What's the difference between an inverted index and a plain old index?

In software engineering we create indexes all the time (e.g., in databases) but I also hear a lot of people talk about inverted indices. Is there something fundamentally different between the two? They sound like the same thing.

One common use is "...to allow fast full-text searching."

The two types denote directionality. One takes you forward through the index, and the other takes you backward (the inverse) through the index. That's it. There's no mystery to uncover here. Otherwise the two types are identical, it's just a question of what information you have, and as a result what information you're trying to find.

To address your inquiry, I don't think there's actually a way to know why the use is what it is today. The only reason it's important to define which is forward and which one is inverted is so that we can all have a conversation about them, and everyone knows which direction we're talking about. Think about the terms "left" and "right": they are relative. Which is which doesn't matter, except that everyone needs to agree which one is "left" and which one is "right" in order for the words to have meaning. If, as a culture, we decided to flip left and right, then you'd have the same issue figuring out what a "right turn" vs a "left turn" is since the agreed upon meaning had changed. However, the naming is arbitrary, so which one is which (in and of itself) doesn't matter - what matters is that we all agree on the meaning.

In your comment where you ask, "please don't just define the terms", you're missing the point, and I think you're just getting hung up on the wording when there is absolutely no difference between them.


For the benefit of future readers, I will now provide several "forward" and "inverted" index examples:

Example 1: Web search

If you're thinking that the inverse of an index is something like the inverse of a function in mathematics, where the inverse is a special thing that has a different form, then you're mistaken: that's not the case here.

In a search engine you have a list of documents (pages on web sites), where you enter some keywords and get results back.

A forward index (or just index) is the list of documents, and which words appear in them. In the web search example, Google crawls the web, building the list of documents, figuring out which words appear in each page.

The inverted index is the list of words, and the documents in which they appear. In the web search example, you provide the list of words (your search query), and Google produces the documents (search result links).

They are both indexes - it's just a question of which direction you're going. Forward is from documents->to->words, inverted is from words->to->documents.

Example 2: DNS

Another example is a DNS lookup (which takes a host name, and returns an IP address) and a reverse lookup (which takes an IP address, and gives you the host name).

Example 3: A book

The index in the back of a book is actually an inverted index, as defined by the examples above - a list of words, and where to find them in the book. In a book, the table of contents is like a forward index: it's a list of documents (chapters) which the book contains, except instead of listing the words in those sections, the table of contents just gives a name/general description of what's contained in those documents (chapters).

Example 4: Your cell phone

The forward index in your cell phone is your list of contacts, and which phone numbers (cell, home, work) are associated with those contacts. The inverted index is what allows you to manually enter a phone number, and when you hit "dial" you see the person's name, rather than the number, because your phone has taken the phone number and found you the contact associated with it.

They called it inverted just because there is already a forward index. Take the example of search engine, it composed by two parts: the first part is "web crawler and parser" which build a index from document to word, the second part is search database which build a index from word to document. Because of the first index exist, we naturally call the second index as inverted index.

If you name the TOC (Table of Content) of a book as index, then you should call the index at the end of book as "inverted index". Or, in other side, you can call the TOC as inverted index.

typically when speaking about index, you mean some added calculations or stored results of procedures which have been done in order to speed up application (e.g. MySQL or other RDBMS Consult MySQL the docs). Indexing can also be related to caching etc.

Inverted index creates file with structure that is primarily intender for (fulltext) searching.

Inverted index consists of two main files:

• Vocabulary
• Occurences

In vocabulary are common words extracted from text (of course after filtering blacklist words like pronouns). The occurences file holds the connection between words and documents (word1 appears in doc1 and doc2, not in doc3). It is represented in a form of a matrix.

In the above image is shown the process of creating the two files mentioned.

If you are further interester in this problematic I can recommend you a great book written by Ricardo Yated - Modern Information Retrieval (See it on Amazon) - about page 200 I think.

Hope it helps :-)

normalocity has already wonderfully differentiated between a forward and an inverted index but for the question of why one is called a forward index and the other an inverted index, maybe this is why they are called that way---

Taking example of search engine crawling and indexing (or building index for a book), a forward index can be built simultaneously while you are crawling the web pages(or reading the book) or going forward. So if you have 10 webpages to crawl(or 10 chapters in a book) you can crawl the first webpage(read the first chapter) and then make a list of words which appear in the webpage(words which appear in the chapter) and continue this process for other webpages(other chapters) so by the time you have crawled all the 10 webpages(read all 10 chapters) your forward index is complete with each webpage(chapter) pointing to a list of words it contains.

But to make an inverted index you have to crawl all the 10 webpages(read the 10 chapters) and and then take each word from each documents list and figure out which documents contain that word. So this is like going backward once you have crawled the webpages(read chapters of the book). So its called an inverted index.

This is just my speculation.

The term "Inverted Word Index" refers to the change in relationship of a single-document containing many-words, to each unique word containing (or identifying) a list of many-documents. This is effectively taking a One-to-Many Relationship (Docs to Words) and Inverting (or reversing) it such that a new "Inverted" One-to-Many Relationship now exists, which is each-unique-word relating to Many-Documents (i.e., all that contain that word). It's origin really is that simple, and the term "inverted index" was used to describe manual indexes of the same type long before computers and electronic high-speed indexing even existed (yes, admittedly, I'm an old, geezer programmer, almost old enough to have considered Grace Hopper a "sweet young lady" age appropriate for courting back when COBOL was a shiny new language). Please don't discard us geezers just yet, as we may occasionally provide a useful, and possibly even valuable, historical tid-bit or two - when our personal RAM is still working, that is. [grin]

There are many types of index. For example, B-tree, R-tree, hash... For different purposes, we must choose correct index.

Inverted index is a special one. Inverted index usually used in full text search engine. Use inverted index we can find out a word's locate in a document(or documents set) as fast as possible. Think about the limit of memory and cpu, other index can't finish this job.

You can read lucene document for more details. It's a open source search engine. http://lucene.apache.org/java/docs/index.html

in inverted indexes, we have the following form:

word1-> list of docs it occurs in (sorted order)

word2-> list of docs it occurs in (sorted order)

It is very useful for search engine query processing as it allows us to find docs that word occurs in .

You can use supervised machine learing to build this inverted index.

One more difference:

Handling updates with the inverted index are expensive in comparison with forward index.

Forward index handles updates easily by reflecting the changes only in the corresponding document index, whereas in the inverted index, the same change has to reflect in multiple positions across the inverted index.