3D Elliptic Fourier Analysis

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px

from sklearn.decomposition import PCA

from ktch.datasets import load_outline_leaf_bending
from ktch.harmonic import EllipticFourierAnalysis
from ktch.plot import explained_variance_ratio_plot

Load the leaf bending outline dataset

data = load_outline_leaf_bending(as_frame=True)
data.coords

		x	y	z
specimen_id	coord_id
1	0	0.000000	0.000000	0.000000
	1	0.000000	-0.046295	0.000000
	2	0.000000	-0.092589	0.000000
	3	0.000630	-0.095962	0.045238
	4	0.002576	-0.098305	0.091431
...	...	...	...	...
60	195	0.000000	0.148530	0.000000
	196	0.000000	0.118824	0.000000
	197	0.000000	0.089118	0.000000
	198	0.000000	0.059412	0.000000
	199	0.000000	0.029706	0.000000

12000 rows × 3 columns

df_meta = data.meta.copy()
df_meta["bending_angle"] = (
    np.degrees(df_meta["alphaB"]).round().astype(int).astype(str) + "\u00b0"
)
df_meta["aspect_ratio"] = df_meta["alpha"]
df_meta

	lmax	c	alpha	A	alphaB	kB	alpha_random	alphaB_random	bending_angle	aspect_ratio
specimen_id
1	0.4	0.65	0.08	1.0	2.443461	0.2	0.060572	2.528513	140°	0.08
2	0.4	0.65	0.08	1.0	2.443461	0.2	0.090911	2.318855	140°	0.08
3	0.4	0.65	0.08	1.0	2.443461	0.2	0.088957	2.417189	140°	0.08
4	0.4	0.65	0.08	1.0	2.443461	0.2	0.074596	2.506030	140°	0.08
5	0.4	0.65	0.08	1.0	2.443461	0.2	0.098990	2.294188	140°	0.08
6	0.4	0.65	0.08	1.0	2.443461	0.2	0.073196	2.492090	140°	0.08
7	0.4	0.65	0.08	1.0	2.443461	0.2	0.077120	2.287193	140°	0.08
8	0.4	0.65	0.08	1.0	2.443461	0.2	0.083971	2.280600	140°	0.08
9	0.4	0.65	0.08	1.0	2.443461	0.2	0.073029	2.431389	140°	0.08
10	0.4	0.65	0.08	1.0	2.443461	0.2	0.099243	2.553002	140°	0.08
11	0.4	0.65	0.08	1.0	1.396263	0.2	0.089302	1.409695	80°	0.08
12	0.4	0.65	0.08	1.0	1.396263	0.2	0.076330	1.242604	80°	0.08
13	0.4	0.65	0.08	1.0	1.396263	0.2	0.060501	1.299788	80°	0.08
14	0.4	0.65	0.08	1.0	1.396263	0.2	0.087227	1.536335	80°	0.08
15	0.4	0.65	0.08	1.0	1.396263	0.2	0.098797	1.548685	80°	0.08
16	0.4	0.65	0.08	1.0	1.396263	0.2	0.076723	1.280753	80°	0.08
17	0.4	0.65	0.08	1.0	1.396263	0.2	0.093675	1.558039	80°	0.08
18	0.4	0.65	0.08	1.0	1.396263	0.2	0.095911	1.566630	80°	0.08
19	0.4	0.65	0.08	1.0	1.396263	0.2	0.078236	1.387295	80°	0.08
20	0.4	0.65	0.08	1.0	1.396263	0.2	0.095689	1.447270	80°	0.08
21	0.4	0.65	0.08	1.0	0.349066	0.2	0.082873	0.390205	20°	0.08
22	0.4	0.65	0.08	1.0	0.349066	0.2	0.064031	0.266366	20°	0.08
23	0.4	0.65	0.08	1.0	0.349066	0.2	0.089630	0.373168	20°	0.08
24	0.4	0.65	0.08	1.0	0.349066	0.2	0.078860	0.330521	20°	0.08
25	0.4	0.65	0.08	1.0	0.349066	0.2	0.087673	0.318159	20°	0.08
26	0.4	0.65	0.08	1.0	0.349066	0.2	0.088925	0.305914	20°	0.08
27	0.4	0.65	0.08	1.0	0.349066	0.2	0.077160	0.372707	20°	0.08
28	0.4	0.65	0.08	1.0	0.349066	0.2	0.083355	0.268017	20°	0.08
