A2SVD Tutorial: Adaptive Singular Value Decomposition

A2SVD Tutorial: Adaptive Singular Value Decomposition#

Sandbox Model — Experimental

This model is part of the CoreRec Sandbox — an experimental collection of algorithms for research and exploration. Sandbox models are not production-tested and may have incomplete implementations. For production-ready models, see the Production Models.

Introduction#

A2SVD extends SVD with adaptive regularization and neighborhood-based refinements for better generalization.

Paper: Koren 2008 - Factorization Meets Neighborhood

How A2SVD Works#

Architecture#

Enhanced SVD with Adaptivity:

  1. Base SVD: Standard latent factor decomposition

  2. Adaptive Regularization: Per-user/item regularization

  3. Neighborhood Integration: Add implicit feedback signals

  4. Bias Modeling: Global, user, item, and temporal biases

Key Innovation: Adaptive λ based on user/item activity

Architecture:

SVD Factors + Neighborhood Implicit + Temporal Bias → Prediction

Mathematical Foundation#

Adaptive Prediction:

r̂_ui = μ + b_u(t) + b_i(t) + q_i^T(p_u + |N(u)|^(-0.5) Σ_{j∈N(u)} y_j)

where:

  • μ: global mean

  • b_u(t), b_i(t): time-dependent biases

  • p_u: user factors

  • q_i: item factors

  • y_j: implicit factors from neighbors

Adaptive Regularization:

λ_u = λ_0 + β/√|R_u|
λ_i = λ_0 + β/√|R_i|

Lower regularization for active users/items

Reference Implementation#

Implementation Note

The code examples below are reference implementations for learning purposes. This is a sandbox model and has not been production-tested. Verify behavior thoroughly before using in production.

Step 1: Import and Load Data#

from corerec.sandbox.collaborative_full.mf_base.a2svd_base import A2SVD_base as A2SVD
from cr_learn import ml_1m
from sklearn.model_selection import train_test_split
import numpy as np

# Load dataset with CORRECT API
data = ml_1m.load()  # Returns dict with 'ratings', 'users', 'movies'
ratings_df = data['ratings']  # DataFrame with user_id, movie_id, rating, timestamp

print(f"Loaded {len(ratings_df)} ratings")

# Split data
train_df, test_df = train_test_split(ratings_df, test_size=0.2, random_state=42)

# Extract arrays for model
train_users = train_df['user_id'].values
train_items = train_df['movie_id'].values
train_ratings = train_df['rating'].values

test_users = test_df['user_id'].values
test_items = test_df['movie_id'].values
test_ratings = test_df['rating'].values

Step 2: Initialize Model#

model = A2SVD(
    name="A2SVD_Model",
    n_factors=150,
    base_reg=0.02,
    adaptive_beta=0.5,
    n_neighbors=50,
    epochs=20,
    batch_size=256,
    learning_rate=0.001,
    verbose=True
)

print(f"Initialized {model.name}")

Step 3: Train#

model.fit(
    user_ids=train_users,
    item_ids=train_items,
    ratings=train_ratings
)

print("Training complete!")

Step 4: Predict#

# Single prediction
score = model.predict(user_id=1, item_id=100)
print(f"Predicted score: {score:.3f}")

# Batch predictions
test_predictions = model.batch_predict(list(zip(test_users[:100], test_items[:100])))

Step 5: Recommend#

# Get top-10 recommendations for user
user_id = 1
recommendations = model.recommend(
    user_id=user_id,
    top_k=10
)

print(f"Top-10 recommendations for User {user_id}:")
for rank, item_id in enumerate(recommendations, 1):
    print(f"  {rank}. Item {item_id}")

Step 6: Evaluate#

from sklearn.metrics import mean_squared_error
import numpy as np

# Predict all test ratings
test_pred = [model.predict(u, i) for u, i in zip(test_users, test_items)]
rmse = np.sqrt(mean_squared_error(test_ratings, test_pred))
print(f"Test RMSE: {rmse:.4f}")

Step 7: Save & Load#

# Save model
model.save('artifacts/a2svd_model')

# Load model
loaded = A2SVD.load('artifacts/a2svd_model')
test_score = loaded.predict(1, 100)
print(f"Loaded model prediction: {test_score:.3f}")

Key Takeaways#

When to Use A2SVD#

✅ Excellent For:

  • Explicit ratings with temporal dynamics

  • Users/items with varying activity levels

  • When simple SVD underfits active users

  • Netflix-style datasets

  • Combining explicit + implicit signals

❌ Not For:

  • Pure implicit feedback (use BPR)

  • Need real-time updates

  • Very small datasets (regularization complex)

  • When simple SVD works fine

Best Practices#

  1. Base Factors: k=100-200

  2. Adaptive λ: β=0.1-1.0

  3. Neighborhood Size: 50-100 similar items

  4. Temporal Bins: Week or month-level

  5. Learning Rate: 0.001-0.01

  6. Epochs: 30-50

  7. Combine Signals: Weight implicit feedback 0.1-0.3

  8. Bias Priority: Optimize biases first

Scaling & Production Considerations#

If you plan to move this sandbox model toward production use, consider:

  • Data Volume: Test with realistic dataset sizes; sandbox implementations may not be optimized for large-scale data.

  • Distributed Training: For datasets exceeding single-machine memory, consider wrapping the model in distributed training frameworks (e.g., PyTorch DDP, Horovod).

  • Hyperparameter Tuning: Use systematic search (Optuna, Ray Tune) rather than manual tuning. The defaults in sandbox models are not tuned for any specific domain.

  • Serving Latency: Profile inference time. Some architectures (e.g., attention-based) may need quantization or ONNX export for low-latency serving.

  • Monitoring: Implement A/B testing and online metrics (CTR, engagement, diversity) before replacing an existing system.

  • Validation: Write comprehensive unit tests and integration tests before deploying. Sandbox models do not have CI coverage.

Further Reading#

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