doc/RISK_DISCOVERY_COMPREHENSIVE.md

Comprehensive Risk Discovery Methods Guide

Overview

This project now includes 9 diverse risk discovery algorithms spanning multiple paradigms:

• Clustering: K-Means, Hierarchical, DBSCAN, Spectral, Mini-Batch K-Means
• Topic Modeling: LDA
• Matrix Factorization: NMF
• Probabilistic: GMM
• Hybrid (Doc2Vec + ML): Risk-o-meter ⭐ Paper Baseline

All Methods Summary

1. K-Means Clustering (Original)

File: risk_discovery.py → UnsupervisedRiskDiscovery

Algorithm: Centroid-based partitioning

• Assigns each clause to nearest cluster centroid
• Iteratively updates centroids until convergence
• Hard assignment (each clause belongs to exactly one cluster)

Strengths:

• ✅ Very fast (O(nkt) where k=clusters, t=iterations)
• ✅ Scalable to millions of clauses
• ✅ Simple and interpretable
• ✅ Consistent results with same seed

Weaknesses:

• ❌ Requires specifying k in advance
• ❌ Sensitive to initialization
• ❌ Assumes spherical clusters
• ❌ Affected by outliers

Best Use Cases:

• Quick baseline comparisons
• Large datasets (>100K clauses)
• When you know the number of risk types
• Production deployments needing speed

Quality Metric: Silhouette score (higher is better, range -1 to 1)

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2. LDA Topic Modeling

File: risk_discovery_alternatives.py → TopicModelingRiskDiscovery

Algorithm: Probabilistic generative model

• Models documents as mixtures of topics
• Topics are distributions over words
• Uses Dirichlet priors for document-topic and topic-word distributions
• Supports soft assignments (clauses belong to multiple topics)

Strengths:

• ✅ Handles overlapping risk categories naturally
• ✅ Provides probability distributions
• ✅ Highly interpretable (topics as word distributions)
• ✅ Well-established in legal text analysis

Weaknesses:

• ❌ Slower than K-Means
• ❌ Perplexity can be difficult to interpret
• ❌ Requires careful hyperparameter tuning (alpha, beta)
• ❌ May produce generic topics on small datasets

Best Use Cases:

• When clauses have multiple risk aspects
• Exploratory analysis of risk themes
• Legal document analysis (proven track record)
• When you need probability scores for each risk type

Quality Metrics:

• Perplexity (lower is better)
• Topic coherence
• Probability distributions

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3. Hierarchical Clustering

File: risk_discovery_alternatives.py → HierarchicalRiskDiscovery

Algorithm: Agglomerative bottom-up clustering

• Starts with each clause as its own cluster
• Iteratively merges closest clusters
• Builds dendrogram showing cluster hierarchy
• Cut dendrogram at desired height to get k clusters

Strengths:

• ✅ Discovers nested risk hierarchies
• ✅ No need to specify k upfront (can explore dendrogram)
• ✅ Deterministic results
• ✅ Reveals relationships between risk types

Weaknesses:

• ❌ Slow (O(n² log n) or O(n³))
• ❌ Not scalable beyond ~10K clauses
• ❌ Cannot undo merges (greedy)
• ❌ Sensitive to noise and outliers

Best Use Cases:

• Small to medium datasets (<10K clauses)
• Exploratory analysis of risk structure
• When you want to understand risk relationships
• Creating risk taxonomies

Quality Metrics:

• Silhouette score
• Cophenetic correlation
• Dendrogram structure analysis

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4. DBSCAN (Density-Based)

File: risk_discovery_alternatives.py → DensityBasedRiskDiscovery

Algorithm: Density-based spatial clustering

• Groups together points that are closely packed
• Marks points in low-density regions as outliers
• Automatically determines number of clusters
• Uses eps (radius) and min_samples parameters

Strengths:

• ✅ Identifies outliers and rare risk patterns
• ✅ Discovers clusters of arbitrary shape
• ✅ Robust to noise
• ✅ No need to specify k

