Bigram Analysis

Bigram analysis is a fundamental technique in computational linguistics that focuses on studying pairs of consecutive elements within a sequence. These elements can be letters, words, or any other discrete units, making the technique versatile across multiple domains.

Core Concepts

A bigram (also called a digram) consists of two adjacent elements in a sequence. For example:

• In text: "the cat" is a word bigram
• In letters: "th" is a character bigram
• In music: two consecutive notes form a musical bigram

Applications

Natural Language Processing

• Language Models use bigrams for:
  • Predictive text
  • Speech recognition
  • Machine translation
• Text Analysis applications include:
  • Authorship attribution
  • Language identification
  • Plagiarism detection

Statistical Analysis

Bigram analysis relies heavily on:

• Probability Theory for likelihood calculations
• Markov Chains for transition probabilities
• Frequency Distribution analysis

Implementation Methods

Counting and Probability

1. Collect all possible bigrams from the corpus
2. Calculate frequencies of each bigram
3. Compute conditional probabilities
4. Create transition matrices

Smoothing Techniques

To handle unseen bigrams, various Smoothing Algorithms are employed:

• Laplace smoothing
• Good-Turing smoothing
• Interpolation methods

Limitations

• Sparsity Problem in data representation
• Limited context compared to larger n-grams
• Data Storage challenges with large corpora

Extensions

Bigram analysis is part of the broader family of N-gram Analysis, which includes:

• Unigrams (single elements)
• Trigrams (three elements)
• Higher-order n-grams

Modern Developments

Recent advances include:

• Neural network integration
• Deep Learning applications
• Hybrid approaches combining with other techniques

Bigram analysis continues to be a cornerstone technique in text analysis, providing a foundation for more complex language processing methods while maintaining computational efficiency.