# levenshtein distance

Published articles for levenshtein distance.

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## Metric Spaces -- A Primer

DevFeed: [Metric Spaces -- A Primer](<https://devfeed.tech/articles/metric-spaces-a-primer-40285.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/08/26/metric-spaces-a-primer/>)

Published: 2012-08-26T12:08:25Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [levenshtein-distance](<https://devfeed.tech/tags/levenshtein-distance.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [metric](<https://devfeed.tech/tags/metric.md>), [symmetry](<https://devfeed.tech/tags/symmetry.md>), [topology](<https://devfeed.tech/tags/topology.md>), [triangle-inequality](<https://devfeed.tech/tags/triangle-inequality.md>)

### AI overview

This tutorial introduces metric spaces as sets equipped with distance functions that satisfy non-negativity, symmetry, and the triangle inequality. It explains that metrics impose a topology and contrasts metric-based work with approaches using non-metrics.

### Source excerpt

The Blessing of Distance We have often mentioned the idea of a "metric" on this blog, and we briefly described a formal definition for it. Colloquially, a metric is simply the mathematical notion of a distance function, with certain well-behaved properties. Since we're now starting to cover a few more metrics (and things which are distinctly not metrics) in the context of machine learning algorithms, we find it pertinent to lay out the definition once again, discuss some implications, and explore a few basic examples.

## Metrics on Words

DevFeed: [Metrics on Words](<https://devfeed.tech/articles/metrics-on-words-40250.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/12/19/metrics-on-words/>)

Published: 2011-12-19T20:59:31Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Programming](<https://devfeed.tech/topics/programming.md>), [Algorithms](<https://devfeed.tech/topics/algorithms.md>), [Code](<https://devfeed.tech/topics/code.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [analysis](<https://devfeed.tech/tags/analysis.md>), [code](<https://devfeed.tech/tags/code.md>), [decoding](<https://devfeed.tech/tags/decoding.md>), [dynamic-programming](<https://devfeed.tech/tags/dynamic-programming.md>), [functional-programming](<https://devfeed.tech/tags/functional-programming.md>), [github](<https://devfeed.tech/tags/github.md>), [levenshtein-distance](<https://devfeed.tech/tags/levenshtein-distance.md>), [linguistics](<https://devfeed.tech/tags/linguistics.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [metric](<https://devfeed.tech/tags/metric.md>), [monoids](<https://devfeed.tech/tags/monoids.md>), [ngrams](<https://devfeed.tech/tags/ngrams.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [string](<https://devfeed.tech/tags/string.md>)

### AI overview

This introductory article defines finite strings over an alphabet and explains that they form a monoid under concatenation, with the empty string as the identity element. It introduces a series on probabilistic analysis of Google's ngrams for tasks including spelling correction, word segmentation, typing prediction, and cipher decoding.

### Source excerpt

We are about to begin a series where we analyze large corpora of English words. In particular, we will use a probabilistic analysis of Google's ngrams to solve various tasks such as spelling correction, word segmentation, on-line typing prediction, and decoding substitution ciphers. This will hopefully take us on a wonderful journey through elementary probability, dynamic programming algorithms, and optimization. As usual, the code implemented in this post is available from this blog's Github page, and we encourage the reader to use the code to implement our suggested exercises.