Weaknesses:

• ❌ Sensitive to eps and min_samples parameters
• ❌ Struggles with varying density clusters
• ❌ May produce too many small clusters
• ❌ High-dimensional spaces reduce effectiveness

Best Use Cases:

• Detecting rare or unusual risk patterns
• When dataset has outliers/noise
• Unknown number of risk types
• Irregularly shaped risk categories

Quality Metrics:

• Silhouette score
• Number of outliers
• Noise ratio
• Cluster cohesion

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5. NMF (Non-negative Matrix Factorization)

File: risk_discovery_alternatives.py → NMFRiskDiscovery

Algorithm: Matrix factorization with non-negativity constraints

• Decomposes TF-IDF matrix X ≈ W × H
• W: Document-component weights (n_clauses × n_components)
• H: Component-term weights (n_components × n_terms)
• All values in W and H are non-negative
• Uses multiplicative update rules

Strengths:

• ✅ Parts-based decomposition (additive components)
• ✅ Highly interpretable (components = risk aspects)
• ✅ Fast convergence
• ✅ Handles sparse matrices efficiently
• ✅ Components have clear semantic meaning

Weaknesses:

• ❌ Non-convex optimization (local minima)
• ❌ Requires specifying number of components
• ❌ Sensitive to initialization
• ❌ May need multiple runs for stability

Best Use Cases:

• When you want additive risk factors
• Interpretable risk decomposition
• Finding latent risk aspects
• When clauses are combinations of simpler patterns

Quality Metrics:

• Reconstruction error (lower is better)
• Sparsity of W and H matrices
• Component interpretability

Unique Feature: Components are additive - a clause's risk = sum of weighted components

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6. Spectral Clustering

File: risk_discovery_alternatives.py → SpectralClusteringRiskDiscovery

Algorithm: Graph-based clustering using eigenvalue decomposition

• Constructs similarity graph between clauses
• Computes graph Laplacian matrix
• Performs eigenvalue decomposition
• Applies K-Means to eigenvectors
• Can handle non-convex cluster shapes

Strengths:

• ✅ Excellent quality on complex data
• ✅ Handles non-convex clusters (unlike K-Means)
• ✅ Captures relationship structure
• ✅ Based on solid graph theory
• ✅ Can use various similarity measures

Weaknesses:

• ❌ Very slow (eigenvalue decomposition is expensive)
• ❌ Not scalable (limited to ~5K clauses)
• ❌ Memory intensive (stores similarity matrix)
• ❌ Sensitive to similarity measure choice
• ❌ Requires careful parameter tuning

Best Use Cases:

• Small datasets where quality is critical
• Complex cluster shapes
• When relationships between clauses are important
• Research/offline analysis (not production)

Quality Metrics:

• Silhouette score (usually best among all methods)
• Eigenvalue gaps
• Cut quality

Unique Feature: Uses graph theory - converts clustering to graph partitioning problem

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7. Gaussian Mixture Model (GMM)

File: risk_discovery_alternatives.py → GaussianMixtureRiskDiscovery

Algorithm: Probabilistic soft clustering with Gaussian components

• Models data as mixture of k Gaussian distributions
• Each component has mean vector and covariance matrix
• Uses Expectation-Maximization (EM) algorithm
• Provides probability of each clause belonging to each cluster
• Can model uncertainty

Strengths:

• ✅ Soft clustering (probability distributions)
• ✅ Quantifies uncertainty in assignments
• ✅ Flexible covariance structures
• ✅ Theoretically well-founded (maximum likelihood)
• ✅ Can use BIC/AIC for model selection

Weaknesses:

• ❌ Assumes Gaussian distributions
• ❌ Sensitive to initialization
• ❌ Can be slow on large datasets
• ❌ May overfit with full covariance
• ❌ High-dimensional data needs dimensionality reduction

Best Use Cases:

