Advanced Techniques in Modern Anomaly Detection: Beyond Basic KDE and Isolation Forest

Advanced Techniques in Modern Anomaly Detection: Beyond Basic KDE and Isolation Forest

Introduction: The Complexity of Modern Anomaly Detection

In today’s complex data landscapes, traditional anomaly detection approaches often fall short. This deep technical dive explores advanced implementations of Kernel Density Estimation (KDE) and Isolation Forest, including ensemble methods, adaptive techniques, and real-world optimization strategies.

Advanced Kernel Density Estimation

Adaptive Bandwidth Selection

Traditional KDE uses fixed bandwidth, but adaptive methods can significantly improve performance:

from sklearn.neighbors import KernelDensity
from sklearn.model_selection import GridSearchCV
import numpy as np

class AdaptiveKDE:
    def __init__(self, bandwidths=np.logspace(-1, 1, 20)):
        self.bandwidths = bandwidths
        self.kde_models = {}
        
    def fit(self, X):
        # Perform cross-validation for each local region
        for region_idx in self._get_regions(X):
            region_data = X[region_idx]
            grid_search = GridSearchCV(
                KernelDensity(kernel='gaussian'),
                {'bandwidth': self.bandwidths},
                cv=5
            )
            grid_search.fit(region_data)
            self.kde_models[region_idx] = grid_search.best_estimator_
            
    def _get_regions(self, X):
        # Implement region splitting logic (e.g., using clustering)
        pass

Multi-Scale KDE

Implementing a multi-scale approach to capture both local and global anomalies:

class MultiScaleKDE:
    def __init__(self, scale_factors=[0.1, 0.5, 1.0, 2.0]):
        self.scale_factors = scale_factors
        self.models = []
        
    def fit(self, X):
        base_bandwidth = self._estimate_base_bandwidth(X)
        for scale in self.scale_factors:
            kde = KernelDensity(
                bandwidth=base_bandwidth * scale,
                kernel='gaussian'
            )
            kde.fit(X)
            self.models.append(kde)
    
    def score_samples(self, X):
        scores = np.zeros((len(self.models), len(X)))
        for i, kde in enumerate(self.models):
            scores[i] = -kde.score_samples(X)
        return np.mean(scores, axis=0)

Enhanced Isolation Forest

Extended Isolation Forest (EIF)

The extended version improves upon the original by considering hyperplanes for splitting:

class ExtendedIsolationForest:
    def __init__(self, n_estimators=100, sample_size=256):
        self.n_estimators = n_estimators
        self.sample_size = sample_size
        self.trees = []
        
    def _random_hyperplane_split(self, X):
        n_features = X.shape[1]
        normal_vector = np.random.normal(size=n_features)
        normal_vector /= np.linalg.norm(normal_vector)
        point = np.random.choice(X, size=1)
        return normal_vector, point
        
    def fit(self, X):
        for _ in range(self.n_estimators):
            tree = self._build_tree(X)
            self.trees.append(tree)

Hybrid Approach: Combining KDE and Isolation Forest

A novel approach combining the strengths of both methods:

class HybridAnomalyDetector:
    def __init__(self, kde_weight=0.4, if_weight=0.6):
        self.kde_weight = kde_weight
        self.if_weight = if_weight
        self.kde = MultiScaleKDE()
        self.iforest = ExtendedIsolationForest()
        
    def fit(self, X):
        self.kde.fit(X)
        self.iforest.fit(X)
        
    def predict(self, X):
        kde_scores = self.kde.score_samples(X)
        if_scores = self.iforest.score_samples(X)
        
        # Normalize scores
        kde_scores = (kde_scores - np.mean(kde_scores)) / np.std(kde_scores)
        if_scores = (if_scores - np.mean(if_scores)) / np.std(if_scores)
        
        # Combine scores
        final_scores = (self.kde_weight * kde_scores + 
                       self.if_weight * if_scores)
        return final_scores

Advanced Optimization Techniques

Feature Importance in Anomaly Detection

def calculate_feature_importance(model, X):
    importances = np.zeros(X.shape[1])
    for feature in range(X.shape[1]):
        X_permuted = X.copy()
        X_permuted[:, feature] = np.random.permutation(X[:, feature])
        
        # Compare scores before and after permutation
        original_scores = model.score_samples(X)
        permuted_scores = model.score_samples(X_permuted)
        
        importances[feature] = np.mean(np.abs(original_scores - permuted_scores))
    
    return importances / np.sum(importances)

Online Learning Implementation

For streaming data scenarios:

class OnlineAnomalyDetector:
    def __init__(self, window_size=1000):
        self.window_size = window_size
        self.data_window = []
        self.model = None
        
    def update(self, new_data):
        self.data_window.extend(new_data)
        if len(self.data_window) > self.window_size:
            self.data_window = self.data_window[-self.window_size:]
            
        # Retrain model on updated window
        self.model = HybridAnomalyDetector()
        self.model.fit(np.array(self.data_window))

Performance Optimization and Scalability

Parallel Processing Implementation

from joblib import Parallel, delayed

class ParallelAnomalyDetector:
    def __init__(self, n_jobs=-1):
        self.n_jobs = n_jobs
        
    def parallel_score(self, X, chunk_size=1000):
        chunks = [X[i:i + chunk_size] for i in range(0, len(X), chunk_size)]
        
        scores = Parallel(n_jobs=self.n_jobs)(
            delayed(self._score_chunk)(chunk) 
            for chunk in chunks
        )
        
        return np.concatenate(scores)

Advanced Evaluation Metrics

Implementation of Specialized Metrics

def calculate_advanced_metrics(y_true, y_pred, scores):
    metrics = {
        'precision_at_k': precision_at_k(y_true, scores, k=100),
        'average_precision': average_precision_score(y_true, scores),
        'area_under_roc': roc_auc_score(y_true, scores),
        'area_under_pr': average_precision_score(y_true, scores)
    }
    
    # Add volume-based metrics
    metrics['volume_ratio'] = calculate_volume_ratio(y_true, y_pred)
    
    return metrics

Real-World Applications and Optimizations

Time Series Anomaly Detection

class TimeSeriesAnomalyDetector:
    def __init__(self, seasonality_period=None):
        self.seasonality_period = seasonality_period
        
    def transform_time_features(self, X):
        # Extract temporal features
        transformed = np.column_stack([
            X,
            self._get_seasonal_features(X),
            self._get_trend_features(X)
        ])
        return transformed

Handling High Cardinality Categorical Features

def handle_categorical_features(X, categorical_columns):
    embeddings = {}
    for col in categorical_columns:
        # Create frequency-based embedding
        value_counts = X[col].value_counts(normalize=True)
        embeddings[col] = value_counts.to_dict()
        
    return embeddings

Conclusion

Modern anomaly detection requires a sophisticated approach that combines multiple techniques and considers various optimization strategies. The implementations provided here serve as a foundation for building robust, scalable anomaly detection systems that can handle real-world complexities.

Remember that these implementations are templates and should be adapted based on specific use cases and requirements. The key is to understand the underlying principles and modify the code accordingly.