29	0.4	0.65	0.08	1.0	0.349066	0.2	0.083693	0.406805	20°	0.08
30	0.4	0.65	0.08	1.0	0.349066	0.2	0.081946	0.311726	20°	0.08
31	0.4	0.65	0.16	1.0	2.443461	0.2	0.173997	2.326146	140°	0.16
32	0.4	0.65	0.16	1.0	2.443461	0.2	0.178168	2.367912	140°	0.16
33	0.4	0.65	0.16	1.0	2.443461	0.2	0.166143	2.497124	140°	0.16
34	0.4	0.65	0.16	1.0	2.443461	0.2	0.142324	2.521001	140°	0.16
35	0.4	0.65	0.16	1.0	2.443461	0.2	0.159544	2.492420	140°	0.16
36	0.4	0.65	0.16	1.0	2.443461	0.2	0.176739	2.296786	140°	0.16
37	0.4	0.65	0.16	1.0	2.443461	0.2	0.170455	2.304695	140°	0.16
38	0.4	0.65	0.16	1.0	2.443461	0.2	0.148710	2.478740	140°	0.16
39	0.4	0.65	0.16	1.0	2.443461	0.2	0.141903	2.555287	140°	0.16
40	0.4	0.65	0.16	1.0	2.443461	0.2	0.171313	2.610918	140°	0.16
41	0.4	0.65	0.16	1.0	1.396263	0.2	0.176521	1.244129	80°	0.16
42	0.4	0.65	0.16	1.0	1.396263	0.2	0.167533	1.252522	80°	0.16
43	0.4	0.65	0.16	1.0	1.396263	0.2	0.175097	1.438110	80°	0.16
44	0.4	0.65	0.16	1.0	1.396263	0.2	0.146855	1.570428	80°	0.16
45	0.4	0.65	0.16	1.0	1.396263	0.2	0.143005	1.422087	80°	0.16
46	0.4	0.65	0.16	1.0	1.396263	0.2	0.174511	1.497144	80°	0.16
47	0.4	0.65	0.16	1.0	1.396263	0.2	0.170496	1.470243	80°	0.16
48	0.4	0.65	0.16	1.0	1.396263	0.2	0.151212	1.282264	80°	0.16
49	0.4	0.65	0.16	1.0	1.396263	0.2	0.176779	1.257857	80°	0.16
50	0.4	0.65	0.16	1.0	1.396263	0.2	0.157964	1.505475	80°	0.16
51	0.4	0.65	0.16	1.0	0.349066	0.2	0.166466	0.346456	20°	0.16
52	0.4	0.65	0.16	1.0	0.349066	0.2	0.177635	0.386719	20°	0.16
53	0.4	0.65	0.16	1.0	0.349066	0.2	0.155776	0.441191	20°	0.16
54	0.4	0.65	0.16	1.0	0.349066	0.2	0.175787	0.407493	20°	0.16
55	0.4	0.65	0.16	1.0	0.349066	0.2	0.146865	0.504861	20°	0.16
56	0.4	0.65	0.16	1.0	0.349066	0.2	0.163440	0.445301	20°	0.16
57	0.4	0.65	0.16	1.0	0.349066	0.2	0.160243	0.366476	20°	0.16
58	0.4	0.65	0.16	1.0	0.349066	0.2	0.158335	0.354346	20°	0.16
59	0.4	0.65	0.16	1.0	0.349066	0.2	0.148304	0.235357	20°	0.16
60	0.4	0.65	0.16	1.0	0.349066	0.2	0.160054	0.206858	20°	0.16

coords = data.coords.to_numpy().reshape(-1, 200, 3)
coords.shape

(60, 200, 3)

Visualize 3D outlines

representative_ids = [0, 10, 20, 30, 40, 50]
bending_order = [ str(deg)+ "\u00b0" for deg in  [20, 80, 140] ]

dfs = []
for sid in representative_ids:
    df = pd.DataFrame(coords[sid], columns=["x", "y", "z"])
    df["idx"] = data.meta.index[sid]
    df["bending_angle"] = df_meta.iloc[sid]["bending_angle"]
    dfs.append(df)
df_vis = pd.concat(dfs, ignore_index=True)

fig = px.line_3d(
    df_vis,
    x="x",
    y="y",
    z="z",
    line_group="idx",
    color="bending_angle",
    category_orders ={"bending_angle":bending_order},
    color_discrete_sequence=px.colors.qualitative.Set2,
)
fig.update_layout(scene=dict(aspectmode="data"))
fig.show()