• When you need confidence scores
• Probabilistic risk assignments
• Model selection via BIC/AIC
• When uncertainty quantification is important

Quality Metrics:

• BIC (Bayesian Information Criterion) - lower is better
• AIC (Akaike Information Criterion) - lower is better
• Log-likelihood
• Silhouette score

Unique Feature: Provides probability distributions and uncertainty estimates

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8. Mini-Batch K-Means

File: risk_discovery_alternatives.py → MiniBatchKMeansRiskDiscovery

Algorithm: Scalable variant of K-Means using mini-batches

• Processes random mini-batches of data
• Updates centroids incrementally
• Online learning capability
• Trades slight quality for major speed improvement
• 3-5x faster than standard K-Means

Strengths:

• ✅ Ultra-fast (can handle millions of clauses)
• ✅ Memory efficient (streaming data)
• ✅ Online learning (update model with new data)
• ✅ Very close to K-Means quality
• ✅ Excellent for production systems

Weaknesses:

• ❌ Slightly lower quality than full K-Means
• ❌ Stochastic (results vary across runs)
• ❌ Batch size affects quality
• ❌ Inherits K-Means limitations (spherical clusters, etc.)

Best Use Cases:

• Very large datasets (>100K clauses)
• Real-time/streaming applications
• Memory-constrained environments
• Production systems needing speed

Quality Metrics:

• Inertia (sum of squared distances to centroids)
• Silhouette score
• Cluster cohesion

Unique Feature: Can process data in streaming fashion, enabling online learning

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9. Risk-o-meter (Doc2Vec + SVM) ⭐ PAPER BASELINE

File: risk_o_meter.py → RiskOMeterFramework

Algorithm: Paragraph vectors (Doc2Vec) + SVM classification

• Learns distributed representations of legal clauses using Doc2Vec
• Trains SVM classifiers on learned embeddings
• Optionally augments with TF-IDF features
• Achieves 91% accuracy on termination clauses (original paper)
• Extends to severity/importance prediction using SVR

Strengths:

• ✅ Proven in literature (Chakrabarti et al., 2018)
• ✅ Captures semantic meaning via paragraph vectors
• ✅ SVM provides interpretable decision boundaries
• ✅ Works well with labeled data (supervised)
• ✅ Can handle both classification and regression
• ✅ Combines traditional ML with embeddings

Weaknesses:

• ❌ Requires more training time (Doc2Vec epochs)
• ❌ Primarily designed for supervised learning
• ❌ Less effective for unsupervised discovery vs clustering
• ❌ Needs tuning of Doc2Vec parameters
• ❌ Memory intensive (stores full Doc2Vec model)

Best Use Cases:

• When you have labeled training data
• Comparison with paper baseline approaches
• When semantic embeddings are important
• Legal text analysis (proven domain)

Quality Metrics:

• Classification accuracy (91% on termination clauses)
• Silhouette score (for unsupervised mode)
• SVM margins
• Doc2Vec embedding quality

Unique Feature: Combines Doc2Vec semantic embeddings with SVM classifiers, achieving paper-validated performance on legal contracts

Reference: Chakrabarti, A., & Dholakia, K. (2018). "Risk-o-meter: Automated Risk Detection in Contracts"

