=Paper=
{{Paper
|id=Vol-2543/rpaper04
|storemode=property
|title=Query Expansion Method Application for Searching in Mathematical Subject Domains
|pdfUrl=https://ceur-ws.org/Vol-2543/rpaper04.pdf
|volume=Vol-2543
|authors=Olga Ataeva,Vladimir Serebryakov,Natalia Tuchkova
|dblpUrl=https://dblp.org/rec/conf/ssi/AtaevaST19
}}
==Query Expansion Method Application for Searching in Mathematical Subject Domains==
https://ceur-ws.org/Vol-2543/rpaper04.pdf
Query Expansion Method Application for Searching
in Mathematical Subject Domains
Olga Ataeva[0000-0003-0367-5575], Vladimir Serebryakov[0000-0003-1423-621X]
and Natalia Tuchkova[0000-0001-6518-5817]
Dorodnicyn Computing Center FRC CSC of RAS, Vavilov str., 40, 11933, Moscow, Russia
oli@ultimeta.ru, serebr@ultimeta.ru, natalia_tuchkova@mail.ru
Abstract. The article focuses on the problem of information retrieval in the mathemati-
cal scientific articles. Issues related to scientific publication “in the scientific infor-
mation environment” are considered. The possibilities of expanding the search query in
the presence of a subject domain thesaurus are discussed. The formulation of an infor-
mation request in specific subject domains is not always possible for an insufficiently
competent user. The query expansion process is of particular importance for subject
domains, where the search is based on special terminology. Automatic query expansion
can serve as a necessary tool with which the user can get a pertinent search result.
Mathematical texts are differed by the presence of a specific structure and the use of
formulas. Formulas can often reflect the main results of research and therefore it is
important to be able to use them in an advanced query. Modern programming tools
allow you to search by formulas and use them for indexing. It is proposed to include
formulas in mathematical thesauruses and in this way to create a context of formulas for
their effective inclusion in search queries. The role of the context defined by the rela-
tions of thesaurus concepts is both to refine the query and to increase the scale of the
sample on request. Examples are implemented for subject areas of ordinary differential
equations, equations of mixed type, special functions of mathematical physics, etc.
Keywords: Comparison of Scientific Texts, Semantic Search, Thesaurus for the
Ontology of Knowledge, Information Query using the Thesaurus, LibMeta
1 Introduction
Many scientific publications are devoted to the problem of expanding queries. It is
known that the unreasonable addition of text in a query leads to additional infor-
mation noise, and only the use of logically related terms can lead to a refinement of
the query and an improvement in the search result. The query expansion tools allow
you to refine the query using hints to the user, narrowing the search field using the-
saurus descriptors, and use the existing relationships of terms (synonyms, abbrevia-
tions, etc.), increasing the search field and thereby receiving additional information
noise. These two processes are in contradiction, but in the end lead to a pertinent re-
sult, that is, satisfying the informational interest of the user. Developments in this
direction have been underway for a long time, and many information systems allow
the expansion of the request. In [1], results are given that indicate that using syno-
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
39
nyms from the WordNet database that are not related to context does not improve the
quality of the information request. And only using the technology of prescribing man-
ual "semantic" links allows you to expand the query to a useful information field, but,
of course, that way it will not be possible to cover any significant number of links. As
a result, there is a need to formulate the problem of automatic accounting for semantic
relations, which is possible in the presence of a thesaurus corresponding to the subject
domain. The particular difficulty of the process of searching for scientific information
is clarifying and expanding the information request. The basis for such search is the
use of special terminology and the connections defined by the domain logic. The hier-
archical presentation of scientific data is also difficult when the problem of establish-
ing associative relationships between concepts appears [2]. Using the example of
problems of mathematical physics and related fields, it is proposed to show how ex-
panding a query by adding mathematical symbols and formulas from the thesaurus
can improve search results.
2 About the Query Expansion Methods
The extension of the information query involves reformulating the original query in
order to improve the search result. This process is directly related to the understand-
ing of the subject of search both from the side of the user (level of competence in a
certain subject area), and from the side of the information retrieval system (it means
availability of information and functional tools of expanding and refining the query).
