=Paper=
{{Paper
|id=Vol-2893/paper_7
|storemode=property
|title=The Effectiveness of Using Bell Inequality Test for Information Retrieval in Arabic Texts
|pdfUrl=https://ceur-ws.org/Vol-2893/paper_7.pdf
|volume=Vol-2893
|authors=Alaa Shaker,Igor Bessmertny
|dblpUrl=https://dblp.org/rec/conf/micsecs/ShakerB20
}}
==The Effectiveness of Using Bell Inequality Test for Information Retrieval in Arabic Texts==
https://ceur-ws.org/Vol-2893/paper_7.pdf
The Effectiveness of Using Bell Inequality Test for
Information Retrieval in Arabic Texts
Alaa Shakera , Alaa Aldarfa and Prof Igor Alexandrovich Bessmertnya
a
ITMO University, Kronverksky Pr. 49, bldg. A, St. Petersburg, 197101, Russia
Abstract
In information retrieval, getting the most relevant documents to the target topic on the top places of
the search results and evaluating a query’s effectiveness are essential tasks. This article suggests a new
method for searching texts in the Arabic language by using a quantum-like semantic model. Also, it
shows the analogy between natural language texts and quantum-like systems by using Bell’s test. The
HAL (Hypertext analog to language) matrix is applied for building the quantum-space. The effect of
the window size of the HAL matrix is also a subject of research. In this work, three experiments are
discussed. The first one is applying semantic-quantum to many Arabic texts and the applicability to
use this model in natural language processing. In the second experiment, the model will be checked for
its ability to find the correlation between titles and texts through a dataset consisting of five-hundred
Arabic texts. Our model will be applied in the third experiment to retrieve data from the Arabic dataset
consisting of a hundred texts with ten queries and evaluate the retrieved data by three criteria (precision,
recall, and F-measure). This approach provides a promising way for information retrieval in Arabic
texts, depending on the relation between words of texts. That will help to order retrieved files to get the
relevant files to a query in the top places, and that will increase the efficiency of the search engine.
Keywords
Bell inequality, entanglement, information retrieval, Hyperspace analog language (HAL), Quantum The-
ory, Arabic language, Natural language processing
1. Introduction
Information retrieval (IR) is obtaining information resources relevant to an information need
from a collection of those resources. The increasing number of internet resources contradicts
with opportunities for effective search. Traditional search engines use statistical algorithms “like
TF-IDF”. These algorithms base on the statistics of words in documents that cannot always be
efficient because they do not take into account the meaning of the query and texts. In contrary,
humans do not care about the number of words in the document; the most essential is finding
what we search for, more precisely, the document’s meaning. Here is a serious problem and the
goal of this work is to find how computers can get the meaning or sense of texts. Although,
Proceedings of the 12th Majorov International Conference on Software Engineering and Computer Systems, December
10–11, 2020, Online Saint Petersburg, Russia
" eng.alaashaker4@gmail.com (A. Shaker); alaadarf2020@gmail.com (A. Aldarf); bia@cs.ifmo.ru
(I. A. Bessmertny)
~ https://github.com/Alaa-Shaker/ (A. Shaker);
https://itmo.ru/ru/viewperson/1134/bessmertnyy_igor_aleksandrovich.htm (I. A. Bessmertny)
0000-0003-2709-0766 (A. Shaker); 0000-0001-7249-5071 (A. Aldarf); 0000-0001-6711-6399 (I. A. Bessmertny)
© 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
humans can easily perform this process, but computers cannot. We need to understand how
human builds an understanding of the text. Meaning is not a real or positive quality of a given
word. It is a net of relations constructed in the text whose value is progressively determined
during the reading process.
Furthermore, reading is not a neutral operation: to read is to determine meaning [1]. Recently,
much research was dedicated to the quantum mechanical framework’s application for informa-
tion retrieval and natural language analysis. Van Rijsbergen, in 2004 was the first to propose
using the quantum semantic model for information retrieval; he aimed to unify vector, logic,
and statistical model [2]. All quantum-like models need to work in a formalized semantic space
[1]. Hyperspace analog to language (HAL) model [3] is a widely used technique to formalize a
textual space by representing the text as a square matrix. Platonov and Bessmertny, in their
work [4] used the quantum semantic model for information retrieval in Russian and English
languages. In this work, we will explore the potential of using a quantum-based model in
information retrieval and its ability to analyze the Arabic natural language. Particularly, the
model will use the HAL matrix to build a textual space, and then the Bell test will be used to
detect whether the document is relevant to the user’s query.