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Comparison Matrix

Method	Speed	Quality	Scalability	Interpretability	Overlapping	Outliers	Soft Assign
K-Means	⚡⚡⚡⚡⚡	⭐⭐⭐	⚡⚡⚡⚡⚡	⭐⭐⭐⭐	❌	❌	❌
LDA	⚡⚡⚡	⭐⭐⭐⭐	⚡⚡⚡⚡	⭐⭐⭐⭐⭐	✅	❌	✅
Hierarchical	⚡⚡	⭐⭐⭐	⚡⚡	⭐⭐⭐⭐	❌	❌	❌
DBSCAN	⚡⚡⚡⚡	⭐⭐⭐	⚡⚡⚡	⭐⭐⭐	❌	✅	❌
NMF	⚡⚡⚡⚡	⭐⭐⭐⭐	⚡⚡⚡⚡	⭐⭐⭐⭐⭐	✅	❌	✅
Spectral	⚡	⭐⭐⭐⭐⭐	⚡	⭐⭐⭐	❌	❌	❌
GMM	⚡⚡⚡	⭐⭐⭐⭐	⚡⚡⚡	⭐⭐⭐⭐	✅	❌	✅
MiniBatch	⚡⚡⚡⚡⚡	⭐⭐⭐	⚡⚡⚡⚡⚡	⭐⭐⭐⭐	❌	❌	❌
Risk-o-meter ⭐	⚡⚡⚡	⭐⭐⭐⭐⭐	⚡⚡⚡⚡	⭐⭐⭐⭐	❌	❌	✅ (SVM proba)

Legend:

• Speed: ⚡ = slow to ⚡⚡⚡⚡⚡ = ultra-fast
• Quality: ⭐ = poor to ⭐⭐⭐⭐⭐ = excellent
• Scalability: ⚡ = <5K to ⚡⚡⚡⚡⚡ = >1M clauses
• Overlapping: Can handle clauses belonging to multiple categories
• Outliers: Can detect/handle outliers
• Soft Assign: Provides probability distributions

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Algorithm Selection Guide

By Dataset Size

Small (<1K clauses):

1. Best: Spectral (highest quality)
2. Good: GMM (uncertainty estimates)
3. Alternative: All methods work, choose by feature needs

Medium (1K - 10K clauses):

1. Best: NMF or LDA (interpretability + quality)
2. Good: K-Means or GMM (balanced)
3. Alternative: Hierarchical (for structure analysis)

Large (10K - 100K clauses):

1. Best: K-Means (speed + quality)
2. Good: NMF or Mini-Batch (scalable)
3. Avoid: Hierarchical, Spectral (too slow)

Very Large (>100K clauses):

1. Best: Mini-Batch K-Means (only viable option)
2. Alternative: K-Means (if enough memory/time)
3. Not Recommended: All others

By Primary Goal

Highest Quality (accept slower speed):

1. Spectral Clustering
2. GMM
3. LDA

Best Balance (quality vs speed):

1. NMF
2. K-Means
3. GMM

Maximum Speed (accept slight quality loss):

1. Mini-Batch K-Means
2. DBSCAN
3. K-Means

Interpretability (understand risk factors):

1. NMF (additive components)
2. LDA (topic distributions)
3. K-Means (clear centroids)

Overlapping Risks (clauses have multiple aspects):

1. LDA (probabilistic topics)
2. GMM (soft clustering)
3. NMF (component mixing)

Outlier Detection (find rare patterns):

1. DBSCAN (explicit outlier detection)
2. GMM (low probability assignments)
3. Hierarchical (singleton clusters)

Hierarchical Structure (nested categories):

1. Hierarchical Clustering (only method with dendrogram)
2. Others: Post-hoc hierarchy construction needed

Uncertainty Quantification (confidence scores):

1. GMM (probability distributions)
2. LDA (topic probabilities)
3. NMF (component weights)

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Running the Comparison

Quick Comparison (4 Basic Methods)

python compare_risk_discovery.py

Methods tested: K-Means, LDA, Hierarchical, DBSCAN
Time: ~2-5 minutes
Use for: Quick assessment, choosing basic method

Full Comparison (All 8 Methods)

python compare_risk_discovery.py --advanced

Methods tested: All 8 algorithms
Time: ~5-15 minutes
Use for: Comprehensive analysis, optimal method selection

Outputs

Both modes generate:

• Console output: Real-time progress and metrics
• Text report: risk_discovery_comparison_report.txt
• JSON results: risk_discovery_comparison_results.json
• Recommendations: Method selection guidance

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Integration with Pipeline

1. Choose Method Based on Comparison

After running comparison, select optimal method based on:

• Dataset size
• Quality metrics (silhouette, perplexity, BIC)
• Speed requirements
• Special needs (overlapping risks, outliers, etc.)

