Keywords Density Optimization

Keyword Density Optimization: Claims and Theories

On March 24 a FINDALL search in Google for keywords density optimization returned 240,000 documents. I found many of these documents belonging to search engine marketing and optimization (SEM, SEO) specialists. Some of them promote keyword density analyzer tools while others talk about things like "right density weighting, "excellent keyword density", KD as a "concentration" or "strength" ratio and the like. Some even take KD for the weight of term i in document j, while others propose localized KD ranges for titles, descriptions, paragraphs, tables, links, urls, etc. One can even find some specialists going after the latest KD "trick" and claiming that optimizing KD values up to a certain range for a given search engine affects the way a search engine scores relevancy and ranks documents.
Given the fact that there are so many KD theories flying around, my good friend Mike Grehan approached me after the Jupitermedia's 2005 Search Engine Strategies Conference held in New York and invited me to do something about it. I felt the "something" should be a balanced article mixed with a bit of IR, semantics and math elements but with no conclusion so readers could draw their own. So, here we go.

Keyword Density Optimization and Calculations

In the search engine marketing literature, keyword density is defined as
Equation 1:
where tf_{i, j} is the number of times term i appears in document j and l is the total number of terms in the document. Equation 1 is a legacy idea found intermingled in the old literature on readability theory, where word frequency ratios are calculated for passages and text windows - phrases, sentences, paragraphs or entire documents - and combined with other readability tests.
The notion of keyword density values predates all commercial search engines and the Internet and can hardly be considered an IR concept. What is worse, KD plays no role on how commercial search engines process text, index documents or assign weights to terms. Why then many optimizers still believe in KD values? The answer is simple: misinformation.
If two documents, D1 and D2, consist of 1000 terms (l = 1000) and repeat a term 20 times (tf = 20), then a keyword density analyzer will tell you that for both documents KD = 20/1000 = 0.020 (or 2%) for that term. Identical values are obtained when tf = 10 and l = 500. Evidently, a keyword density analyzer does not establishes which document is more relevant. A density analysis or KD ratio tells us nothing about:

1. the relative distance between keywords in documents (proximity)
2. where in a document the terms occur (distribution)
3. the co-citation frequency between terms (co-occurrence)
4. the main theme, topic, and sub-topics (on-topic issues) of the documents

Thus, KD is divorced from content quality, semantics and relevacy.
Under these circumstances one can hardly talk about optimizing term weights for ranking purposes. Add to this copy style issues and you get a good idea of why this article's title is The Keyword Density of Non-Sense. The following five search engine implementations illustrate the point:

1. Linearization
2. Tokenization
3. Filtration
4. Stemming
5. Weighting

Linearization - Document Content as a Stream of Characters

Linearization is the process of ignoring markup tags from a web document so its content is reinterpreted as a stream of characters to be scored. This process is carried out tag-by-tag and as tags are declared and found in the source code. As illustrated in Figure 1, linearization affects the way search engines "see", "read" and "judge" Web content --sort of speak. Here the content of a website is rendered using two nested html tables, each consisting of one large cell at the top and the common 3-column cell format. We assume that no other text and html tags are present in the source code. The numbers at the top-right corner of the cells indicate in which order a search engine finds and interprets the content of the cells.

Figure 1. Linearization of table-based Web content.

The box at the bottom of Figure 1 illustrates how a search engine probably "sees", "reads" and "interprets" the content of this document after linearization. Note the lack of coherence and theming. Two term sequences illustrate the point: "Find Information About Food on sale!" and "Clients Visit our Partners". This state of the content is probably hidden from the untrained eyes of average users. Clearly, linearization has a detrimental effect on keyword positioning, proximity, distribution and on the effective content to be "judged" and scored. The effect worsens as more nested tables and html tags are used, to the point that after linearization content perceived as meritorious by a human can be interpreted as plain garbage by a search engine. Thus, computing localized KD values is a futile exercise.

