Project: s41467-024-46773-z | Function: delve_fs (python)

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Complete the masked function based on the algorithm description.
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**DESCRIPTION:** Implements the main DELVE feature selection algorithm with two-step approach: dynamic seed identification from co-varying feature modules and Laplacian score-based feature ranking along cellular trajectory graphs

**KEY TERMS:** {
  "k": "number of nearest neighbors for kNN graph construction",
  "num_subsamples": "number of neighborhoods to subsample (m=1000)",
  "n_clusters": "number of feature modules for K-means clustering",
  "null_iterations": "permutation test iterations for dynamic variance testing",
  "delta_mean": "average pairwise change in expression matrix Δ",
  "modules": "feature cluster assignments with p-values",
  "selected_features": "ranked features by Laplacian scores"
}

**CONTEXT CODE:** import anndata
import scipy
import numpy as np
import pandas as pd
import logging
logging.basicConfig(level=logging.INFO)
from sklearn.cluster import KMeans
from sklearn.neighbors import NearestNeighbors
from sklearn.decomposition import PCA
import multiprocessing as mp
from functools import partial
from tqdm import tqdm
from sketchKH import *

def delve_fs(adata = None,
            k: int = 10,
            num_subsamples: int = 1000,
            n_clusters: int = 5,
            null_iterations: int = 1000,
            random_state: int = 0,
            n_random_state: int = 10,
            n_pcs = None,
            n_jobs: int = -1):
    """Performs DELVE feature selection 
        - step 1: identifies dynamic seed features to construct a between-cell affinity graph according to dynamic cell state progression
        - step 2: ranks features according to their total variation in signal along the approximate trajectory graph using the Laplacian score
    
    Parameters
    adata: anndata.AnnData
        annotated data object where adata.X is the attribute for preprocessed data (dimensions = cells x features)
    k: int (default = 10)
        number of nearest neighbors for between cell affinity kNN graph construction
    num_subsamples: int (default = 1000)
        number of neighborhoods to subsample when estimating feature dynamics  
    n_clusters: int (default = 5)
        number of feature modules
    null_iterations: int (default = 1000)
        number of iterations for gene-wise permutation testing
    random_state: int (default = 0)
        random seed parameter
    n_random_state: int (default = 10)
        number of kmeans clustering initializations
    n_pcs: int (default = None)
        number of principal components to compute pairwise Euclidean distances for between-cell affinity graph construction. If None, uses adata.X
    n_jobs = int (default = -1)
        number of tasks
    ----------
    Returns
    delta_mean: pd.DataFrame
        dataframe containing average pairwise change in expression of all features across subsampled neighborhoods (dimensions = num_subsamples x features)
    modules: pd.DataFrame
        dataframe containing feature-cluster assignments and permutation p-values (dimensions = features x 2)
    selected_features: pd.DataFrame
        dataframe containing ranked features and Laplacian scores following feature selection (dimensions = features x 1)
    ----------
    """
    # MASKED: Implements the main DELVE feature selection algorithm with two-step approach: dynamic seed identification from co-varying feature modules and Laplacian score-based feature ranking along cellular trajectory graphs implementation
    raise NotImplementedError("This function is masked for testing purposes.")

def seed_select(X = None,
                feature_names = None,
                obs_names = None,
                k: int = 10, 
                num_subsamples: int = 1000,
                n_clusters: int = 5,
                null_iterations: int = 1000,
                random_state: int = 0,
                n_random_state: int = 10,
                n_pcs = None,
                n_jobs: int = -1):
    """Identifies dynamic seed clusters
    Parameters
    X: np.ndarray (default = None)
        array containing normalized and preprocessed data (dimensions = cells x features)
    feature_names: np.ndarray (default = None)
        array containing feature names
    obs_names: np.ndarray (default = None)
        array containing cell names   
    k: int (default = 10)
        number of nearest neighbors for between cell affinity kNN graph construction
    num_subsamples: int (default = 1000)
        number of neighborhoods to subsample when estimating feature dynamics  
    n_clusters: int (default = 5)
        number of feature modules
    null_iterations: int (default = 1000)
        number of iterations for gene-wise permutation testing
    random_state: int (default = 0)
        random seed parameter
    n_random_state: int (default = 10)
        number of kmeans clustering initializations
    n_pcs: int (default = None)
        number of principal components to compute pairwise Euclidean distances for between-cell affinity graph construction. If None, uses adata.X
    n_jobs = int (default = -1)
        number of tasks
    ----------
    Returns
    sub_idx: np.andarray
        array containing indices of subsampled neighborhoods
    adata_sub: anndata.AnnData
        annotated data object containing subsampled means (dimensions = num_subsamples x features)
    delta_mean: pd.DataFrame
        dataframe containing average pairwise change in expression of all features across subsampled neighborhoods (dimensions = num_subsamples x features)
    modules: pd.DataFrame
        dataframe containing feature-cluster assignments and permutation p-values (dimensions = features x 2)
    ----------
    """
    # MASKED: Identifies dynamic feature modules through K-means clustering on average pairwise expression changes across cellular neighborhoods with permutation testing for statistical significance implementation
    raise NotImplementedError("This function is masked for testing purposes.")

def feature_select(X = None,
                    feature_names = None,
                    dyn_feats = None,
                    k: int = 10,
                    n_pcs = None, 


Complete the function implementation replacing "raise NotImplementedError".