2. Main Work
In this paper, we try to apply a quantum theory to search in Arabic texts. Firstly, we need to
form textual space, then the vector representation of text and pairs of words, after that basis, to
study if there is quantum entanglement between two query words in the text using the Bell’s
test.
2.1. Hyperspace analog language
To apply quantum laws to find the relationship between two words in texts, we need to build
a textual space. For that, we apply the HAL model [2], which is a widely used technique to
formalize a document as a square matrix [5]. Also, HAL is a sensitive array for the links between
two terms: row and column vectors record the co-occurrence information of previous and later
words separately. The model is sensitive to direction, which helps to get the right representing
of the context of the text that Boolean logic cannot do. For example, in the two statements,
“Marx criticized the economists” and “The economists criticized Marx”. The queries “Marx”,
“criticized” and “the economists” are commutative, whereas semantics seems not commutative
[6, 7].
HAL vectors’ value is affected by the window’s size; a wider window means a greater chance
for associations between two terms, but the large size may suffer from underfitting. On the
other hand, the small window size means a strong association between two words and may
suffer from overfitting. The words in the documents correspond to the labels of columns and
rows. Each component of the word vector is inversely proportional to the distance between the
considered word and the document’s other corresponding words. We can limit the full context
we are interested in by managing the window size. By setting the window’s size, we can expand
or reduce the width of the considered context.
Table 1
HAL matrix of the sentence "The basic concept of the word association"
The Basic Concept Of Word Association
The 2 3 4 5 0 0
Basic 5 0 0 0 0 0
Concept 4 5 0 0 0 0
Of 3 4 5 0 0 0
Word 5+1 2 3 4 0 5
Association 4 1 1 3 5 0
There is an example of the HAL matrix that can explain it clearly [8]. In this example, the
sentence “The basic concept of the word association “with the window’s length W = 5 was used.
The resulting matrix appears in Table 1. Each time the word pair occurs in the text the HAL
matrix cell increments by the value W – D, where D – the distance between these words in the
window.
In the Table 1, the intersection between the column labeled “Concept” and the row labeled
“of” is equal to five because there is no word between them(5-0=5). This value decreases when
the distance increases; for example, the intersection between the row labeled “the” and the
column labeled “Basic” is equal to three because there are two words between them (5-2=3).
Another example, we notice that intersection between the row labeled “word” and the column
labeled “the” equals to (5 + 1), that because the word “the” occurs twice on the left of the word
“word”, in the first occurrence there is no word between them so (5-0=5), and in the second one
there are four words so (5-4=1); therefore the total equals to ((5-0)+(5-4)=5+1). We can see the
HAL matrix’s direction sensitive feature.
2.2. Building Textual Space
As mentioned previously, we need to build a textual space that depends on the HAL square
matrix, so we need to describe this space in geometric terms and provide it with the basis that
generates its vectors. In the N-dimensional HAL matrix, each document will have an associated
vector. The vector state of the document is the sum of all the words’ vectors the document
contains. Each word vector state is extracted from the lines of the symmetric HAL matrix. The
document vector state is defined as in equitation 1:
𝑁
∑︁
|Ψ> = |𝑊𝑖 > (1)
𝑖
where |Ψ > represents the vector of the whole document, and |𝑊𝑖 > the vector of the word i.
We are now interested in analyzing how two words are connected within a document, namely,
word A and word B. By concatenating between the corresponding row and column vectors from
the HAL matrix related to the word, the two words can be represented as |𝑊𝐴 >, |𝑊{︀𝐵 > .