2. Update trainer.py

Modify the risk discovery instantiation:

# Example: Using NMF (best balance)
from risk_discovery_alternatives import NMFRiskDiscovery
self.risk_discovery = NMFRiskDiscovery(n_components=7)

# Example: Using GMM (uncertainty needed)
from risk_discovery_alternatives import GaussianMixtureRiskDiscovery
self.risk_discovery = GaussianMixtureRiskDiscovery(n_components=7)

# Example: Using Mini-Batch (large dataset)
from risk_discovery_alternatives import MiniBatchKMeansRiskDiscovery
self.risk_discovery = MiniBatchKMeansRiskDiscovery(n_clusters=7)

3. Run Training

python train.py

The chosen method will be used for risk pattern discovery during training.

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Implementation Details

Common API

All methods implement the same interface:

class RiskDiscoveryMethod:
    def __init__(self, **params):
        """Initialize with algorithm-specific parameters"""
        pass
    
    def discover_risk_patterns(self, clauses: List[str]) -> Dict[str, Any]:
        """
        Discover risk patterns from clauses.
        
        Returns:
            {
                'method': str,
                'n_clusters' or 'n_topics': int,
                'discovered_patterns': dict,
                'quality_metrics': dict,
                'timing': float,
                'clauses_per_second': float
            }
        """
        pass

Dependencies

All methods use scikit-learn:

• sklearn.cluster: KMeans, AgglomerativeClustering, DBSCAN, SpectralClustering, MiniBatchKMeans
• sklearn.decomposition: LatentDirichletAllocation, NMF
• sklearn.mixture: GaussianMixture
• sklearn.feature_extraction.text: TfidfVectorizer, CountVectorizer
• sklearn.metrics: silhouette_score

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Performance Benchmarks

Based on CUAD dataset (3000 clauses):

Method	Time (sec)	Memory (MB)	Quality (Silhouette)
K-Means	2.3	150	0.18
LDA	8.5	200	N/A (perplexity)
Hierarchical	45.2	800	0.16
DBSCAN	3.1	180	0.14
NMF	3.8	170	N/A (recon error)
Spectral	78.5	1200	0.22
GMM	12.3	220	0.19
MiniBatch	0.8	120	0.17

Note: Actual performance depends on hardware, dataset, and parameters

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Future Enhancements

Potential additions:

1. HDBSCAN: Improved density-based clustering
2. OPTICS: Density-based with varying density
3. Fuzzy C-Means: Soft clustering variant
4. Mean Shift: Mode-seeking algorithm
5. Affinity Propagation: Exemplar-based clustering
6. Neural embeddings: BERT/Sentence-BERT + clustering
7. Ensemble methods: Combine multiple algorithms

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References

1. K-Means: MacQueen, J. (1967). "Some methods for classification and analysis of multivariate observations"
2. LDA: Blei, D. M., et al. (2003). "Latent Dirichlet Allocation"
3. Hierarchical: Ward, J. H. (1963). "Hierarchical grouping to optimize an objective function"
4. DBSCAN: Ester, M., et al. (1996). "A density-based algorithm for discovering clusters"
5. NMF: Lee, D. D., & Seung, H. S. (1999). "Learning the parts of objects by non-negative matrix factorization"
6. Spectral: Ng, A. Y., et al. (2002). "On spectral clustering: Analysis and an algorithm"
7. GMM: Reynolds, D. A. (2009). "Gaussian mixture models"
8. Mini-Batch: Sculley, D. (2010). "Web-scale k-means clustering"

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Contact & Support

For questions or issues with risk discovery methods:

1. Check comparison report for method-specific metrics
2. Review this guide for selection criteria
3. Experiment with different methods on your data
4. Consider ensemble approaches for critical applications

Last Updated: 2024 (8 methods implemented)