🔍 How a Few Lines of Code Can Save You Thousands
This essay explores a simple but powerful idea: many business-critical problems don't require expensive software, large AI models, or heavy infrastructure. Sometimes, just a few thoughtful lines of code can reveal profound insights. If you're curious how structure can emerge from raw data streams -- without supervision or training -- this is a compelling place to begin.
While the examples below focus on language, the principles extend far beyond -- to customer journeys, clickstreams, sensor logs, biological signals, and more. Wherever there's a sequence, there's potential for structure.
To demonstrate this idea in action, we built a lightweight interactive tool: Try the live demo: Discover Patterns in Any Sequence.
The demo is powered by a compact JavaScript-based algorithm originally developed by Mikhael Margolin and me. Despite its simplicity -- the core logic fits in just a few lines of code -- it has been successfully applied in marketing, finance, behavioral analytics, and even stock trading strategy development.
For a deeper walkthrough of how the tool works -- and how to apply it to your own data -- see the section near the end of this essay.
Introduction
Businesses often overinvest in complex tools: neural networks, paid APIs, or massive analytics platforms. Yet some of the most revealing insights come from lightweight algorithms designed with clarity of purpose.
This essay introduces a minimalist pattern-discovery method. Originally designed to understand unknown languages, it turns out to be broadly applicable to real-world tasks like analyzing customer behavior or optimizing user flows.
It doesn't require labeled data, pretrained models, or assumptions about the source. Just a symbolic stream — and a bit of math.
A Language Without Spaces
Consider the beginning of Homer’s Iliad and strip it of spaces, punctuation, and capitalization:
Even if you're a fluent English speaker, this uninterrupted stream is hard to read. But a machine can learn to segment and understand it — without knowing any English — by identifying statistical patterns.
Just Counting
The above text can be considered a sequence (S) of elements (e) from an alphabet (A) consisting of 26 lowercase English letters. The algorithm begins by reading the sequence one symbol at a time. It maintains:
- N: Total number of elements of A seen so far in S
- Ne: Count of each individual element e of A seen so far in S
- Pe = Ne / N: Empirical probabilities of each element e
In parallel, the algorithm also counts all pairs of consecutive symbols occurring in the sequence:
- M: Total number of adjacent pairs seen in S so far (which is always N–1)
- Me₁e₂: Count of each pair e₁, e₂ in S
- Pe₁e₂ = Me₁e₂ / M: Empirical probability of each observed pair
Discovering Patterns
The next step is to calculate the value of a pair, defined as the logarithm of the probability ratio:
What does this formula tell us? If two events are independent, then the probability of seeing them together equals the product of their individual probabilities. In that case, the ratio is 1 and the logarithm is 0 — indicating no meaningful connection.
But if the ratio is greater than 1 — and especially if it exceeds a predefined threshold — then the co-occurrence of those events is likely not random. They form a meaningful pattern.
For example, consider the English letters 't' and 'h': Pt = 0.09, Ph = 0.06, Pth = 0.02. This gives us: Pth / (Pt × Ph) = 3.6, and Vth ≈ 1.28. If our threshold were 0.5, this pair clearly qualifies as a pattern.
Growing the Alphabet
What happens next? Once a high-value pair like "th" is found, it is added as a new element to the alphabet. We started with an alphabet of 26 elements — the single lowercase characters 'a' through 'z'. Now we add the newly discovered pattern 'th' as the 27th element, thus extending the alphabet. We don't need a new symbol; we simply treat "th" as an atomic unit whenever it appears.
This closes the logical loop. The algorithm continues as before — reading the sequence element-by-element — but now using an expanded alphabet. With composite elements like "th", it can now detect larger structures such as "the". For example, if "the" appears more frequently than expected based on the probabilities of "th" and "e", it too becomes a candidate pattern. When discovered, we’ve effectively uncovered the first real English word — unsupervised.
The principle remains the same: any unusually valuable pair of existing alphabet elements is added as a new element. Acting this way, the system can recursively discover all the words in the unformatted text. Over time, it builds a vocabulary of meaningful patterns — without needing labels or prior knowledge.
Early Stage: Emergence of Short Structures
Let’s walk through what the algorithm actually discovers when applied to a real stream of unstructured text — in this case, the beginning of Homer’s Iliad. What follows are snapshots from different stages of the learning process.
