Filtering and Transforming Cosine Similarity Scores from Large Matrix Calculations Using Pandas Dataframes and Scikit-learn's Cosine Similarity Function

Filtering Cosine Similarity Scores into a Pandas DataFrame

Overview

In this article, we will explore how to filter cosine similarity scores from large matrix calculations using pandas dataframes and scikit-learn’s cosine similarity function. We’ll discuss the challenges of working with massive datasets and how to approach filtering and transforming these values in an efficient manner.

Introduction

When dealing with large corpus sizes, directly calculating all possible combinations between documents can result in enormous matrices that are difficult to handle. Cosine similarity is often used for text classification tasks because it measures the similarity between two vectors (document representations) based on their angle in a high-dimensional space. We will discuss how to leverage batch processing and pandas dataframes to filter these scores.

Background

The cosine similarity function calculates the dot product of two vectors, normalized by the magnitudes of each vector. This results in a value that indicates the level of similarity between the input documents.

[ cosine_similarity(X_i, X_j) = \frac{X_i \cdot X_j}{||X_i|| ||X_j||} ]

In our case, we’re working with TF-IDF (Term Frequency-Inverse Document Frequency) matrices, which are constructed using scikit-learn’s TfidfVectorizer. These matrices represent the frequency of words in each document and provide a way to compute cosine similarities.

Problem Statement

We want to calculate all possible combinations of cosine similarities between documents from a large corpus. While doing so, we need to filter out similarity scores below a certain threshold (0.65) and have each data value be assigned an index and column name that are the document IDs corresponding to these values.

However, the filtering process is turning the cosine similarity scores into boolean (True/False) values instead of retaining their original values.

Solution

We can break down the problem into smaller parts using batch processing. We calculate the cosine similarities for each submatrix by utilizing cosine_similarity(tfidf_matrix[i:i+BATCH_SIZE], tfidf_matrix) to generate an mxN matrix, where m is the number of documents in our current batch and N is the total number of documents.

Batch Processing

# Import necessary libraries.
from sklearn.feature_extraction.text import TfidfVectorizer
import pandas as pd
import numpy as np

# Assuming 'corpus' is a list variable that contains all document IDs sorted in ascending order.
tfidf_vectorizer = TfidfVectorizer()
tfidf_matrix = tfidf_vectorizer.fit_transform(corpus)

matrix_length = tfidf_matrix.shape[0]

BATCH_SIZE = 10
FILTER_THRESHOLD = 0.6

# Variable to store the final filtered dataframe.
df = []

Looping Through Submatrices and Applying Transformations

for i in range(0, matrix_length - BATCH_SIZE, BATCH_SIZE):
    # Compute cosine similarity for a submatrix.
    subMatrix = cosine_similarity(tfidf_matrix[i:i+BATCH_SIZE], tfidf_matrix)

    # Set the proper index of the submatrix in a dataframe.
    similarity_values = pd.DataFrame(
        subMatrix, 
        index = range(i, i+BATCH_SIZE), 
        columns= range(0, matrix_length))

    # Apply the stack transformation from the follow-up clarification.
    stacked_df = question_followup_transformer(similarity_values)

    # Filter all scores below the filter threshold.
    filtered_df = stacked_df.query("Score > {}".format(FILTER_THRESHOLD))

    # Append dataframe to a list.
    df.append(filtered_df)

Combining All Dataframes

# Concatenate all dataframes into one final dataframe.
df = pd.concat(df, ignore_index=True)

Full Implementation

Please see the below code block for the full implementation of this problem:

from sklearn.feature_extraction.text import TfidfVectorizer
import pandas as pd
import numpy as np
from scipy.spatial.distance import cosine

def question_followup_transformer(df):
  return df.stack().reset_index().rename(columns={'level_0':'ID1','level_1':'ID2', 0:'Score'})

# Assuming 'corpus' is a list variable that contains all document IDs sorted in ascending order.
corpus = ['doc1', 'doc2', ...] # This can be any text documents.

tfidf_vectorizer = TfidfVectorizer()
tfidf_matrix = tfidf_vectorizer.fit_transform(corpus)

matrix_length = tfidf_matrix.shape[0]

BATCH_SIZE = 10
FILTER_THRESHOLD = 0.6

df = []
for i in range(0, matrix_length - BATCH_SIZE, BATCH_SIZE):
    # Compute cosine similarity for a submatrix.
    subMatrix = cosine_similarity(tfidf_matrix[i:i+BATCH_SIZE], tfidf_matrix)

    # Set the proper index of the submatrix in a dataframe.
    similarity_values = pd.DataFrame(
        subMatrix, 
        index = range(i, i+BATCH_SIZE), 
        columns= range(0, matrix_length))

    # Apply the stack transformation from the follow-up clarification.
    stacked_df = question_followup_transformer(similarity_values)

    # Filter all scores below the filter threshold.
    filtered_df = stacked_df.query("Score > {}".format(FILTER_THRESHOLD))

    # Append dataframe to a list.
    df.append(filtered_df)

# Concatenate all dataframes into one final dataframe.
df = pd.concat(df, ignore_index=True)

Explanation

This code is divided into several sections that explain how to solve the problem. We use batch processing and pandas dataframes to filter cosine similarity scores.

The main concept is to process each submatrix separately by utilizing cosine_similarity(tfidf_matrix[i:i+BATCH_SIZE], tfidf_matrix) to compute similarities between documents in our current batch. We then apply a stack transformation using question_followup_transformer() as per the provided follow-up clarification.

We then filter out scores below the given threshold (0.65) and append each filtered dataframe to a list.

Finally, we concatenate all dataframes into one final dataframe and return it as our solution.

Example Use Cases

This code can be used in various NLP applications where you need to compute cosine similarities between multiple documents from a large corpus. For instance, document clustering or text classification tasks benefit greatly from these similarity measures.

The advantages of this approach are:

It’s highly parallelizable which makes it efficient for dealing with massive datasets.
It processes individual submatrices instead of the full matrix, reducing memory requirements significantly.
By filtering scores before storing them in a dataframe, you avoid having to process all possible combinations between documents.

However, there is one trade-off: this approach requires multiple iterations over the entire corpus to obtain the final result. Therefore, it might not be suitable for very large datasets where processing time becomes too long due to memory constraints or computation complexity.

In such cases, you may need to consider other approaches like using a sparse matrix data type (like scipy’s csr_matrix) to reduce space requirements or utilizing more advanced algorithms designed specifically for handling massive matrices efficiently.

Last modified on 2024-03-02