{︀ }︀
By applying the
{︀ Gram-Schmidt}︀orthogonalization process to the non-orthogonal basis |𝑊𝐴 >
, |𝑊𝐵 > and |𝑊𝐵 >, |𝑊𝐴 > getting two orthogonal coordinates: first orthogonal basis
}︀
|𝑢𝐴 >, |𝑢𝐴⊥ > for the first word and |𝑢𝐵 >, |𝑢𝐵⊥ > for the second one. Now we can
{︀ }︀ {︀ }︀
project the document vector on these orthogonal bases, and the vector of the whole document
can be represented as the following equitation:
|Ψ> = 𝑎|𝑢𝐴 > +𝑏|𝑢𝐴⊥ >
(2)
|Ψ> = 𝑐|𝑢𝐵 > +𝑑|𝑢𝐵⊥ >
where the coefficients a, b, c and d of basis vectors can be calculated by projecting the vector of
the document onto the bases vectors, for example, the coefficient (a) of vector |𝑢𝐴 > can be
calculated as in the following equitation:
<𝑢𝐴 |Ψ >
𝑎 = √︀ (3)
<𝑢𝐴 |Ψ >2 + < 𝑢𝐴⊥ |Ψ >2
2.3. Test Bell inequality (CHSH)
Bell inequality test is used in physics to determine whether there is entanglement between two
particles. In this work, we investigate the ability to study the relation between two words in the
text. This approach was proposed in [1, 9]. In this model, the following form of Bell’s inequality
CHSH is used as presented in the following equitation:
𝑆𝑏𝑒𝑙𝑙 = |𝐸(𝐴, 𝐵) − 𝐸(𝐴, 𝐶)| + |𝐸(𝐵, 𝐷) + 𝐸(𝐶, 𝐷)| (4)
Where A, B, C, and D are tests, and E (X, Y) stands for the expectation
√ value of the outcome
of mutual tests X and Y. The case where Bell’s results in [2,2 √ 2] can be achieved where the
two particles under study are in entanglement.
√ The value 2 2, also known as the Tsirelsons
bound [10, 11]. The zone between 2 2 and 4 is called the "no-signaling" region. The maximum
value is four can be attained with logical probabilistic constructions, often named Popescu and
Rohrlich boxes (PR boxes) [12]. An area where the results are less than two that means there is
no entanglement between the two particles.
2.3.1. The Bell’s Inequality Operators:
The purpose of these operators is to quantify a query within our formalism. The query operators
return +1 if the document meaning corresponds to the meaning we are interested in and −1 in
the orthogonal direction. Operators spin Pauli matrix will be used, which is explicated as in
equitation: (︂ )︂
1 0
ˆ
𝐴= (5)
0 −1
The other operators can be defined using another Pauli matrix operator:
(︂ )︂
0 1
ˆ
𝐴𝑥 = (6)
1 0
This operator switches the vector state components, which can be interpreted as a measure of a
different meaning in the document.
More convenient with calculations{︀to make all operations based on one basis, that is the basis
of the word A shown in equitation.2 |𝑢𝐴 >, |𝑢𝐴⊥ > , for doing that we need to transform the
}︀
operators (𝐵
ˆ , 𝐵ˆ𝑥 ) of basis |𝑢𝐵 >, |𝑢𝐵⊥ > to the basis of the word A |𝑢𝐴 >, |𝑢𝐴⊥ > , to
{︀ }︀ {︀ }︀
do that we need a transformation matrix from |𝑢𝐵 >, |𝑢𝐵⊥ > to |𝑢𝐴 >, |𝑢𝐴⊥ > , which
{︀ }︀ {︀ }︀
is shown in the following equitation:
(︂ )︂ (︃ √︀
2
)︃
< 𝑢𝐵 |𝑢𝐴 > < 𝑢𝐵 |𝑢𝐴⊥ > 𝑝 1 − 𝑝
𝑀= = √︀ (7)
< 𝑢𝐵⊥ |𝑢𝐴 > < 𝑢𝐵⊥ |𝑢𝐴⊥ > − 1 − 𝑝2 𝑝
Now the operators of the basis word B can be transformed into basis associated with the
word A by using the transformation matrix M. For example, in equitation 8, the operator 𝐵
ˆ is
converted to the basis of word A:
(︃ √︀ )︃
2.𝑝 2−1 2.𝑝. 1 − 𝑝 2
−1
ˆ = 𝑀 .𝐴
𝐵 ˆ .𝑀 = √︀ (8)
2. 1 − 𝑝2 1 − 2.𝑝2
2.3.2. Form Bell’s Inequality:
To determine the degree to which the document corresponds to the word A and word B
simultaneously [13], a combination of operators(𝐴
ˆ ,𝐵
ˆ ) with considering of using the Born rule
can be used as shown in equitation (9):
ˆ .𝐵
<𝐴 ˆ >𝜓 =< 𝜓|𝐴
ˆ .𝐵
ˆ |𝜓 > (9)
Concretely, we calculate quantum means defined in equitation. 5, using different query operators
which can be considered as measuring devices, and then determine the Bell query parameter:
ˆ .𝐵
ˆ + >𝜓 + < 𝐴ˆ𝑥 .𝐵
ˆ + >𝜓 ⃒ + ⃒ < 𝐴 ˆ .𝐵
ˆ − >𝜓 − < 𝐴 ˆ 𝑥 .𝐵
ˆ − >𝜓 ⃒ (10)
⃒ ⃒ ⃒ ⃒
𝑆𝑞𝑢𝑒𝑟𝑦 = ⃒ < 𝐴
where the other operators are defined as the following equitation:
ˆ +𝐵 ˆ𝑥 ˆ −𝐵 ˆ𝑥
ˆ + = −𝐵 √
𝐵 ˆ− = 𝐵 √
,𝐵 ˆ 𝑥 = 𝑀 −1 .𝐴
,𝐵 ˆ 𝑥 .𝑀 (11)
2 2
3. Results of Experiment
This section provides the results of this approach. The texts were taken from web sites in the
Arabic language as a result of a Google search using a two-word query. The experiments of
using a quantum-like semantic model for retrieving data in the Arabic language are divided
into three sections.
