#outlier-analysis

Implement anomaly detection systems for fraud detection, network security, and quality control applications. Statistical methods: 1. Z-score analysis: standard deviation-based detection, threshold ±3 for outliers. 2. Interquartile Range (IQR): Q3 + 1.5*IQR upper bound, Q1 - 1.5*IQR lower bound. 3. Modified Z-score: median-based, robust to outliers, threshold ±3.5. Machine learning approaches: 1. Isolation Forest: tree-based isolation, anomaly score calculation, contamination parameter tuning. 2. One-Class SVM: unsupervised learning, normal behavior boundary, nu parameter optimization. 3. Local Outlier Factor (LOF): density-based detection, local density comparison, k-nearest neighbors. Deep learning methods: 1. Autoencoders: reconstruction error-based detection, bottleneck representation, threshold tuning. 2. Variational Autoencoders (VAE): probabilistic approach, reconstruction probability, latent space analysis. 3. LSTM autoencoders: sequential data anomalies, time series patterns, prediction error analysis. Time series anomaly detection: 1. Prophet: trend and seasonality decomposition, confidence intervals, changepoint detection. 2. Seasonal decomposition: residual analysis, seasonal pattern deviations. 3. Moving averages: deviation from expected patterns, adaptive thresholds. Evaluation metrics: 1. Precision: true anomalies / detected anomalies, minimize false alarms. 2. Recall: detected anomalies / total anomalies, maximize anomaly capture. 3. F1-score: balanced precision and recall, compare different methods. Real-time detection: streaming data processing, concept drift adaptation, online learning algorithms, alert systems with severity levels, investigation workflows for detected anomalies.