176 | 1.2260e+00 | 8.7468e-06 | 1.850e+01 | 1.000e+00 | 8.618e-01 | 0.002 |
| 87 | 0.980176 | 1.2260e+00 | 8.7327e-06 | 1.432e+01 | 1.000e+00 | 1.334e+00 | 0.002 |
| 88 | 0.980176 | 1.2260e+00 | 8.2775e-06 | 2.217e+01 | 1.000e+00 | 1.032e+00 | 0.002 |
| 89 | 0.980176 | 1.2260e+00 | 8.7811e-06 | 1.716e+01 | 1.000e+00 | 1.598e+00 | 0.002 |
| 90 | 0.980176 | 1.2260e+00 | 8.6705e-06 | 1.328e+01 | 1.000e+00 | 2.474e+00 | 0.002 |
| 91 | 0.980177 | 1.2259e+00 | 8.4991e-06 | 2.055e+01 | 1.000e+00 | 9.574e-01 | 0.002 |
| 92 | 0.980177 | 1.2259e+00 | 8.6603e-06 | 1.591e+01 | 1.000e+00 | 1.482e+00 | 0.002 |
| 93 | 0.980177 | 1.2259e+00 | 8.0501e-06 | 2.462e+01 | 1.000e+00 | 1.147e+00 | 0.002 |
| 94 | 0.980177 | 1.2259e+00 | 8.5048e-06 | 1.906e+01 | 1.000e+00 | 8.877e-01 | 0.002 |
| 95 | 0.980177 | 1.2259e+00 | 8.3868e-06 | 2.950e+01 | 1.000e+00 | 1.374e+00 | 0.002 |
| 96 | 0.980177 | 1.2259e+00 | 9.5861e-06 | 1.142e+01 | 1.000e+00 | 2.127e+00 | 0.002 |
| 97 | 0.980178 | 1.2259e+00 | 8.7613e-06 | 1.767e+01 | 1.000e+00 | 1.646e+00 | 0.002 |
| 98 | 0.980178 | 1.2259e+00 | 8.9700e-06 | 1.368e+01 | 1.000e+00 | 1.274e+00 | 0.002 |
| 99 | 0.980178 | 1.2259e+00 | 7.8132e-06 | 2.117e+01 | 1.000e+00 | 1.972e+00 | 0.002 |
| 100 | 0.980178 | 1.2259e+00 | 9.5240e-06 | 1.639e+01 | 1.000e+00 | 1.527e+00 | 0.002 |
|----------|------------|------------|-------------|------------|------------|------------|------------|
Iter | VarExpl | SSE | |dSSE|/SSE | muC | mualpha | muS | Time(s)
|----------|------------|------------|-------------|------------|------------|------------|------------|
| 101 | 0.980178 | 1.2258e+00 | 8.5607e-06 | 2.536e+01 | 1.000e+00 | 1.181e+00 | 0.002 |
| 102 | 0.980178 | 1.2258e+00 | 8.7858e-06 | 1.963e+01 | 1.000e+00 | 1.829e+00 | 0.002 |
| 103 | 0.980179 | 1.2258e+00 | 8.7585e-06 | 1.519e+01 | 1.000e+00 | 1.415e+00 | 0.002 |
| 104 | 0.980179 | 1.2258e+00 | 8.6764e-06 | 2.352e+01 | 1.000e+00 | 2.191e+00 | 0.002 |
| 105 | 0.980179 | 1.2258e+00 | 9.0183e-06 | 1.820e+01 | 1.000e+00 | 1.696e+00 | 0.002 |
| 106 | 0.980179 | 1.2258e+00 | 8.8824e-06 | 1.409e+01 | 1.000e+00 | 1.313e+00 | 0.002 |
| 107 | 0.980179 | 1.2258e+00 | 8.6711e-06 | 2.181e+01 | 1.000e+00 | 1.016e+00 | 0.002 |
| 108 | 0.980180 | 1.2258e+00 | 8.7784e-06 | 1.688e+01 | 1.000e+00 | 1.572e+00 | 0.002 |
| 109 | 0.980180 | 1.2258e+00 | 8.8722e-06 | 1.306e+01 | 1.000e+00 | 2.434e+00 | 0.002 |
| 110 | 0.980180 | 1.2257e+00 | 8.7731e-06 | 2.022e+01 | 1.000e+00 | 9.419e-01 | 0.002 |
| 111 | 0.980180 | 1.2257e+00 | 8.7979e-06 | 1.565e+01 | 1.000e+00 | 1.458e+00 | 0.002 |
| 112 | 0.980180 | 1.2257e+00 | 8.4729e-06 | 2.423e+01 | 1.000e+00 | 1.128e+00 | 0.002 |
| 113 | 0.980180 | 1.2257e+00 | 8.9500e-06 | 1.875e+01 | 1.000e+00 | 8.734e-01 | 0.002 |
| 114 | 0.980181 | 1.2257e+00 | 8.9462e-06 | 1.451e+01 | 1.000e+00 | 1.352e+00 | 0.002 |
| 115 | 0.980181 | 1.2257e+00 | 8.9787e-06 | 2.246e+01 | 1.000e+00 | 2.093e+00 | 0.002 |
| 116 | 0.980181 | 1.2257e+00 | 8.9491e-06 | 1.739e+01 | 1.000e+00 | 1.620e+00 | 0.002 |
| 117 | 0.980181 | 1.2257e+00 | 8.9754e-06 | 1.346e+01 | 1.000e+00 | 1.254e+00 | 0.002 |
| 118 | 0.980181 | 1.2257e+00 | 8.8896e-06 | 2.083e+01 | 1.000e+00 | 9.703e-01 | 0.002 |
| 119 | 0.980181 | 1.2256e+00 | 8.8829e-06 | 1.612e+01 | 1.000e+00 | 1.502e+00 | 0.002 |
