Yes you figured out the origin of the term. Word stemming comes from stem cells as the concept is the same. As stem cells are the root for all other cells the words also have stems.
This can be best explained by an example:
As you see all the previous words have a root. A word that is the prefix in all of them. That is the stem word.
The stem word does not always have to be a valid word. It will be a succession of letters that is left after known suffixes are stripped from words. Known suffixes include: ing,es,ed,li,less,ful and so on.
The concept is very simple but the result is worth every penny! Stemming allows you to find related words with different forms or misspellings. Stemming will point out related words and search engines love stems.
I use the Porter Stemming Algorythm with it's PHP implementation, but tweaked it a bit. I got my own custom version ;)
By stemming every word in a keyphrase and then ordering the results alphabetically you can find similar phrases like: feeling well, wellness feeling or any variations. Trust me, you'll put it to good use!
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