3D EFA without normalization

efa = EllipticFourierAnalysis(n_harmonics=20, n_dim=3)

coef = efa.fit_transform(coords, norm=False)
coef.shape

(60, 126)

Reconstruction from coefficients

coords_recon = efa.inverse_transform(coef, t_num=200, norm=False)

sid = 0
df_orig = pd.DataFrame(coords[sid], columns=["x", "y", "z"])
df_orig["type"] = "original"
df_rec = pd.DataFrame(coords_recon[sid], columns=["x", "y", "z"])
df_rec["type"] = "reconstructed"
df_cmp = pd.concat([df_orig, df_rec], ignore_index=True)

fig = px.line_3d(df_cmp, x="x", y="y", z="z", color="type")
fig.update_layout(scene=dict(aspectmode="data"))
fig.show()

3D EFA

efa = EllipticFourierAnalysis(n_harmonics=20, n_dim=3)

coef = efa.fit_transform(coords, norm=True)
coef.shape

(60, 126)

Reconstruction from coefficients

coords_recon = efa.inverse_transform(coef, t_num=200, norm=True)

representative_ids = [0, 10, 20, 30, 40, 50]

dfs = []
for sid in representative_ids:
    df = pd.DataFrame(coords_recon[sid], columns=["x", "y", "z"])
    df["idx"] = data.meta.index[sid]
    df["bending_angle"] = df_meta.iloc[sid]["bending_angle"]
    dfs.append(df)
df_vis = pd.concat(dfs, ignore_index=True)

fig = px.line_3d(
    df_vis, x="x", y="y", z="z",
    line_group="idx",
    color="bending_angle",
    category_orders ={"bending_angle":bending_order},
    color_discrete_sequence=px.colors.qualitative.Set2
    )
fig.update_layout(scene=dict(aspectmode="data"))
fig.show()

PCA

pca = PCA(n_components=12)
pcscores = pca.fit_transform(coef)

df_pca = pd.DataFrame(pcscores, columns=[f"PC{i+1}" for i in range(12)])
df_pca.index = df_meta.index
df_pca = df_pca.join(df_meta)
df_pca