| 120 | 0.980182 | 1.2256e+00 | 9.2186e-06 | 1.248e+01 | 1.000e+00 | 1.162e+00 | 0.002 |
| 121 | 0.980182 | 1.2256e+00 | 8.8778e-06 | 1.931e+01 | 1.000e+00 | 1.799e+00 | 0.002 |
| 122 | 0.980182 | 1.2256e+00 | 9.2538e-06 | 1.495e+01 | 1.000e+00 | 1.393e+00 | 0.002 |
| 123 | 0.980182 | 1.2256e+00 | 9.0276e-06 | 2.314e+01 | 1.000e+00 | 1.078e+00 | 0.002 |
| 124 | 0.980182 | 1.2256e+00 | 9.1088e-06 | 1.791e+01 | 1.000e+00 | 1.668e+00 | 0.002 |
| 125 | 0.980183 | 1.2256e+00 | 9.0611e-06 | 2.772e+01 | 1.000e+00 | 1.291e+00 | 0.002 |
| 126 | 0.980183 | 1.2256e+00 | 9.1043e-06 | 2.146e+01 | 1.000e+00 | 9.995e-01 | 0.002 |
| 127 | 0.980183 | 1.2256e+00 | 2.6405e-06 | 1.661e+01 | 1.000e+00 | 1.547e+00 | 0.002 |
| 128 | 0.980183 | 1.2256e+00 | 9.1533e-07 | 2.571e+01 | 1.000e+00 | 2.395e+00 | 0.001 |
|----------|------------|------------|-------------|------------|------------|------------|------------|
| 128 | 0.980183 | 1.2256e+00 | 9.1533e-07 | 2.571e+01 | 1.000e+00 | 2.395e+00 | 0.001 |
|----------|------------|------------|-------------|------------|------------|------------|------------|
```
Contact
-------
Please send comments, suggestions or bug reports to
<dchristop@econ.uoa.gr> or <dem.christop@gmail.com>
GitHub repository:
https://github.com/dchristop/geom_archetypal
https://github.com/dchristop/geom_archetypal/issues
Raw data
{
"_id": null,
"home_page": null,
"name": "geom-archetypal",
"maintainer": null,
"docs_url": null,
"requires_python": ">=3.8",
"maintainer_email": "Demetris Christopoulos <dchristop@econ.uoa.gr>",
"keywords": "geometrical archetypal analysis, convex hull, grid archetypal",
"author": null,
"author_email": "Demetris Christopoulos <dchristop@econ.uoa.gr>",
"download_url": "https://files.pythonhosted.org/packages/4e/7b/ee120ed3e767fc4134793fc2f04e52004c41b3e46a9efbdd15886e64ac80/geom_archetypal-1.0.2.tar.gz",
"platform": null,
"description": "# geom_archetypal\r\n## Geometrical Archetypal Analysis\r\n\r\nOverview\r\n--------\r\n\r\ngeom_archetypal is a Python Module for performing Grid Archetypal Analysis (GAA) by using\r\na properly modified version of the PCHA algorithm.\r\n\r\nBasic functions are:\r\n\r\n- `fast_archetypal()` Archetypal Analysis (AA) with given data rows as archetypes\r\n- `grid_archetypal` For a data matrix n x d finds the Grid Archetypes and performs AA\r\n- `closer_grid_archetypal` For a data matrix n x d finds the Closer Grid Archetypes and performs AA\r\n- `archetypal_pcha()` Principal Convex Hull Analysis (PCHA)\r\n\r\nInstallation\r\n------------\r\nOn the terminal of your operating system write and press enter:\r\n\r\n```python\r\n$ pip install geom_archetypal\r\n```\r\n\r\nUsage\r\n-----\r\n```python\r\n# Load Module:\r\nfrom geom_archetypal import *\r\n# Set seed:\r\nseed=20240518\r\nnp.random.seed(seed)\r\n# Create random data\r\nn=100\r\nd=2\r\ndf = np.random.random((n, d))\r\n# grid_atrchetypal()\r\nBY, A, B, AM, AMDF, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (\r\n grid_archetypal(df, diag_less = 1e-6, verbose = True))\r\npd.DataFrame(BY)\r\nAMDF\r\n[SSE, varexpl, fin_iters, time_elapsed, diagsum_final]\r\nFast Archetypal Analysis:\r\nCompute the compositions when the archetypes are already given\r\n|--------|--------------|--------------|-------------------------|\r\n| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |\r\n|--------|--------------|--------------|-------------------------|\r\n| 