In the first section, a quantum-like semantic model will be checked to find the entanglement
of two words in the text. Our model’s first step is to prepare the Arabic text for removing
undesirable stop words. The second step is to use a stemmer to get the word’s root because the
same word takes many shapes depending on the grammatical construction. After that, we build
an index of words included in the text to help in the HAL matrix building with different window
Figure 1: The results of Bell’s inequality test on two extracted texts from Google search result.
sizes, in which each row and column corresponds to a unique word in the text, afterward, we
extract the document vector and two vectors representing the query words. Next, a series of
Bell’s test measurements were performed for each window size used to build the HAL matrix.
The result of the performed experiment appears in Figure 1. The three texts were taken from
Google’s result. The blue line represents the result of Bell’s test of the text entitled “domestic
cats 1” in the Arabic language (1 ) related strongly to the search topic "domestic cats" in Arabic
( ). It is noted that from a suitable window size (50 words), the line reaches the beginning of the
entanglement range, and with the increase of the HAL window size, an increase is observed
with the values of the Bell’s test results. This indicates a proportional dependency between the
window size and the Bell’s result. At the same time, a red line represents the result of Bell’s test
of text entitled “domestic cats 2”, which is a little bit relevant to the subject search. We can note
that this line does not reach the entanglement range until a considerable value (more than 150
words of HAL size window).
The green line represents the result of Bell’s test; this text talks about specific news domestic
cats’ in New Zealand. This text is not closely related to the topic search. Therefore, this line
does not reach the entanglement range.
In Figure 2, another example shows a series of Bell tests of three texts; the topic search
was "Euphrates River" in the Arabic language ( ). It is noted that the line of text is entitled
"Euphrates River 1", and the line of text is entitled "Euphrates River 2", these two lines reach the
entanglement range because the two texts are related extensively to the topic search. During the
previous two texts, a lot of information was mentioned about the river (riverbed, the civilizations
based on it, its economic importance).
Another line entitled "Euphrates River 3" does not reach the threshold of entanglement
because this text talks about a crisis that was happening to the river, so the text just mentioned
the river’s name as a location.
Figure 2: The results of Bell’s inequality test on three extracted texts from Google search result.
In the second section, a quantum-like semantic model will be checked whether it can find the
entanglement of two words in a large dataset of Arabic texts. For doing this mission, a dataset
with five-hundred Arabic texts was collected. It contains six columns; each record includes
fields for text, pair of words, and class to which type text belongs.
Figure 3: The precise of Bell test result with using five hundred Arabic texts.
Each text in the documents extracted from web pages is related to a pair of words. As
mentioned above, each text will go through a set of processing stages that aims to delete stop
words and symbols and obtain roots of the text’s words. After that, we build a HAL matrix with
different window sizes, vectorize text by getting three vectors for representing document and
pair of words, then compute a value of Bell’s test for each size of HAL window, to check the
accuracy of each size of them.
Figure 3 shows the quantum semantic model’s precision results in determining the degree of
correlation between the two words of the title and the text.
It is noted that for a small window size of 5 words, the precision is 89.5%, but in the window’s
small size, the number of words studied is small, which means falling in under-fitting. On
other side, a large window size, such as 100 words with precision 88.5% of detection relevance a
text to the title, will lead to many words included in calculation operation, consequently, to
over-fitting.
Under-fitting and over-fitting are considered as challenges facing the model and its ability
to be generalized to new data. For this reason, the medium window size is chosen to avoid
this problem, for example, 80 words, which corresponds to an accuracy of 89% in identifying
whether the text belongs to the title. These results allow to conclude that the quantum-semantic
model can be used to classify a textual dataset into pre-defined classes based on topic mining,
an unsupervised text analytics algorithm used to find the group of texts related to the meaning.