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	...	lmax	c	alpha	A	alphaB	kB	alpha_random	alphaB_random	bending_angle	aspect_ratio
specimen_id
1	-1.212191	1.121579	0.107171	0.011560	0.012842	0.001138	-0.002117	-0.000665	5.195792e-04	0.000332	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.060572	2.528513	140°	0.08
2	-0.936970	0.436713	0.028150	0.005296	-0.004628	0.001218	-0.000426	-0.000119	-3.270928e-04	-0.000379	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.090911	2.318855	140°	0.08
3	-1.035797	0.439970	0.047183	0.004650	-0.004887	0.000129	-0.000774	-0.000030	-2.139763e-04	-0.000394	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.088957	2.417189	140°	0.08
4	-1.145406	0.728617	0.075460	0.008020	0.000725	-0.001096	-0.000554	0.000422	2.015761e-04	-0.000002	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.074596	2.506030	140°	0.08
5	-0.912451	0.301951	0.016461	0.004460	-0.006107	0.000491	0.000658	0.000267	-4.775718e-04	0.000075	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.098990	2.294188	140°	0.08
6	-1.133819	0.771139	0.073925	0.008667	0.001817	-0.000782	-0.000424	0.000412	2.093879e-04	0.000050	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.073196	2.492090	140°	0.08
7	-0.906528	0.758235	0.025590	0.009584	0.001321	0.000946	0.001348	0.000506	-1.056459e-04	0.000153	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.077120	2.287193	140°	0.08
8	-0.897786	0.598010	0.021691	0.007696	-0.002021	0.001004	0.000776	0.000309	-2.412954e-04	-0.000039	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.083971	2.280600	140°	0.08
9	-1.069214	0.803718	0.060063	0.009552	0.002635	-0.000024	0.000220	0.000442	1.188405e-04	0.000132	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.073029	2.431389	140°	0.08
10	-1.153353	0.201580	0.064673	0.000142	-0.008252	-0.002337	-0.001004	0.000056	-2.327827e-04	-0.000266	...	0.4	0.65	0.08	1.0	2.443461	0.2	0.099243	2.553002	140°	0.08
11	0.098271	0.584667	-0.070353	0.000910	-0.003291	0.000134	-0.000159	-0.000284	1.208559e-04	-0.000146	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.089302	1.409695	80°	0.08
12	0.409715	0.866223	-0.078336	-0.004074	0.001146	-0.002104	0.000748	0.000136	2.644008e-04	-0.000073	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.076330	1.242604	80°	0.08
13	0.479149	1.371337	-0.078663	-0.005317	0.015571	-0.000932	0.000856	-0.001264	-3.552821e-04	-0.000120	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.060501	1.299788	80°	0.08
14	-0.043950	0.641566	-0.067710	0.002521	-0.002334	0.000573	0.000627	-0.000120	2.669955e-05	-0.000117	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.087227	1.536335	80°	0.08
15	-0.113632	0.414991	-0.066985	0.002730	-0.005277	0.000412	0.000743	0.000109	-3.860665e-05	0.000190	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.098797	1.548685	80°	0.08
16	0.355298	0.864501	-0.078721	-0.003226	0.001113	-0.001853	0.000901	0.000137	2.508130e-04	-0.000074	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.076723	1.280753	80°	0.08
17	-0.102059	0.508699	-0.065106	0.002932	-0.004082	0.000865	0.000324	-0.000143	-2.991154e-05	-0.000056	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.093675	1.558039	80°	0.08
18	-0.121821	0.467478	-0.065432	0.002982	-0.004627	0.000701	0.000571	-0.000006	-4.302129e-05	0.000058	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.095911	1.566630	80°	0.08
19	0.202180	0.844041	-0.077693	-0.000848	0.000793	-0.001103	0.001261	0.000145	1.984502e-04	-0.000068	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.078236	1.387295	80°	0.08
20	0.018057	0.463559	-0.069791	0.001618	-0.004887	0.000130	0.000180	-0.000058	8.152559e-05	0.000060	...	0.4	0.65	0.08	1.0	1.396263	0.2	0.095689	1.447270	80°	0.08
21	1.395888	0.273970	0.029565	-0.007117	-0.002888	-0.000400	-0.000432	0.000188	2.413662e-04	0.000073	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.082873	0.390205	20°	0.08
22	1.900065	0.629052	0.074601	-0.016125	0.008819	0.000725	-0.000925	0.000235	-1.295535e-03	0.000062	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.064031	0.266366	20°	0.08
23	1.312209	0.126744	0.033607	-0.002834	-0.004087	0.000589	-0.000661	-0.000273	3.846086e-04	-0.000025	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.089630	0.373168	20°	0.08
24	1.529104	0.313506	0.044290	-0.008627	-0.001265	-0.000009	-0.000039	0.000378	2.528159e-05	0.000031	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.078860	0.330521	20°	0.08
25	1.399288	0.122454	0.045810	-0.003021	-0.003469	0.001047	-0.000126	-0.000142	2.996893e-04	-0.000061	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.087673	0.318159	20°	0.08
26	1.393050	0.089307	0.048629	-0.002012	-0.003558	0.001354	-0.000096	-0.000240	3.159606e-04	-0.000099	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.088925	0.305914	20°	0.08
27	1.510394	0.385975	0.034734	-0.010259	-0.000794	-0.000713	-0.000342	0.000435	-6.106588e-07	0.000077	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.077160	0.372707	20°	0.08
28	1.521174	0.167297	0.058388	-0.004676	-0.002244	0.001328	0.000450	0.000133	1.237559e-04	-0.000085	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.083355	0.268017	20°	0.08
29	1.364556	0.269302	0.025877	-0.006852	-0.003181	-0.000500	-0.000550	0.000141	2.802554e-04	0.000081	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.083693	0.406805	20°	0.08
30	1.497570	0.231904	0.047980	-0.006423	-0.002178	0.000534	0.000109	0.000229	1.266806e-04	-0.000008	...	0.4	0.65	0.08	1.0	0.349066	0.2	0.081946	0.311726	20°	0.08