1 | 2.626019e+01 | 2.078703e+00 | 11.632968|\r\n| 2 | 2.078703e+00 | 8.176473e-01 | 1.542298|\r\n| 3 | 8.176473e-01 | 1.286832e+00 | 0.364605|\r\n| 4 | 8.176473e-01 | 1.563447e-01 | 4.229772|\r\n| 5 | 1.563447e-01 | 1.204240e-01 | 0.298286|\r\n| 6 | 1.204240e-01 | 1.948338e-01 | 0.381914|\r\n| 7 | 1.204240e-01 | 1.339817e-02 | 7.988091|\r\n| 8 | 1.339817e-02 | 6.356475e-03 | 1.107799|\r\n|--------|--------------|--------------|-------------------------|\r\nTime for the 8 A updates was 0 secs\r\n|----------|------------|--------------|-------------------|--------------|\r\n| Iter | VarExpl | SSE | SSE_8 / SSE_0 | muA |\r\n|----------|------------|--------------|-------------------|--------------|\r\n| 8 | 0.999903 | 6.356475e-03 | 0.000242 | 7.4650e-01|\r\n|----------|------------|--------------|-------------------|--------------|\r\nThe sum of diagonal elements for the sub-matrix of closer grid points is 4.0\r\nThe ideal sum would be 4\r\n#closer_grid_archetypal(\r\nBY, A, B, ADF, imins, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (\r\n closer_grid_archetypal(df, diag_less = 1e-6, verbose = True))\r\npd.DataFrame(BY)\r\nADF\r\n[SSE, varexpl, fin_iters, time_elapsed, diagsum_final]\r\nFast Archetypal Analysis:\r\nCompute the compositions when the archetypes are already given\r\n|--------|--------------|--------------|-------------------------|\r\n| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |\r\n|--------|--------------|--------------|-------------------------|\r\n| 1 | 2.339832e+01 | 2.111296e+00 | 10.082445|\r\n| 2 | 2.111296e+00 | 5.136190e-01 | 3.110626|\r\n| 3 | 5.136190e-01 | 6.213599e-01 | 0.173395|\r\n| 4 | 5.136190e-01 | 1.098227e-01 | 3.676804|\r\n| 5 | 1.098227e-01 | 6.322219e-02 | 0.737090|\r\n| 6 | 6.322219e-02 | 8.338054e-02 | 0.241763|\r\n| 7 | 6.322219e-02 | 1.851679e-02 | 2.414316|\r\n| 8 | 1.851679e-02 | 1.440165e-02 | 0.285741|\r\n| 9 | 1.440165e-02 | 1.325812e-02 | 0.086251|\r\n| 10 | 1.325812e-02 | 1.334901e-02 | 0.006809|\r\n| 11 | 1.325812e-02 | 1.243129e-02 | 0.066512|\r\n|--------|--------------|--------------|-------------------------|\r\nTime for the 11 A updates was 0 secs\r\n|----------|------------|--------------|-------------------|--------------|\r\n| Iter | VarExpl | SSE | SSE_11 / SSE_0 | muA |\r\n|----------|------------|--------------|-------------------|--------------|\r\n| 11 | 0.999799 | 1.243129e-02 | 0.000531 | 5.3748e-01|\r\n|----------|------------|--------------|-------------------|--------------|\r\nThe sum of diagonal elements for the sub-matrix of closer grid points is 4.0\r\nThe ideal sum would be 4\r\n# fast_archetypal(): we use the imins from closer_grid_archetypal() above\r\nBY, A, B, irows, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (\r\n fast_archetypal(df, irows = imins, verbose = True, diag_less = 1e-6))\r\npd.DataFrame(BY)\r\n[SSE,varexpl,fin_iters, time_elapsed, diagsum_final]\r\nFast Archetypal Analysis:\r\nCompute the compositions when the archetypes are already given\r\n|--------|--------------|--------------|-------------------------|\r\n| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |\r\n|--------|--------------|--------------|-------------------------|\r\n| 1 | 2.240585e+01 | 1.936972e+00 | 10.567465|\r\n| 2 | 1.936972e+00 | 5.236400e-01 | 2.699052|\r\n| 3 | 5.236400e-01 | 5.861317e-01 | 0.106617|\r\n| 4 | 5.236400e-01 | 1.122365e-01 | 3.665504|\r\n| 5 | 1.122365e-01 | 7.476762e-02 | 0.501138|\r\n| 6 | 7.476762e-02 | 8.903380e-02 | 0.160233|\r\n| 7 | 7.476762e-02 | 1.994893e-02 | 2.747951|\r\n| 8 | 1.994893e-02 | 1.549558e-02 | 0.287395|\r\n| 9 | 1.549558e-02 | 1.457414e-02 | 0.063225|\r\n|--------|--------------|--------------|-------------------------|\r\nTime for the 9 A updates was 0 secs\r\n|----------|------------|--------------|-------------------|--------------|\r\n| Iter | VarExpl | SSE | SSE_9 / SSE_0 | muA |\r\n|----------|------------|--------------|-------------------|--------------|\r\n| 9 | 0.999764 | 1.457414e-02 | 0.000650 | 8.9580e-01|\r\n|----------|------------|--------------|-------------------|--------------|\r\n# archetypal_pcha()\r\nBY, A, B, SSE, varexpl, BY0, converges, iterations, total_time = (\r\n archetypal_pcha(df, kappas = 3, conv_crit=1E-6, maxiter=2000, verbose=True))\r\npd.DataFrame(BY0)\r\npd.DataFrame(BY)\r\n[SSE, varexpl, converges, iterations, total_time]\r\nPCHA Archetypal Analysis:\r\nPrincipal Convex Hull Analysis / Archetypal Analysis\r\nThe mumber of Archetypes will be kappas = 3\r\nTo stop algorithm press control C\r\n|----------|------------|------------|-------------|------------|------------|------------|------------|\r\n Iter | VarExpl | SSE | |dSSE|/SSE | muC | mualpha | muS | Time(s) \r\n|----------|------------|------------|-------------|------------|------------|------------|------------|\r\n| 1 | 0.969057 | 1.9137e+00 | 7.0437e-01 | 1.548e+00 | 1.000e+00 | 1.154e+00 | 0.004 | \r\n| 2 | 0.973296 | 1.6515e+00 | 1.5874e-01 | 2.396e+00 | 1.000e+00 | 8.929e-01 | 0.004 | \r\n| 3 | 0.974737 | 1.5623e+00 | 5.7068e-02 | 7.418e+00 | 1.000e+00 | 1.382e+00 | 0.003 | \r\n| 4 | 0.975468 | 1.5171e+00 | 2.9789e-02 | 1.148e+01 | 1.000e+00 | 1.070e+00 | 0.004 | \r\n| 5 | 0.975934 | 1.4883e+00 | 1.9357e-02 | 1.777e+01 | 1.000e+00 | 1.656e+00 | 0.003 | \r\n| 6 | 0.976253 | 1.4686e+00 | 1.3440e-02 | 1.376e+01 | 1.000e+00 | 1.282e+00 | 0.004 | \r\n| 7 | 0.976555 | 1.4499e+00 | 1.2862e-02 | 2.129e+01 | 1.000e+00 | 1.984e+00 | 0.002 | \r\n| 8 | 0.976821 | 1.4335e+00 | 1.1475e-02 | 3.296e+01 | 1.000e+00 | 1.535e+00 | 0.002 | \r\n| 9 | 0.977052 | 1.4192e+00 | 1.0097e-02 | 2.551e+01 | 1.000e+00 | 1.188e+00 | 0.002 | \r\n| 10 | 0.977240 | 1.4075e+00 | 8.2598e-03 | 1.975e+01 | 1.000e+00 | 9.197e-01 | 0.002 | \r\n| 11 | 0.977397 | 1.3978e+00 | 6.9319e-03 | 1.528e+01 | 1.000e+00 | 1.424e+00 | 0.002 | \r\n| 12 | 0.977546 | 1.3886e+00 | 6.6443e-03 | 5.914e+00 | 1.000e+00 | 2.204e+00 | 0.002 | \r\n| 13 | 0.977713 | 1.3783e+00 | 7.4633e-03 | 4.577e+00 | 1.000e+00 | 8.528e-01 | 0.002 | \r\n| 14 | 0.977873 | 1.3684e+00 | 7.2652e-03 | 7.085e+00 | 1.000e+00 | 1.320e+00 | 0.002 | \r\n| 15 | 0.978040 | 1.3581e+00 | 7.6022e-03 | 5.484e+00 | 1.000e+00 | 1.022e+00 | 0.002 | \r\n| 16 | 0.978221 | 1.3469e+00 | 8.2898e-03 | 4.244e+00 | 1.000e+00 | 1.582e+00 | 0.002 | \r\n| 17 | 0.978424 | 1.3344e+00 | 9.4027e-03 | 6.570e+00 | 1.000e+00 | 1.224e+00 | 0.002 | \r\n| 18 | 0.978628 | 1.3217e+00 | 9.5674e-03 | 5.085e+00 | 1.000e+00 | 9.474e-01 | 0.002 | \r\n| 19 | 0.978841 | 1.3086e+00 | 1.0053e-02 | 3.935e+00 | 1.000e+00 | 1.467e+00 | 0.002 | \r\n| 20 | 0.979046 | 1.2959e+00 | 9.7856e-03 | 6.092e+00 | 1.000e+00 | 5.675e-01 | 0.002 | \r\n| 21 | 0.979247 | 1.2835e+00 | 9.6734e-03 | 4.715e+00 | 1.000e+00 | 8.785e-01 | 0.002 | \r\n| 22 | 0.979447 | 1.2710e+00 | 9.7607e-03 | 7.298e+00 | 1.000e+00 | 1.360e+00 | 0.002 | \r\n| 23 | 0.979640 | 1.2592e+00 | 9.4451e-03 | 5.649e+00 | 1.000e+00 | 1.052e+00 | 0.002 | \r\n| 24 | 0.979829 | 1.2474e+00 | 9.4144e-03 | 8.744e+00 | 1.000e+00 | 8.146e-01 | 0.002 | \r\n| 25 | 0.979933 | 1.2410e+00 | 5.1822e-03 | 6.767e+00 | 1.000e+00 | 1.261e+00 | 0.002 | \r\n| 26 | 0.980005 | 1.2366e+00 | 3.5570e-03 | 1.048e+01 | 1.000e+00 | 1.952e+00 | 0.002 | \r\n| 27 | 0.980053 | 1.2336e+00 | 2.4384e-03 | 1.622e+01 | 1.000e+00 | 7.553e-01 | 0.002 | \r\n| 28 | 0.980086 | 1.2315e+00 | 1.6616e-03 | 1.255e+01 | 1.000e+00 | 1.169e+00 | 0.002 | \r\n| 29 | 0.980109 | 1.2301e+00 | 1.1472e-03 | 1.943e+01 | 1.000e+00 | 9.049e-01 | 0.002 | \r\n| 30 | 0.980124 | 1.2292e+00 | 7.7082e-04 | 1.504e+01 | 1.000e+00 | 1.401e+00 | 0.002 | \r\n| 31 | 0.980135 | 1.2285e+00 | 5.2532e-04 | 2.327e+01 | 1.000e+00 | 1.084e+00 | 0.002 | \r\n| 32 | 0.980142 | 1.2281e+00 | 3.7454e-04 | 1.801e+01 | 1.000e+00 | 1.678e+00 | 0.002 | \r\n| 33 | 0.980147 | 1.2277e+00 | 2.5874e-04 | 1.394e+01 | 1.000e+00 | 1.299e+00 | 0.002 | \r\n| 34 | 0.980151 | 1.2275e+00 | 1.7650e-04 | 1.079e+01 | 1.000e+00 | 2.011e+00 | 0.002 | \r\n| 35 | 0.980154 | 1.2274e+00 | 1.2759e-04 | 1.670e+01 | 1.000e+00 | 1.556e+00 | 0.002 | \r\n| 36 | 0.980155 | 1.2273e+00 | 9.8252e-05 | 1.293e+01 | 1.000e+00 | 1.204e+00 | 0.002 | \r\n| 37 | 0.980157 | 1.2272e+00 | 7.7710e-05 | 1.001e+01 | 1.000e+00 | 9.321e-01 | 0.002 | \r\n| 38 | 0.980158 | 1.2271e+00 | 5.6505e-05 | 1.549e+01 | 1.000e+00 | 1.443e+00 | 0.002 | \r\n| 39 | 0.980159 | 1.2270e+00 | 4.9600e-05 | 1.199e+01 | 1.000e+00 | 1.117e+00 | 0.002 | \r\n| 40 | 0.980160 | 1.2270e+00 | 4.1790e-05 | 9.278e+00 | 1.000e+00 | 1.729e+00 | 0.002 | \r\n| 41 | 0.980161 | 1.2269e+00 | 3.7995e-05 | 1.436e+01 | 1.000e+00 | 1.338e+00 | 0.002 | \r\n| 42 | 0.980161 | 1.2269e+00 | 3.6791e-05 | 1.112e+01 | 1.000e+00 | 2.071e+00 | 0.002 | \r\n| 43 | 0.980162 | 1.2268e+00 | 3.3335e-05 | 1.721e+01 | 1.000e+00 | 1.603e+00 | 0.002 | \r\n| 44 | 0.980163 | 1.2268e+00 | 3.1141e-05 | 1.332e+01 | 1.000e+00 | 1.241e+00 | 0.002 | \r\n| 45 | 0.980163 | 1.2268e+00 | 3.3211e-05 | 1.031e+01 | 1.000e+00 | 9.602e-01 | 0.002 | \r\n| 46 | 0.980164 | 1.2267e+00 | 3.3546e-05 | 7.977e+00 | 1.000e+00 | 1.486e+00 | 0.002 | \r\n| 47 | 0.980165 | 1.2267e+00 | 3.1603e-05 | 1.235e+01 | 1.000e+00 | 1.150e+00 | 0.002 | \r\n| 48 | 0.980165 | 1.2266e+00 | 3.0910e-05 | 1.911e+01 | 1.000e+00 | 1.781e+00 | 0.002 | \r\n| 49 | 0.980166 | 1.2266e+00 | 3.1031e-05 | 1.479e+01 | 1.000e+00 | 1.378e+00 | 0.002 | \r\n| 50 | 0.980167 | 1.2266e+00 | 3.1274e-05 | 1.145e+01 | 1.000e+00 | 1.067e+00 | 0.002 | \r\n| 51 | 0.980167 | 1.2265e+00 | 3.0282e-05 | 1.772e+01 | 1.000e+00 | 1.651e+00 | 0.002 | \r\n| 52 | 0.980168 | 1.2265e+00 | 3.0849e-05 | 1.372e+01 | 1.000e+00 | 1.278e+00 | 0.002 | \r\n| 53 | 0.980168 | 1.2265e+00 | 3.1283e-05 | 1.062e+01 | 1.000e+00 | 9.890e-01 | 0.002 | \r\n| 54 | 0.980169 | 1.2264e+00 | 3.0494e-05 | 1.643e+01 | 1.000e+00 | 1.531e+00 | 0.002 | \r\n| 55 | 0.980170 | 1.2264e+00 | 3.1566e-05 | 1.272e+01 | 1.000e+00 | 1.185e+00 | 0.002 | \r\n| 56 | 0.980170 | 1.2263e+00 | 3.0652e-05 | 9.844e+00 | 1.000e+00 | 1.834e+00 | 0.002 | \r\n| 57 | 0.980171 | 1.2263e+00 | 2.6192e-05 | 3.048e+01 | 1.000e+00 | 1.420e+00 | 0.002 | \r\n| 58 | 0.980171 | 1.2263e+00 | 1.1450e-05 | 2.359e+01 | 1.000e+00 | 1.099e+00 | 0.002 | \r\n| 59 | 0.980171 | 1.2263e+00 | 9.3466e-06 | 1.826e+01 | 1.000e+00 | 1.701e+00 | 0.002 | \r\n| 60 | 0.980171 | 1.2263e+00 | 8.4407e-06 | 2.826e+01 | 1.000e+00 | 1.316e+00 | 0.002 | \r\n| 61 | 0.980171 | 1.2263e+00 | 8.4114e-06 | 2.187e+01 | 1.000e+00 | 1.019e+00 | 0.002 | \r\n| 62 | 0.980172 | 1.2263e+00 | 9.1324e-06 | 1.693e+01 | 1.000e+00 | 1.577e+00 | 0.002 | \r\n| 63 | 0.980172 | 1.2262e+00 | 8.8070e-06 | 1.310e+01 | 1.000e+00 | 1.221e+00 | 0.002 | \r\n| 64 | 0.980172 | 1.2262e+00 | 8.6021e-06 | 2.028e+01 | 1.000e+00 | 9.447e-01 | 0.002 | \r\n| 65 | 0.980172 | 1.2262e+00 | 8.4549e-06 | 1.570e+01 | 1.000e+00 | 1.462e+00 | 0.002 | \r\n| 66 | 0.980172 | 1.2262e+00 | 8.9234e-06 | 1.215e+01 | 1.000e+00 | 1.132e+00 | 0.002 | \r\n| 67 | 0.980172 | 1.2262e+00 | 8.7704e-06 | 1.881e+01 | 1.000e+00 | 8.759e-01 | 0.002 | \r\n| 68 | 0.980173 | 1.2262e+00 | 8.6715e-06 | 1.455e+01 | 1.000e+00 | 1.356e+00 | 0.002 | \r\n| 69 | 0.980173 | 1.2262e+00 | 8.0681e-06 | 2.253e+01 | 1.000e+00 | 1.049e+00 | 0.002 | \r\n| 70 | 0.980173 | 1.2262e+00 | 8.8384e-06 | 1.744e+01 | 1.000e+00 | 1.624e+00 | 0.002 | \r\n| 71 | 0.980173 | 1.2262e+00 | 8.6672e-06 | 2.699e+01 | 1.000e+00 | 1.257e+00 | 0.002 | \r\n| 72 | 0.980173 | 1.2261e+00 | 8.1818e-06 | 2.089e+01 | 1.000e+00 | 9.731e-01 | 0.002 | \r\n| 73 | 0.980174 | 1.2261e+00 | 8.9279e-06 | 1.617e+01 | 1.000e+00 | 1.506e+00 | 0.002 | \r\n| 74 | 0.980174 | 1.2261e+00 | 8.5495e-06 | 2.503e+01 | 1.000e+00 | 1.166e+00 | 0.002 | \r\n| 75 | 0.980174 | 1.2261e+00 | 8.5998e-06 | 1.937e+01 | 1.000e+00 | 9.023e-01 | 0.002 | \r\n| 76 | 0.980174 | 1.2261e+00 | 8.6971e-06 | 1.499e+01 | 1.000e+00 | 1.397e+00 | 0.002 | \r\n| 77 | 0.980174 | 1.2261e+00 | 8.5365e-06 | 2.321e+01 | 1.000e+00 | 1.081e+00 | 0.002 | \r\n| 78 | 0.980174 | 1.2261e+00 | 8.5858e-06 | 1.796e+01 | 1.000e+00 | 1.673e+00 | 0.002 | \r\n| 79 | 0.980175 | 1.2261e+00 | 8.4775e-06 | 2.780e+01 | 1.000e+00 | 1.295e+00 | 0.002 | \r\n| 80 | 0.980175 | 1.2261e+00 | 8.5313e-06 | 2.152e+01 | 1.000e+00 | 1.002e+00 | 0.002 | \r\n| 81 | 0.980175 | 1.2261e+00 | 8.6361e-06 | 1.665e+01 | 1.000e+00 | 1.552e+00 | 0.002 | \r\n| 82 | 0.980175 | 1.2260e+00 | 8.1931e-06 | 2.578e+01 | 1.000e+00 | 1.201e+00 | 0.002 | \r\n| 83 | 0.980175 | 1.2260e+00 | 8.6973e-06 | 1.995e+01 | 1.000e+00 | 9.294e-01 | 0.002 | \r\n| 84 | 0.980175 | 1.2260e+00 | 8.5786e-06 | 1.544e+01 | 1.000e+00 | 1.439e+00 | 0.002 | \r\n| 85 | 0.980176 | 1.2260e+00 | 8.3171e-06 | 2.391e+01 | 1.000e+00 | 1.114e+00 | 0.002 | \r\n| 86 | 0.980176 | 1.2260e+00 | 8.7468e-06 | 1.850e+01 | 1.000e+00 | 8.618e-01 | 0.002 | \r\n| 87 | 0.980176 | 1.2260e+00 | 8.7327e-06 | 1.432e+01 | 1.000e+00 | 1.334e+00 | 0.002 | \r\n| 88 | 0.980176 | 1.2260e+00 | 8.2775e-06 | 2.217e+01 | 1.000e+00 | 1.032e+00 | 0.002 | \r\n| 89 | 0.980176 | 1.2260e+00 | 8.7811e-06 | 1.716e+01 | 1.000e+00 | 1.598e+00 | 0.002 | \r\n| 90 | 0.980176 | 1.2260e+00 | 8.6705e-06 | 1.328e+01 | 1.000e+00 | 2.474e+00 | 0.002 | \r\n| 91 | 0.980177 | 1.2259e+00 | 8.4991e-06 | 2.055e+01 | 1.000e+00 | 9.574e-01 | 0.002 | \r\n| 92 | 0.980177 | 1.2259e+00 | 8.6603e-06 | 1.591e+01 | 1.000e+00 | 1.482e+00 | 0.002 | \r\n| 93 | 0.980177 | 1.2259e+00 | 8.0501e-06 | 2.462e+01 | 1.000e+00 | 1.147e+00 | 0.002 | \r\n| 94 | 0.980177 | 1.2259e+00 | 8.5048e-06 | 1.906e+01 | 1.000e+00 | 8.877e-01 | 0.002 | \r\n| 95 | 0.980177 | 1.2259e+00 | 8.3868e-06 | 2.950e+01 | 1.000e+00 | 1.374e+00 | 0.002 | \r\n| 96 | 0.980177 | 1.2259e+00 | 9.5861e-06 | 1.142e+01 | 1.000e+00 | 2.127e+00 | 0.002 | \r\n| 97 | 0.980178 | 1.2259e+00 | 8.7613e-06 | 1.767e+01 | 1.000e+00 | 1.646e+00 | 0.002 | \r\n| 98 | 0.980178 | 1.2259e+00 | 8.9700e-06 | 1.368e+01 | 1.000e+00 | 1.274e+00 | 0.002 | \r\n| 99 | 0.980178 | 1.2259e+00 | 7.8132e-06 | 2.117e+01 | 1.000e+00 | 1.972e+00 | 0.002 | \r\n| 100 | 0.980178 | 1.2259e+00 | 9.5240e-06 | 1.639e+01 | 1.000e+00 | 1.527e+00 | 0.002 | \r\n|----------|------------|------------|-------------|------------|------------|------------|------------|\r\n Iter | VarExpl | SSE | |dSSE|/SSE | muC | mualpha | muS | Time(s) \r\n|----------|------------|------------|-------------|------------|------------|------------|------------|\r\n| 101 | 0.980178 | 1.2258e+00 | 8.5607e-06 | 2.536e+01 | 1.000e+00 | 1.181e+00 | 0.002 | \r\n| 102 | 0.980178 | 1.2258e+00 | 8.7858e-06 | 1.963e+01 | 1.000e+00 | 1.829e+00 | 0.002 | \r\n| 103 | 0.980179 | 1.2258e+00 | 8.7585e-06 | 1.519e+01 | 1.000e+00 | 1.415e+00 | 0.002 | \r\n| 104 | 0.980179 | 1.2258e+00 | 8.6764e-06 | 2.352e+01 | 1.000e+00 | 2.191e+00 | 0.002 | \r\n| 105 | 0.980179 | 1.2258e+00 | 9.0183e-06 | 1.820e+01 | 1.000e+00 | 1.696e+00 | 0.002 | \r\n| 106 | 0.980179 | 1.2258e+00 | 8.8824e-06 | 1.409e+01 | 1.000e+00 | 1.313e+00 | 0.002 | \r\n| 107 | 0.980179 | 1.2258e+00 | 8.6711e-06 | 2.181e+01 | 1.000e+00 | 1.016e+00 | 0.002 | \r\n| 108 | 0.980180 | 1.2258e+00 | 8.7784e-06 | 1.688e+01 | 1.000e+00 | 1.572e+00 | 0.002 | \r\n| 109 | 0.980180 | 1.2258e+00 | 8.8722e-06 | 1.306e+01 | 1.000e+00 | 2.434e+00 | 0.002 | \r\n| 110 | 0.980180 | 1.2257e+00 | 8.7731e-06 | 2.022e+01 | 1.000e+00 | 9.419e-01 | 0.002 | \r\n| 111 | 0.980180 | 1.2257e+00 | 8.7979e-06 | 1.565e+01 | 1.000e+00 | 1.458e+00 | 0.002 | \r\n| 112 | 0.980180 | 1.2257e+00 | 8.4729e-06 | 2.423e+01 | 1.000e+00 | 1.128e+00 | 0.002 | \r\n| 113 | 0.980180 | 1.2257e+00 | 8.9500e-06 | 1.875e+01 | 1.000e+00 | 8.734e-01 | 0.002 | \r\n| 114 | 0.980181 | 1.2257e+00 | 8.9462e-06 | 1.451e+01 | 1.000e+00 | 1.352e+00 | 0.002 | \r\n| 115 | 0.980181 | 1.2257e+00 | 8.9787e-06 | 2.246e+01 | 1.000e+00 | 2.093e+00 | 0.002 | \r\n| 116 | 0.980181 | 1.2257e+00 | 8.9491e-06 | 1.739e+01 | 1.000e+00 | 1.620e+00 | 0.002 | \r\n| 117 | 0.980181 | 1.2257e+00 | 8.9754e-06 | 1.346e+01 | 1.000e+00 | 1.254e+00 | 0.002 | \r\n| 118 | 0.980181 | 1.2257e+00 | 8.8896e-06 | 2.083e+01 | 1.000e+00 | 9.703e-01 | 0.002 | \r\n| 119 | 0.980181 | 1.2256e+00 | 8.8829e-06 | 1.612e+01 | 1.000e+00 | 1.502e+00 | 0.002 | \r\n| 120 | 0.980182 | 1.2256e+00 | 9.2186e-06 | 1.248e+01 | 1.000e+00 | 1.162e+00 | 0.002 | \r\n| 121 | 0.980182 | 1.2256e+00 | 8.8778e-06 | 1.931e+01 | 1.000e+00 | 1.799e+00 | 0.002 | \r\n| 122 | 0.980182 | 1.2256e+00 | 9.2538e-06 | 1.495e+01 | 1.000e+00 | 1.393e+00 | 0.002 | \r\n| 123 | 0.980182 | 1.2256e+00 | 9.0276e-06 | 2.314e+01 | 1.000e+00 | 1.078e+00 | 0.002 | \r\n| 124 | 0.980182 | 1.2256e+00 | 9.1088e-06 | 1.791e+01 | 1.000e+00 | 1.668e+00 | 0.002 | \r\n| 125 | 0.980183 | 1.2256e+00 | 9.0611e-06 | 2.772e+01 | 1.000e+00 | 1.291e+00 | 0.002 | \r\n| 126 | 0.980183 | 1.2256e+00 | 9.1043e-06 | 2.146e+01 | 1.000e+00 | 9.995e-01 | 0.002 | \r\n| 127 | 0.980183 | 1.2256e+00 | 2.6405e-06 | 1.661e+01 | 1.000e+00 | 1.547e+00 | 0.002 | \r\n| 128 | 0.980183 | 1.2256e+00 | 9.1533e-07 | 2.571e+01 | 1.000e+00 | 2.395e+00 | 0.001 | \r\n|----------|------------|------------|-------------|------------|------------|------------|------------|\r\n| 128 | 0.980183 | 1.2256e+00 | 9.1533e-07 | 2.571e+01 | 1.000e+00 | 2.395e+00 | 0.001 | \r\n|----------|------------|------------|-------------|------------|------------|------------|------------|\r\n\r\n```\r\n\r\n\r\nContact\r\n-------\r\n\r\nPlease send comments, suggestions or bug reports to\r\n<dchristop@econ.uoa.gr> or <dem.christop@gmail.com>\r\n\r\nGitHub repository:\r\n\r\nhttps://github.com/dchristop/geom_archetypal\r\n\r\nhttps://github.com/dchristop/geom_archetypal/issues\r\n",
"bugtrack_url": null,
"license": "Copyright (c) 2024 Demetris Christopoulos Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.",
"summary": "Geometric Archetypal Analysis",
"version": "1.0.2",
"project_urls": {
"Funding": "https://www.insead.edu/hoffmann-institute",
"Homepage": "https://github.com/dchristop/geom_archetypal",
"Issues": "https://github.com/dchristop/geom_archetypal/issues"
},
"split_keywords": [
"geometrical archetypal analysis",
" convex hull",
" grid archetypal"
],
"urls": [
{
"comment_text": "",
"digests": {
"blake2b_256": "fa45d91f119b4433b6323828a9525720e48532e46c1bfe4d08404a2f13fbae66",
"md5": "a640629149274d5c0ad9bdf781b5520f",
"sha256": "a28715d9f5a1749960808c46245ab53d98e13ff3cfcce9acf602327f6d00049f"
},
"downloads": -1,
"filename": "geom_archetypal-1.0.2-py3-none-any.whl",
"has_sig": false,
"md5_digest": "a640629149274d5c0ad9bdf781b5520f",
"packagetype": "bdist_wheel",
"python_version": "py3",
"requires_python": ">=3.8",
"size": 13224,
"upload_time": "2024-05-18T10:49:11",
"upload_time_iso_8601": "2024-05-18T10:49:11.648731Z",
"url": "https://files.pythonhosted.org/packages/fa/45/d91f119b4433b6323828a9525720e48532e46c1bfe4d08404a2f13fbae66/geom_archetypal-1.0.2-py3-none-any.whl",
"yanked": false,
"yanked_reason": null
},
{
"comment_text": "",
"digests": {
"blake2b_256": "4e7bee120ed3e767fc4134793fc2f04e52004c41b3e46a9efbdd15886e64ac80",
"md5": "1906a8bf4f2389b2abd32d547294ce24",
"sha256": "6807d142ea47235feeb32cfc78b57016d41f5ccbb23d69bb08434500f5e0e856"
},
"downloads": -1,
"filename": "geom_archetypal-1.0.2.tar.gz",
"has_sig": false,
"md5_digest": "1906a8bf4f2389b2abd32d547294ce24",
"packagetype": "sdist",
"python_version": "source",
"requires_python": ">=3.8",
"size": 17366,
"upload_time": "2024-05-18T10:49:13",
"upload_time_iso_8601": "2024-05-18T10:49:13.736647Z",
"url": "https://files.pythonhosted.org/packages/4e/7b/ee120ed3e767fc4134793fc2f04e52004c41b3e46a9efbdd15886e64ac80/geom_archetypal-1.0.2.tar.gz",
"yanked": false,
"yanked_reason": null
}
],
"upload_time": "2024-05-18 10:49:13",
"github": true,
"gitlab": false,
"bitbucket": false,
"codeberg": false,
"github_user": "dchristop",
"github_project": "geom_archetypal",
"travis_ci": false,
"coveralls": false,
"github_actions": false,
"lcname": "geom-archetypal"
}
