aaanalysis.NumericalFeature.filter_correlation

static NumericalFeature.filter_correlation(X, max_cor=0.7)

Filter features based on Pearson correlation.

Parameters:

• X (array-like, shape (n_samples, n_features)) – Feature matrix. Rows typically correspond to proteins and columns to features.

• max_cor (float, default=0.5) – Maximum Pearson correlation [0-1] of feature scales used as threshold for filtering.

Returns:

1D boolean array with shape (n_features) indicating which features are selected (True) or not (False).

Return type:

is_selected

Notes

• Features in X should be provided in decreasing order of importance. The first occurring features will be kept, while subsequent features that correlate with them will be removed.

Examples

To filter positively correlating features, you can use the NumericalFeature.filter_correlation() method. We first load features to creat a feature matrix (X) using the DOM_GSEC example dataset (see [Breimann25a]):

import aaanalysis as aa
aa.options["verbose"] = False
df_seq = aa.load_dataset(name="DOM_GSEC")
df_feat = aa.load_features()
aa.display_df(df=df_feat, show_shape=True, n_rows=5)

# Create feature matrix
sf = aa.SequenceFeature()
df_parts = sf.get_df_parts(df_seq=df_seq)
X = sf.feature_matrix(features=df_feat["feature"], df_parts=df_parts)

DataFrame shape: (150, 15)

	feature	category	subcategory	scale_name	scale_description	abs_auc	abs_mean_dif	mean_dif	std_test	std_ref	p_val_mann_whitney	p_val_fdr_bh	positions	feat_importance	feat_importance_std
1	TMD_C_JMD_C-Seg...3,4)-KLEP840101	Energy	Charge	Charge	Net charge (Kle...n et al., 1984)	0.244000	0.103666	0.103666	0.106692	0.110506	0.000000	0.000000	31,32,33,34,35	0.970400	1.438918
2	TMD_C_JMD_C-Seg...3,4)-FINA910104	Conformation	α-helix (C-cap)	α-helix termination	Helix terminati...n et al., 1991)	0.243000	0.085064	0.085064	0.098774	0.096946	0.000000	0.000000	31,32,33,34,35	0.000000	0.000000
3	TMD_C_JMD_C-Seg...6,9)-LEVM760105	Shape	Side chain length	Side chain length	Radius of gyrat... (Levitt, 1976)	0.233000	0.137044	0.137044	0.161683	0.176964	0.000000	0.000001	32,33	1.554800	2.109848
4	TMD_C_JMD_C-Seg...3,4)-HUTJ700102	Energy	Entropy	Entropy	Absolute entrop...Hutchens, 1970)	0.229000	0.098224	0.098224	0.106865	0.124608	0.000000	0.000001	31,32,33,34,35	3.111200	3.109955
5	TMD_C_JMD_C-Seg...6,9)-RADA880106	ASA/Volume	Volume	Accessible surface area (ASA)	Accessible surf...olfenden, 1988)	0.223000	0.095071	0.095071	0.114758	0.132829	0.000000	0.000002	32,33	0.000000	0.000000

Providing X as positional argument, the NumericalFeature.filter_correlation() method will return a 1D boolean array called is_selected:

# Filter features
nf = aa.NumericalFeature()
is_selected = nf.filter_correlation(X)
n = sum(is_selected)
print(f"{n} features were selected")
print(is_selected[0:5])

74 features were selected
[ True False False False False]

We can use is_select to obtain a filtered feature matrix:

import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

# Create filtered feature matrix
X_filter = X.T[is_selected].T

# Show filtering effect
sns.heatmap(data=pd.DataFrame(X).corr(), cmap="viridis", vmin=-1)
plt.title(f"Before filtering (no correlation, features={X.shape[1]})")
plt.show()

plt.title(f"After filtering (0.7 correlation, features={X_filter.shape[1]})")
sns.heatmap(data=pd.DataFrame(X_filter).corr(), cmap="viridis", vmin=-1)
plt.show()

is_selected an directly be used to filter the feature DataFrame:

# Create filtered feature DataFrame
df_feat_selected = df_feat[is_selected]
aa.display_df(df=df_feat_selected, show_shape=True, n_rows=5)