31	-0.964406	-0.547059	0.002380	-0.009928	0.003770	0.001159	0.001010	0.000236	1.190184e-04	0.000090	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.173997	2.326146	140°	0.16
32	-0.995482	-0.588329	0.007357	-0.011664	0.004883	0.001041	0.000952	0.000277	3.944896e-04	-0.000080	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.178168	2.367912	140°	0.16
33	-1.084258	-0.534348	0.027336	-0.012744	0.001073	-0.000244	0.000548	-0.000191	1.501517e-04	0.000003	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.166143	2.497124	140°	0.16
34	-1.103990	-0.332649	0.037067	-0.008456	-0.004835	-0.001270	0.000250	-0.000419	-4.231776e-04	0.000217	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.142324	2.521001	140°	0.16
35	-1.081148	-0.481900	0.029774	-0.011638	-0.000656	0.000172	-0.000081	-0.000507	1.641188e-04	-0.000331	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.159544	2.492420	140°	0.16
36	-0.944329	-0.560544	-0.001406	-0.009806	0.004606	0.001423	0.000978	0.000315	2.221716e-04	-0.000010	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.176739	2.296786	140°	0.16
37	-0.947443	-0.515159	0.000247	-0.008860	0.002833	0.001258	0.000954	0.000162	-2.426856e-05	0.000138	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.170455	2.304695	140°	0.16
38	-1.071686	-0.381330	0.029611	-0.008917	-0.003227	-0.000261	0.000127	-0.000506	-2.460090e-04	-0.000004	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.148710	2.478740	140°	0.16
39	-1.129563	-0.340092	0.042721	-0.009278	-0.005135	-0.001730	0.000113	-0.000464	-3.810645e-04	0.000181	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.141903	2.555287	140°	0.16
40	-1.160450	-0.608589	0.042258	-0.017069	0.002021	-0.001675	0.000585	-0.000203	4.786634e-04	0.000006	...	0.4	0.65	0.16	1.0	2.443461	0.2	0.171313	2.610918	140°	0.16
41	-0.100311	-0.512332	-0.061102	0.000277	0.003444	-0.000393	-0.001453	0.000471	6.027916e-05	-0.000128	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.176521	1.244129	80°	0.16
42	-0.079981	-0.441534	-0.061914	0.000620	0.001185	-0.000248	-0.001414	0.000194	-1.683988e-05	0.000093	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.167533	1.252522	80°	0.16
43	-0.259471	-0.477805	-0.061752	-0.000556	0.003429	0.000534	-0.000928	0.000441	-6.780287e-06	-0.000085	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.175097	1.438110	80°	0.16
44	-0.302468	-0.225359	-0.060633	0.001001	-0.002737	0.001199	-0.000374	-0.000215	-2.950729e-04	0.000315	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.146855	1.570428	80°	0.16
45	-0.152787	-0.194943	-0.065320	0.001167	-0.003807	0.000371	-0.000481	-0.000161	-2.123430e-04	0.000508	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.143005	1.422087	80°	0.16
46	-0.307667	-0.469121	-0.060844	-0.000789	0.003396	0.000805	-0.000743	0.000429	-3.411932e-05	-0.000063	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.174511	1.497144	80°	0.16
47	-0.275157	-0.439585	-0.061692	-0.000384	0.002311	0.000701	-0.000792	0.000313	-8.908570e-05	0.000045	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.170496	1.470243	80°	0.16
48	-0.052624	-0.296443	-0.062555	0.001237	-0.002283	0.000227	-0.001640	-0.000360	-4.048301e-07	0.000094	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.151212	1.282264	80°	0.16
49	-0.112605	-0.512113	-0.061268	0.000202	0.003539	-0.000323	-0.001436	0.000476	6.406333e-05	-0.000145	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.176779	1.257857	80°	0.16
50	-0.274825	-0.335715	-0.059410	0.000581	-0.000319	0.001512	-0.001492	-0.000330	-3.504779e-05	-0.000270	...	0.4	0.65	0.16	1.0	1.396263	0.2	0.157964	1.505475	80°	0.16
51	0.666826	-0.751041	0.016709	0.010780	0.002460	-0.000799	0.000803	0.000095	-1.436529e-04	0.000089	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.166466	0.346456	20°	0.16
52	0.578040	-0.806088	0.008922	0.010286	0.005021	-0.001514	0.000503	0.000469	-2.606051e-04	-0.000155	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.177635	0.386719	20°	0.16
53	0.653467	-0.624203	0.006614	0.009087	-0.000103	-0.000554	-0.000854	-0.000533	1.463360e-04	-0.000157	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.155776	0.441191	20°	0.16
54	0.572528	-0.783451	0.005996	0.009685	0.004365	-0.001549	0.000388	0.000436	-2.251687e-04	-0.000036	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.175787	0.407493	20°	0.16
55	0.659641	-0.513237	-0.004183	0.006170	-0.002880	-0.000997	-0.000403	-0.000293	2.174160e-04	0.000516	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.146865	0.504861	20°	0.16
56	0.608625	-0.678892	0.002987	0.008683	0.001219	-0.001112	-0.000207	-0.000031	-6.913243e-06	0.000121	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.163440	0.445301	20°	0.16
57	0.686187	-0.696469	0.015975	0.010500	0.001120	-0.000493	0.000174	-0.000254	3.747075e-06	-0.000045	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.160243	0.366476	20°	0.16
58	0.706113	-0.689142	0.018765	0.010884	0.000886	-0.000274	0.000101	-0.000391	3.554720e-05	-0.000137	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.158335	0.354346	20°	0.16
59	0.863564	-0.675819	0.039638	0.012348	-0.000697	0.000855	0.001824	-0.000443	5.866481e-05	0.000142	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.148304	0.235357	20°	0.16
60	0.804667	-0.784796	0.042667	0.014671	0.002395	0.000714	0.001847	-0.000351	-1.425091e-04	-0.000275	...	0.4	0.65	0.16	1.0	0.349066	0.2	0.160054	0.206858	20°	0.16

