Making effective use of the Internet is increasingly about creating better and more intelligent applications and search engines. Here is a brief introduction into how search engines work:

01) Define the corpus, search space/data;
02) Separate the corpus into documents;
03) Generate features for each document;
04) Generate a representation of each document;
05) Study the feature/vector space;
06) Cluster documents;
07) Reduce dimensionality;
08) Accept input Queries;
09) Find the cosine angles against the query vector;
10) Find the sought vector column;
11) Output results to user in some way;

Each document in a corpus (database) is described by a set of keywords called index terms. We assign weights to index terms according to their relevance (frequency of occurrence for instance), this is how we go about creating the index, that we can then search.

Corpus preparation:
Web pages of interest are analysed and cleaned by removing hypertext tags or any other hyper language; Pages are then broken down into documents where each document is scanned through searching for words/terms of interest: those which make a document unique, not standard words.

Extract terms of interest:
Bear in mind that terms of interest must be invariant, that is be characteristic of a document, not generic and easy to find in any corpus/document. The idea is to find a signature per document.

Build term-by-document matrix:
The search space is defined by N dimensions where the chosen terms/features of a document is a point in the N term space, this allows conceptual/semantic searches.

Each document becomes a column vector, each row represents a term. Each row identifies the frequency of a term across the analysed corpus, at first we simply build the matrix by counting the terms for each document.

Compress the matrix:
There are two basic techniques/methods, Compress Row Storage (Scans matrix row by row) and Compress Column Storage (Scans matrix column by column) Both use three arrays.

Normalis the matrix:
Normalisation implies transforming column vectors to unit vectors: i.e. vectors of unit length

Unit document vectors contain frequency of terms; the normalisation is applied because the semantic content of a document is generally determined the relative frequency of terms.

Singular Value Decomposition:
This simplifies a symmetric matrix into three matrices Two are identical and represent the eigenvectors: the new dimensions. The third is diagonal and represents the eigenvalues, that is the spread of the corpus along these new dimensions.

A geometric interpretation:
The corpus is first formated, stemmed and is then stored in a compact term-by-document matrix. Each column of such matrix is then normalised to produce the likelihood of a term across the corpus, or, equivalently, the frequency of terms in a document.

The term-by-document matrix is then decomposed to calculate eigen values and vectors. Eigen vectors represent a new Cartesian coordinate frame spanning the same search space, BUT, they indicate the most important dimenions/axis along which documents mainly lie. Eigen value do quantify the spread of documents along these new axes/eigen vectors.

Queries:
Queries must be based on defined features/terms within the term-by-document matrix, matching in a vector space such as this is implemented by multiplying the query vector against the terms by document matrix,ie matching a query vector q against the documents of the matrix.

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