Burning the Trees and Keyword Weight Fights

In the best-case scenario, linearization shows whether words, phrases and passages end competing for relevancy in a distorted lexicographical tree. I call this phenomenon "burning the trees". It is one of the most overlooked web design and optimization problems.
Constructing a lexicographical tree out of linearized content reveals the actual state and relationship between nouns, adjectives, verbs, and phrases as they are actually embedded in documents. It shows the effective data structure that is been used. In many cases, linearization identifies local document concepts (noun groups) and hidden grammatical patterns. Mandelbrot has used the patterned nature of languages observed in lexicographical trees to propose a measure he calls the "temperature of discourse". He writes:

"The 'hotter' the discourse, the higher the probability of use of rare words." (1)

However, from the semantics standpoint, word rarity is a context-dependent state. Often terms that are considered "rare" in relation with the topic being discussed

1. are off-topic or misplaced terms.
2. are losely associated with the topic.
3. have low document co-occurrence.
4. exhibit low database co-occurrence.
5. have high IDF (inverse document frequency) values.

Thus, the temperature of a discourse should indeed increase as more "rare" words are used. A lexicographical tree representation in which such terms are color coded in red should help us to visualize the "degree and extension of the burns". Thus, in my view "burning the trees" is a natural consequence of misplacing words or using off-topic terms.
Term misplacement and lack of connectivity is often found in "baby" grammar. In fact, the evolution of sentence construction is inherently driven by production rules determined by underlying fractal patterns. To illustrate, in Fractals and Sentence Production, Chapter 9 of From Complexity to Creativity (2, 3), Ben Goertzel uses an L-System model to explain that the beginning of early childhood grammar is the two-word sentence in which the iterative pattern involving nouns (N) and verbs( V) is driven by a re-write rule in which a verb is replaced by a verb-noun sequence; i.e., (V → V N)
Figure 2 shows the tree-like pattern generated when (V → V N) is applied to the NV initial seed or axiom.

Figure 2. Tree-like pattern for the (V → V N) production rule.

After four iterations i, three combinations emerge:

1. noun groups; i.e., NN, NNN, NNN, NNNN
2. the NVN combination
3. the NV combination

Noun groups are important in Local Context Analysis (LCA) and query expansion studies. While the NVN combination is normally used to describe actions or events, the NV combination is a natural sequence found in spoken and written constructions. With regard to the NV combination, Goertzel explains:

"The reason N V is a more natural combination is because it occurs at an earlier step in the derivation process." (3)

To illustrate, consider the following case:

Noun-Verb Pattern Evolution in Early Childhood Grammar

Iteration	Pattern	Example
0	NV	Stevie byebye
1	NVN	Stevie byebye car

It is now comprehensible why many Web documents do not deliver any appealing message to search engines. After linearization, it can be realized that these may be "speaking" either incoherently or like babies. [By the way, L-System algorithms, named after A. Lindermayer, have been used for many years in the study of tree-like patterns (4)].
"Burning the trees" explains why repeating terms in a document, moving around on-page factors or invoking link strategies, not necessarily improves relevancy. In many instances one can get the opposite result. I recommend SEOs to start incorporating lexicographic and word pattern techniques, linearization strategies and local context analysis (LCA) into their optimization mix. (5)
In Figure 1, "burning the trees" was the result of improper positioning of text. However in many cases the effect is a byproduct of sloppy Web design, poor usability or improper use of the HTML DOM structure (another kind of tree). This underscores an important W3C recommendation: that html tables should be used for presenting tabular data, not for designing Web documents. In most cases, professional web designers can do better by replacing tables with cascading style sheets (CSS).
"Burning the trees" often leads to another phenomenon I call "keyword weight fights". It is a recurrent problem encountered during topic identification (topic spotting), text segmentation (based on topic changes) and on-topic analysis (6). Considering that co-occurrence patterns of words and word classes provide important information about how a language is used and semantics (meaning) is transmited, misplaced keywords and text without clear topic transitions difficult the work of text summarization editors (humans or machine-based) that need to generate representative headings and outlines from documents.
Thus, the "fight" unnecessarily difficults topic disambiguation and the work of human abstractors that during document classification need to answer questions like

• "What does this document or passage is about?"
• "What is the theme or category of this document, section or paragraph?"
• "How does this block of links relate to the content?", etc.

While linearization renders localized KD values useless, document indexing makes a myth out of this metric. Let see why.