60 rows × 22 columns

fig, ax = plt.subplots()
explained_variance_ratio_plot(pca, ax=ax, verbose=True)

Explained variance ratio:
['PC1 0.710479191426253', 'PC2 0.28719947416604474', 'PC3 0.00225194144906072', 'PC4 5.183288037026648e-05', 'PC5 1.587220975385232e-05', 'PC6 8.440474770760988e-07', 'PC7 6.213528822494952e-07', 'PC8 1.0970573778645286e-07', 'PC9 6.60747998962157e-08', 'PC10 2.645205525212001e-08', 'PC11 1.0271482863927864e-08', 'PC12 5.522156049005053e-09']
Cumsum of Explained variance ratio:
['PC1 0.710479191426253', 'PC2 0.9976786655922978', 'PC3 0.9999306070413585', 'PC4 0.9999824399217287', 'PC5 0.9999983121314826', 'PC6 0.9999991561789596', 'PC7 0.9999997775318419', 'PC8 0.9999998872375797', 'PC9 0.9999999533123796', 'PC10 0.9999999797644348', 'PC11 0.9999999900359177', 'PC12 0.9999999955580737']

<Axes: >

fig, ax = plt.subplots()
sns.scatterplot(
    data=df_pca,
    x="PC1",
    y="PC2",
    hue="bending_angle",
    hue_order=bending_order,
    style="aspect_ratio",
    palette="Set2",
    ax=ax,
)

<Axes: xlabel='PC1', ylabel='PC2'>

Morphospace

def project_3d_to_2d(points, azim=-60, elev=30):
    """Project 3D points onto 2D plane from given viewpoint.
    Uses the same azimuth/elevation as matplotlib.
    """
    az = np.radians(azim)
    el = np.radians(elev)
    R = np.array([
        [-np.sin(az),            np.cos(az),            0         ],
        [-np.sin(el)*np.cos(az), -np.sin(el)*np.sin(az), np.cos(el)],
    ])
    projected = points @ R.T
    return projected[:, 0], projected[:, 1]


def get_pc_scores_for_morphospace(ax, num=5):
    xrange = np.linspace(ax.get_xlim()[0], ax.get_xlim()[1], num)
    yrange = np.linspace(ax.get_ylim()[0], ax.get_ylim()[1], num)
    return xrange, yrange


def plot_recon_morphs_3d(
    pca,
    efa,
    fig,
    ax,
    n_PCs_xy=[1, 2],
    morph_num=3,
    morph_scale=1.0,
    morph_color="lightgray",
    morph_alpha=0.7,
    view=(-60, 30),
):
    """Plot reconstructed shapes in PC space with oblique 2D projection."""
    pc_scores_h, pc_scores_v = get_pc_scores_for_morphospace(ax, morph_num)
    for pc_score_h in pc_scores_h:
        for pc_score_v in pc_scores_v:
            pc_score = np.zeros(pca.n_components_)
            n_PC_h, n_PC_v = n_PCs_xy
            pc_score[n_PC_h - 1] = pc_score_h
            pc_score[n_PC_v - 1] = pc_score_v

            arr_coef = pca.inverse_transform([pc_score])

