Overcoming High-Dimensional Data Challenges: A Personal Journey with Dimensionality Reduction

Working with large datasets and high-dimensional data can be both fascinating and challenging. Recently, I faced a significant issue while handling a large document – approximately 3GB – which required some serious problem-solving. This blog explores my journey of overcoming these challenges through dimensionality reduction, offering practical insights and steps to optimize high-dimensional data storage and search operations.

The Problem: High-Dimensional Data and Indexing Constraints

In one of my recent projects, I was dealing with embedding vectors representing complex data points. Each vector had 3072 dimensions, capturing intricate details essential for my application. However, this high-dimensional data introduced several challenges:

1. Computational Expense: Processing and storing such high-dimensional data required substantial computational resources.

2. Overfitting Risks: In machine learning models, excessive dimensions can lead to overfitting, where the model performs well on training data but poorly on unseen data.

3. Indexing Constraints: The real kicker came when I tried to create an index on these vectors using the HNSW (Hierarchical Navigable Small World) index in PostgreSQL. The system threw an error, stating, "column cannot have more than 2000 dimensions for HNSW index."

Here's the exact error message I encountered:

```

sqlalchemy.exc.InternalError: (psycopg2.errors.InternalError_) column cannot have more than 2000 dimensions for hnsw index

[SQL: CREATE INDEX IF NOT EXISTS embedding_vector_idx ON shankara_embeddings USING hnsw (embedding vector_l2_ops) WITH (m = 16, ef_construction = 64)]

(Background on this error at: https://sqlalche.me/e/20/2j85)

```

The Solution: Dimensionality Reduction

To overcome this challenge, I decided to reduce the dimensions of my vectors. Dimensionality reduction techniques like Principal Component Analysis (PCA) allow us to transform high-dimensional data into a lower-dimensional space while preserving essential information. Think of it as resizing a detailed image to a smaller size, keeping the main features intact.

Here's how I tackled the issue:

Step-by-Step Guide to Dimensionality Reduction

1. Reduce Dimensions Using PCA

I started by applying PCA to my existing vectors to reduce their dimensions from 3072 to 1500.

```python

import numpy as np

import pandas as pd

from sklearn.decomposition import PCA

from sqlalchemy import create_engine

# Load vectors from the database

engine = create_engine('postgresql+psycopg2://username:password@localhost/dbname')

query = "SELECT id, embedding FROM shankara_embeddings"

data = pd.read_sql(query, engine)

# Convert embeddings to arrays

vectors = np.array([np.array(embedding) for embedding in data['embedding']])

# Apply PCA to reduce dimensions

pca = PCA(n_components=1500)

reduced_vectors = pca.fit_transform(vectors)

# Update the dataframe with reduced vectors

data['embedding_reduced'] = [list(vector) for vector in reduced_vectors]

# Write back to the database

data.to_sql('shankara_embeddings', engine, if_exists='replace', index=False, method='multi')

```

2. Update the Embedding Column in the Database Schema

- Add a New Column: Temporarily add a new column to store the reduced vectors.

```sql

ALTER TABLE shankara_embeddings ADD COLUMN embedding_reduced vector(1500);

```

- Populate the New Column with Reduced Vectors: Use Python and SQLAlchemy to update the new column.

- Drop the Old Column and Rename the New Column: Remove the old column and rename the new column.

```sql

ALTER TABLE shankara_embeddings DROP COLUMN embedding;

ALTER TABLE shankara_embeddings RENAME COLUMN embedding_reduced TO embedding;

```

3. Update the Alembic Migration Script

Modify your Alembic migration script to create the index with the new column.

```python

from alembic import op

revision = 'c1d86abd2629'

down_revision = 'previous_revision_id'

branch_labels = None

depends_on = None

def upgrade():

op.execute("""

CREATE INDEX IF NOT EXISTS embedding_vector_idx

ON shankara_embeddings

USING hnsw (embedding vector_l2_ops)

WITH (m = 16, ef_construction = 64)

""")

def downgrade():

op.execute("""

DROP INDEX IF EXISTS embedding_vector_idx

""")

```

4. Run the Migration

Apply the changes by running your Alembic migration.

```bash

alembic upgrade head

```

The Outcome

By reducing the dimensions of my vectors, I was able to:

1. Improve Performance: Database operations became faster and more efficient.

2. Enhance Resource Efficiency: The system used less memory and computational power.

3. Ensure Compatibility: The data complied with the limitations of the HNSW indexing technique.

Conclusion

Dimensionality reduction is a powerful technique to optimize the storage and search of high-dimensional data. By following the steps outlined in this blog, I was able to enhance the performance of my database operations while maintaining the integrity of my data. Embrace dimensionality reduction to navigate the complexities of high-dimensional data with ease and efficiency.

This journey taught me valuable lessons about the importance of understanding and optimizing data structures. If you're facing similar challenges, I hope this guide helps you find a solution that works for you.