Abstract
Have you ever wondered why some people spell words exactly as they sound? For individuals who tend to spell phonetically such as early learners, second-language speakers, or those with intellectual disabilities, traditional spell-checkers often fail. My research explores how dimensionality reduction techniques like Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) can improve phonetic spelling correction. By mapping phonemes into structured mathematical spaces, I developed a model that predicts intended words based on similarity measures like cosine distance. This study bridges the gap between linguistics, machine learning, and computational mathematics, offering new insights into how we process and correct phonetic spelling errors.
From Sounds to Spelling: Why Phonetic Correction Matters
Imagine a child writing the word “pitcha” instead of “picture”. To us, it’s clear what they mean, but to a standard spell-checker, this word is unrecognisable. That’s because most spell-check systems rely on dictionary-based corrections, which fail when someone spells words exactly how they sound. This problem extends beyond classrooms. Individuals with dyslexia, second-language speakers, and those with intellectual disabilities often rely on phonetic spelling, making traditional autocorrect systems ineffective.
My research focuses on mathematically improving phonetic spelling correction using dimensionality reduction techniques to represent phonemes efficiently and make better predictions.
How Can Mathematics Fix Spelling?
Instead of treating words as simple letter sequences, my approach represents them as high-dimensional numerical vectors using n-grams. N-grams break words into smaller phonetic chunks:
- The word “hello” can be broken into bigrams (he, el, ll, lo).
- Or into trigrams (hel, ell, llo).
But instead of just listing these n-grams, we encode them into a large numerical vector that has an entry for every possible bigram or trigram in English. Each word’s vector contains mostly zeros, with a 1 marking the positions of the specific n-grams that appear in the word.
The challenge? There are thousands of possible bigrams and trigrams, and any given word only contains a handful of them. This makes our word representations high-dimensional and sparse, meaning they are computationally expensive and inefficient to process.
That’s where Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) come in. These statistical techniques compress the data, keeping only the most meaningful phonetic patterns while reducing redundancy – allowing us to efficiently compare words even in a massive feature space.
Choosing the Right Distance: Cosine versus Euclidean versus Manhattan
Once words are mapped into this reduced space, I use distance metrics to evaluate how “far” a sequence of characters (like a mis-spelled word) is from another sequence of characters (like a correctly spelled word). The closest correct spellings, according to this distance, are then predicted to be the intended word. Here’s how the metrics compared:
- Cosine Similarity → Best for phonetic matches, as it measures the angle between vectors, making it less sensitive to scale.
- Euclidean Distance → Favoured shorter words, often missing phonetic context due to absolute magnitude differences.
- Manhattan Distance → Struggled with multi-syllabic words, as its stepwise counting failed to capture phoneme relationships effectively.
What’s Next? The Future of Phonetic Correction
While this method significantly improved phonetic word retrieval, there’s still room to grow. Future research could integrate:
- Hidden Markov Models (HMMs) to predict likely phoneme sequences.
- Neural networks or Word2Vec embeddings to enhance phonetic similarity.
- Real-time phonetic correction tools for assistive communication software.
By combining mathematics, machine learning, and linguistic analysis, we move one step closer to making phonetic spelling correction smarter and more accessible!
Final Thoughts
This project highlights how mathematics can solve real-world language challenges. By applying dimensionality reduction and vector-based similarity, we can improve spell-checking systems and create tools that work for everyone – including those who rely on phonetic spelling.
What if your autocorrect really understood you? Maybe one day, thanks to mathematics, it will!
Louisa Best
Deakin University