The third section of the experiment is to test the quantum semantic model’s ability to retrieve
text. For this goal, an Arabic text dataset was built contains 100 Arabic texts related to ten
different subjects (Syrian War, Ibn Sina (Avicenna), relativity theory, children’s education,
Pharaonic Civilization, Organic Chemistry, Euphrates river, Russian economy, Astronomy
science, Psychology science). Each record contains five fields (the first one has Arabic text, the
second and third fields contain pair of words related to the text, the fourth one for class, and
the last field for saving source link).
To evaluate the quantum semantic model’s performance, we use precision and recall, which
are commonplace measures in information retrieval [14]. Another criterion for measuring the
quality of an information retrieval system is the F-measure that combines precision and recall.
The F-measure only produces a high result when Precision and Recall are both balanced.
Table 2 shows the values of the three criteria for evaluating the information retrieval system
from executing ten queries.
Table 2
The results of the quantum-semantic model for ten query
Query Precise Recall F-measure
Syrian war 0.43 0.90 0.581955
Son Sina 1.00 1.00 1.00
Relativity theory 0.91 1.00 0.95288
Children’s education 0.625 1.00 0.769231
Pharaonic civilization 0.90 0.91 0.90
Organic chemistry 0.91 1.00 0.95288
Euphrates river 0.91 1.00 0.95288
Russian economy 0.669 1.00 0.80167
Astronomy science 0.455 1.00 0.61591
Psychology science 0.315 1.00 0.47908
The results listed in the Table 2 show the existence of discrepancy. We note that the precision
values of four queries (Ibn Sina, relativity theory, organic chemistry, and the Euphrates River)
were greater than 90 percent. Firstly, because these topics are explicit and the words used in
them are in a “static” linguistic state, changes occur on them so limited, so it is easy to get the
root for those words. For example (Ibn Sina, relativism, chemistry, river, the Euphrates) only
exist in one linguistic case, which means that the two desirable words will be studied without
neglecting them in some places or studying other words.
On the opposite side, we find a query such as “psychology science” that gets less accuracy
because these words (psychology, science) are also used in texts classified as belonging to “Ibn
Sina”, because he was a doctor and had some medical opinions in this field, and they also existed
in the texts classified as belonging to children’s education.
4. Conclusion
The semantic vectors in HAL are representations for measures of context. The HAL method
has already been used for the analogies with quantum theory by Bruza and Woods [15] and by
Wittek and Dar´any [16] for extracting spectral content from the semantic space. HAL shows
high potentiality because it is a simple way to build a semantic space. Bell’s test results in the
first experiment, which appear in Figure 1 and Figure 2 show a strong correlation between Bell’s
test and the window size used in building the HAL array. This correlation can be explained by
the fact that with the increase in the HAL window size, more words will be involved in the
study, and the length of the studied context will be longer. Therefore, we should choose the
appropriate window size value, preferably medium. Fair window size value also helps to avoid
study unnecessary words. The words that are located far from the query word have not got a
relation with query words. Also, a small HAL window size means fewer context words will
be studied, which may lead to ignoring the wanted words. In this experiment, we saw that we
could get better ordering results related to the subject search.
The second experiment, which was conducted on a large number of texts in the Arabic
language, shows the ability of the quantum semantic model to determine whether the studied
text is related to the research topic or not. Furthermore, we can say that the quantum semantic
model can be used to separate text into paragraphs based on specific topics, where the quantum
semantic model determines whether the text or paragraph is relevant to the √ topic or not that
depends on the result of Bell’s test, whether it is located in the range [2, 2 2] or not, and its
ability to classify texts into a pre-defined group.
From the testing of the model shown in this work, we see in the third experiment an attempt
to retrieve texts related to the search’s subject from the database. According to the evaluation
of more than one criterion, the results were acceptable to some extent, such as precision, recall,
and F-measure.
The proposed model is still at the development stage and needs some improvements to include
studying the entanglement between more than one pair of words and the possibility of merging
it with other algorithms to be used in classifying and retrieving texts to give more accurate
results.
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A. Online Resources
Here there are the links to texts used in the first experiment. The link to the dataset contains
five-hundred Arabic texts used in the second experiment and the link to the dataset used in the
third experiment to evaluate the result of queries.
• The source link of text entitled "domestic cats",
• The source link of text entitled "domestic cats 2",
• The source link of text entitled "domestic cats 3",
• The source link of text entitled "information engineering 1",
• The source link of text entitled "information engineering 2",
• The source link of text entitled "information engineering 3",
• The link of dataset used in the second experiment,
• The link of dataset used in the thrid experiment