            ax_width = ax.get_window_extent().width
            fig_width = fig.get_window_extent().width
            fig_height = fig.get_window_extent().height
            morph_size = morph_scale * ax_width / (fig_width * morph_num)
            loc = ax.transData.transform((pc_score_h, pc_score_v))
            axins = fig.add_axes(
                [
                    loc[0] / fig_width - morph_size / 2,
                    loc[1] / fig_height - morph_size / 2,
                    morph_size,
                    morph_size,
                ],
                anchor="C",
            )

            recon = efa.inverse_transform(arr_coef, norm=False)
            x, y = project_3d_to_2d(recon[0], azim=view[0], elev=view[1])

            axins.plot(
                x.astype(float), y.astype(float), color=morph_color, alpha=morph_alpha
            )
            axins.axis("equal")
            axins.axis("off")

morph_num = 5
morph_scale = 0.8
morph_color = "gray"
morph_alpha = 0.8
view = (-120, 60)


fig = plt.figure(figsize=(16, 16), dpi=200)

#########
# PC1 vs PC2
#########
ax = fig.add_subplot(2, 2, 1)
sns.scatterplot(
    data=df_pca,
    x="PC1",
    y="PC2",
    hue="bending_angle",
    hue_order=bending_order,
    style="aspect_ratio",
    palette="Set2",
    ax=ax,
    legend=True,
)

plot_recon_morphs_3d(
    pca,
    efa,
    morph_num=morph_num,
    morph_scale=morph_scale,
    morph_color=morph_color,
    morph_alpha=morph_alpha,
    fig=fig,
    ax=ax,
    view=view,
)

ax.patch.set_alpha(0)
ax.set(xlabel="PC1", ylabel="PC2")

print("PC1-PC2 done")

#########
# PC2 vs PC3
#########
ax = fig.add_subplot(2, 2, 2)
sns.scatterplot(
    data=df_pca,
    x="PC2",
    y="PC3",
    hue="bending_angle",
    hue_order=bending_order,
    style="aspect_ratio",
    palette="Set2",
    ax=ax,
    legend=True,
)

plot_recon_morphs_3d(
    pca,
    efa,
    morph_num=morph_num,
    morph_scale=morph_scale,
    morph_color=morph_color,
    morph_alpha=morph_alpha,
    fig=fig,
    ax=ax,
    n_PCs_xy=[2, 3],
    view=view,
)

ax.patch.set_alpha(0)
ax.set(xlabel="PC2", ylabel="PC3")

print("PC2-PC3 done")

#########
# PC3 vs PC1
#########
ax = fig.add_subplot(2, 2, 3)
sns.scatterplot(
    data=df_pca,
    x="PC3",
    y="PC1",
    hue="bending_angle",
    hue_order=bending_order,
    style="aspect_ratio",
    palette="Set2",
    ax=ax,
    legend=True,
)

plot_recon_morphs_3d(
    pca,
    efa,
    morph_num=morph_num,
    morph_scale=morph_scale,
    morph_color=morph_color,
    morph_alpha=morph_alpha,
    fig=fig,
    ax=ax,
    n_PCs_xy=[3, 1],
    view=view,
)

ax.patch.set_alpha(0)
ax.set(xlabel="PC3", ylabel="PC1")

print("PC3-PC1 done")

#########
# Explained variance
#########
ax = fig.add_subplot(2, 2, 4)
explained_variance_ratio_plot(pca, ax=ax, verbose=True)

PC1-PC2 done
PC2-PC3 done

PC3-PC1 done
Explained variance ratio:
['PC1 0.710479191426253', 'PC2 0.28719947416604474', 'PC3 0.00225194144906072', 'PC4 5.183288037026648e-05', 'PC5 1.587220975385232e-05', 'PC6 8.440474770760988e-07', 'PC7 6.213528822494952e-07', 'PC8 1.0970573778645286e-07', 'PC9 6.60747998962157e-08', 'PC10 2.645205525212001e-08', 'PC11 1.0271482863927864e-08', 'PC12 5.522156049005053e-09']
Cumsum of Explained variance ratio:
['PC1 0.710479191426253', 'PC2 0.9976786655922978', 'PC3 0.9999306070413585', 'PC4 0.9999824399217287', 'PC5 0.9999983121314826', 'PC6 0.9999991561789596', 'PC7 0.9999997775318419', 'PC8 0.9999998872375797', 'PC9 0.9999999533123796', 'PC10 0.9999999797644348', 'PC11 0.9999999900359177', 'PC12 0.9999999955580737']

<Axes: >