Tokenization, Filtration and Stemming

Document indexing is the process of transforming document text into a representation of text and consists of three steps: tokenization, filtration and stemming.
During tokenization terms are lowercased and punctuation removed. Rules must be in place so digits, hyphens and other symbols can be parsed properly. Tokenization is followed by filtration. During filtration commonly used terms and terms that do not add any semantic meaning (stopwords) are removed. In most IR systems survival terms are further reduced to common stems or roots. This is known as stemming. Thus, the initial content of length l is reduced to a list of terms (stems and words) of length l' (i.e., l' <>). These processes are described in Figure 3.

Figure 3. Important steps during the indexing of a
document: tokenization, filtration and stemming.

Similar lists can be extracted from individual documents and merged to conform an index of terms. This index can be used for different purposes; for instance, to compute term weights and to represent documents and queries as term vectors in a term space. Evidently, document linearization is a critical GAP Analysis step. If linearization shows that you have already "burned the trees", a search engine will be indexing just that.

Weighting - Term Weighting Schemes

The weight of a term in a document consists of three different types of term weighting: local, global, and normalization. The term weight is given by
Equation 2:
where L_{i, j} is the local weight for term i in document j, G_i is the global weight for term i and N_j is the normalization factor for document j. Local weights are functions of how many times each term occurs in a document, global weights are functions of how many times documents containing each term appears in the collection, and the normalization factor corrects for discrepancies in the lengths of the documents.
In the classic Term Vector Space model





which reduces to the well-known tf*IDF weighting scheme
Equation 6:
where log(D/d_i) is the Inverse Document Frequency (IDF), D is the number of documents in the collection (the database size) and d_i is the number of documents containing term i.
Equation 6 is just one of many term weighting schemes found in the term vector literature. Depending on how L, G and N are defined, different weighting schemes can be proposed for documents and queries.

KD values as estimators of term weights?

The only way that KD values could be taken for term weights; i.e.
Equation 7:
is if global weights are ignored and the normalization factor N_j is redefined in terms of document lengths
Equations 8 and 9:
However, G_i = IDF = 1 constraints the collection size D (corpus) to be equal to ten times (D = 10*d) the number of documents containing term i and N_j = 1/l_j implies no stopword filtration. These conditions are not observed in commercial search systems.
Using a probabilistic term vector scheme in which IDF is defined as
Equation 10:
does not help either since the condition G_i = IDF = 1 implies that D = 11*d. Additional unrrealistic constraints can be derived for other weighting schemes when G_i = 1.
To sum up, the assumption that KD values could be taken for estimates of term weights or that these values could be used for optimization purposes amounts to the Keyword Density of Non-Sense.

Related Material

KD values and on-page factors are local observables. Some search engine marketers claim these could be used to understand the nature of some terms and weights deemed as "negative". These are terms that when used in a document or in a query seem to impact document relevancy and retrieval. I discuss the nature of these terms in Term Weights in a MySQL Environment (7). Unlike keyword density which is a local, on-page factor, Equation 10 reveals that these negative weights are not a local but a global phenomenon, taking place at the database level.

Next: Fractal Patterns, L-Systems and Semantics

Prev: Grammar, Semantics, Knowledge and Fractals

Acknowledgements

The author thanks Mike Grehan, editor of E-Marketing-News, for publishing the original version of this article. This one is just an updated and expanded version.

References

1. The Fractal Geometry of Nature, Benoit B. Mandelbrot, Chapter 38, W. H. Freeman (1983).
2. From Complexity to Creativity: Computational Models of Evolutionary, Autopoietic and Cognitive Dynamics, Ben Goertzel, Plenum Press (1997).
3. Fractals and Sentence Production, Ben Goertzel, Ref 2, Chapter 9, Plenum Press (1997).
4. The Algorithmic Beauty of Plants, P. Prusinkiewicz and A. Lindenmayer, Springer-Verlag, New York (1990).
5. Topic Analysis Using a Finite Mixture Model, Hang Li and Kenji Yamanish.
6. Improving the Effectiveness of Information Retrieval with Local Context Analysis, Jinxi Xu, W. Bruce Croft.
7. Term Weights in a MySQL Environment, E. Garcia

This article is written by Dr. E. Garcia. Have a look on this original post - The Keyword Density of Non-Sense

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