DataFrame shape: (74, 15)

	feature	category	subcategory	scale_name	scale_description	abs_auc	abs_mean_dif	mean_dif	std_test	std_ref	p_val_mann_whitney	p_val_fdr_bh	positions	feat_importance	feat_importance_std
1	TMD_C_JMD_C-Seg...3,4)-KLEP840101	Energy	Charge	Charge	Net charge (Kle...n et al., 1984)	0.244000	0.103666	0.103666	0.106692	0.110506	0.000000	0.000000	31,32,33,34,35	0.970400	1.438918
9	TMD_C_JMD_C-Seg...,10)-WILM950103	Polarity	Hydrophobicity (interface)	Hydrophobicity (interface)	Hydrophobicity ...e et al., 1995)	0.212000	0.141305	-0.141305	0.168603	0.217235	0.000000	0.000005	33,34	1.747200	2.150664
10	TMD_C_JMD_C-Seg...6,9)-AURR980110	Conformation	α-helix	α-helix (middle)	Normalized posi...ora-Rose, 1998)	0.211000	0.125350	0.125350	0.160819	0.174121	0.000000	0.000005	32,33	1.788800	2.700803
14	TMD_C_JMD_C-Seg...4,5)-LEVM760105	Shape	Side chain length	Side chain length	Radius of gyrat... (Levitt, 1976)	0.204000	0.105513	0.105513	0.132849	0.145219	0.000000	0.000009	33,34,35,36	1.992000	2.929460
16	TMD_C_JMD_C-Seg...3,4)-PRAM820102	Shape	Shape and Surface	Slope in Regression	Slope in Regres...nnuswamy, 1982)	0.199000	0.073023	-0.073023	0.087336	0.107750	0.000000	0.000017	31,32,33,34,35	0.616000	0.847660

Decreasing the correlation threshold (max_cor, default=0.7) will result in a stricter filtering and less selected features:

is_selected = nf.filter_correlation(X, max_cor=0.3)

# Create filtered feature matrix
X_filter = X.T[is_selected].T

# Show filtering effect
plt.title(f"After filtering (0.3 correlation, features={X_filter.shape[1]})")
sns.heatmap(data=pd.DataFrame(X_filter).corr(), cmap="viridis", vmin=-1)
plt.show()

# Create filtered feature DataFrame
df_feat_selected = df_feat[is_selected]
aa.display_df(df=df_feat_selected, show_shape=True, n_rows=5)

DataFrame shape: (15, 15)

	feature	category	subcategory	scale_name	scale_description	abs_auc	abs_mean_dif	mean_dif	std_test	std_ref	p_val_mann_whitney	p_val_fdr_bh	positions	feat_importance	feat_importance_std
1	TMD_C_JMD_C-Seg...3,4)-KLEP840101	Energy	Charge	Charge	Net charge (Kle...n et al., 1984)	0.244000	0.103666	0.103666	0.106692	0.110506	0.000000	0.000000	31,32,33,34,35	0.970400	1.438918
20	JMD_N_TMD_N-Seg...1,2)-KARP850101	Structure-Activity	Flexibility	Flexibility (0 ...igid neighbors)	Flexibility par...s-Schulz, 1985)	0.196000	0.062671	0.062671	0.083456	0.090427	0.000000	0.000023	1,2,3,4,5,6,7,8,9,10	1.574400	1.835403
29	JMD_N_TMD_N-Pat...,10)-AURR980116	Conformation	α-helix (C-cap)	α-helix (C-terminal, C-cap)	Normalized posi...ora-Rose, 1998)	0.184000	0.112728	-0.112728	0.166431	0.183800	0.000001	0.000061	11,15	0.857600	1.339550
63	TMD-Pattern(C,5...,12)-PRAM820102	Shape	Shape and Surface	Slope in Regression	Slope in Regres...nnuswamy, 1982)	0.167000	0.077343	0.077343	0.135340	0.134263	0.000012	0.000228	19,22,26	1.301600	1.697263
88	JMD_N_TMD_N-Pat...,15)-RADA880106	ASA/Volume	Volume	Accessible surface area (ASA)	Accessible surf...olfenden, 1988)	0.155000	0.059593	-0.059593	0.104862	0.110749	0.000050	0.000508	6,9,12,15	0.482000	0.672000