NumericalFeature.filter_correlation

static NumericalFeature.filter_correlation(X, max_cor=0.7)

Filter features based on Pearson correlation.

Removes redundant columns from a feature matrix by iterating through features in order and discarding any feature that exceeds max_cor Pearson correlation with an already-kept feature. Use this after CPP.run() to reduce the selected feature set to a non-redundant subset.

Added in version 0.1.0.

Parameters:

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

• max_cor (float, default=0.7) – 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.

• The number of selected features (True entries) can be fewer than n_features when redundant columns are removed; raise max_cor to retain more (admitting more redundancy).

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 [Breimann25]):

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