Below is an excerpt showing the progression of discovered patterns. The patterns already identified are delimited by pipes. Initially, only 1-character patterns appear. Soon after, the first 2-character combination — the word 'of' — is discovered. The "th" pattern discussed above appears on line three. The word "the" appears by line eight, and the word "and" appears on line nine. You’ll also spot grammatical endings like "ing" — essential components of English.
Later Stages: Longer Structure Formation
What happens at later stages? As expected, longer and more stable structures begin to emerge — confirming the recursive nature of the algorithm.
As you can see, the most valuable structures detected are not always full words. They include prefixes, suffixes, prepositions, proper names, and frequently used multi-word phrases — all discovered without supervision.
Discovered Synonym-Like Pairs
An interesting feature of this algorithm is its ability to group patterns by their contextual or functional similarity. That is, it can identify forms that tend to appear in similar environments — even if they are not classical synonyms. These contextually interchangeable forms reflect how language (or behavior) conveys meaning through usage.
Below are some examples of these contextually similar pairs, sorted by their importance score:
your his 0.207
ed ing 0.186
him them 0.177
the his 0.173
it him 0.173
he she 0.170
had was 0.169
me him 0.167
his their 0.164
has had 0.160
should would 0.153
would will 0.150
her him 0.145
are were 0.142
uponthe onthe 0.141
ulysses minerva 0.139
hand spear 0.136
These include personal pronouns, verb forms, and even proper names or conceptually related objects — all inferred purely from the structure of the input.
From Letters to Anything Else
The method is completely general. Instead of letters, your symbols could be:
- Webpages visited during a user session
- Customer service actions
- Sensor readings or sound events
- Clicks, queries, or logs
- Bird calls or animal vocalizations
As long as the symbols in your data are distinguishable and indivisible, the algorithm applies. This makes it incredibly flexible across domains. For example, in the context of a website:
Website = alphabet. Each page = a character. A session = a sequence. Patterns = discovered user journeys. Synonyms = contextually similar behaviors across users.
Now imagine that these contextually learned patterns — journeys, habits, transitions — can be directly mapped to key business outcomes: conversions, churn, upsell opportunities, or operational inefficiencies.
You don't need external vendors, universal and powerful ML/AI algorithms, GPUs, distributed systems, off-the-shelf analytics suites or prebuilt AI pipelines. And you certainly don't need to spend thousands on SaaS analytics platforms.
All you need is a symbolic stream, a few lines of code, and a willingness to look for structure where others see noise.
Why This Matters
Sometimes, a small, explainable algorithm is faster, cheaper, and easier to integrate. It doesn’t replace ML — but it often precedes it, offering first-pass insights that make future decisions more grounded.
This is especially important for startups, small teams, or anyone trying to solve real problems without over-engineering.
Exploring the Algorithm Yourself: The 1D Data Explorer Tool
Curious to try the algorithm yourself? The 1D Data Explorer is an interactive tool that lets you explore how patterns and synonym-like structures emerge in real data — one chunk at a time.
You can start by selecting the type of atom — the indivisible unit of data. Atoms can be characters, words, URLs, or any basic symbol appropriate to your domain. The tool allows you to analyze sequences of these atoms, detect patterns, and observe how structural relationships form.
Your input should be a delimited sequence of symbols. For example, for character-level analysis, the delimiter may be null; for word-level analysis, it may be a space. You can experiment with custom delimiters too.
Once you load your data, choose a chunk size and click “Run First Chunk”. The algorithm will scan your data, calculate co-occurrence frequencies, evaluate pattern values, and begin expanding the alphabet of discovered units.
The results are displayed across several tabs:
- Patterns Tab: Lists discovered sequences, their frequency, length, and value.
- Synonyms Tab: Shows pairs of patterns with similar contextual behavior — an unsupervised form of synonymy.
- Dynamics Tab: Tracks the learning progression as patterns accumulate over time.
- Outcomes Tab: Summarizes overall statistics of discovered structures.
You don’t need to adjust the algorithm's parameters initially — defaults are tuned for general use. But for advanced exploration, you can modify thresholds, chunk size, and filtering rules to suit your dataset and discovery goals.
To revisit the tool, click here.
Conclusion
Before you invest in complex stacks, ask yourself: Could a lightweight solution get us 80% of the way there?
The pattern-discovery algorithm is a reminder that sometimes, intelligence doesn’t require scale — it requires structure. And structure can be found anywhere, if you know how to look.