It was noted in [4] that the history of studies of the expansion of an information
query can be traced from 1965, when a formalized description of the relevance of
search query results based on a vector feedback model (known as Rocchio algo-
rithm). Earlier research into the "weight estimates" of related and non-related terms
when expanding the query belongs to Spark Jones [6] and van Rijsbergen [7]. The
idea of Relevance Feedback (RF) is to engage the user in the search process in order
to improve the final list of results. In particular, the user informs the system of the
relevance of the documents in the initial list of search results. The Rocchio algorithm
is a classic algorithm for implementing the RF method. It adds a relevance feedback
model to the vector space model [8]. The automatic generation of thesauruses was
discussed by Qui and Frei [9] and Schütze [10]. The use of local and global methods
for expanding queries has been investigated by Croft et al. [11].
These works became the foundation for further research in the field of expanding
the information request for text documents, there were not enough tools for pro-
cessing symbolic information. Currently, software has been developed that allows the
use of formulas and symbolic expressions in databases, which opens up the possibility
of using formula entries to expand a search query. The most famous example of such
an information resource is Zentralblatt MATH [12].
This study proposes an approach based on taking into account relations from relat-
ed domains, based on associative relations of terms and thesaurus formulas. Earlier, a
technology was proposed for filling the addressee thesaurus and thesaurus of ordinary
40
differential equations and mixed type equations [13, 14]. This technology is for the
informed (competent) users.
If the user is not sufficiently familiar with the subject area, then any information
can be a replenishment of the addressee (recipient's) thesaurus. A search query exten-
sion for a such user can be a useful hint in the search process.
It is known that the same mathematical expressions are found in the description of
various phenomena. This fact is important to use a pair: “formula + term” to search in
a specific subject area. Moreover, the formula, of course, can be associated with vari-
ous terms that make up the semantic context of various subject domains. This allows
us to consider options for expanding the information request for the ontology of one
subject domain and ontologies of various subject domains.
2.1 Query Expansion "within the subject domain"
The option of expanding the information request is being considered, as a result of
which it is expected to achieve greater coverage of related data in a certain subject
domain. Such a situation arises if it is necessary immediately as a result of one request
to obtain a variety of information on a specific topic. The recipient may be satisfied
with the search result or at the next stage of the search try to refine the request.
A simple example is a search in scientific texts by the name of the author, and then
a selection by keyword or other known data. In particular, mathematicians are often
more comfortable communicating in the language of formulas. To search for a math-
ematical result, a specialist must be given the opportunity to expand the query with
formulas. It is proposed to use specialized LibMeta thesaurus [3], where along with
definitions in the natural language there are symbolic expressions, formulas. This
approach allows you to refine the query within the subject domain, using a mathemat-
ical entry in TeX notation, regardless of the language of the source. For example, the
well-known equation for the Gellerstedt problem is logically connected with a number
of items, Fig. 1.
Fig. 1. Scheme for using a symbolic expression in a search fields.
41
On a request for an author: “Moiseev E.I.” (Моисеев Е.И., in Russian) and a refine-
ment of the “Gellerstedt problem” (задача Геллерстедта, in Russian), a whole list of
related terms can be obtained. Among other things, there is a term with a formula
expression, since it is stored in the corresponding thesaurus article relating to equa-
tions of a mixed type. It is this hint in the form of a formula that will allow you to
make a choice when searching inside the subject area for “equations of mathematical
physics of a mixed type”. You can then use this expression as an extension of the
search query and obtain other search results related to this equation.
2.2 Query Expansion for “related subject domains”
It is known that the same phenomena encountered in the natural sciences can be mod-
eled in various fields of knowledge, and identical (similar) symbolic expressions can
be used. For example, the “wave equation” is used to model various technical pro-
cesses. The record of the wave equation is almost the same everywhere. The structure
of the formula, i.e. its record, in different cases of use can be the same, only interpre-
tations of the input and output data are different, except for the natural time parameter
or input data.
For example: u tt a u xx , and in TeX notation: $u_{tt}=a^2u_{xx}$ – the equa-
2
tion of free transverse vibrations of a string, although it can also be found in other
applications. On the example of Fig. 2 shows the increase in the search fields for sci-
entific publications due to the terminology of related fields and the reformulation of
the query.
Fig. 2. Query extension scheme for related subject domain, where: Sd is the “subject do-
main”, EqMathPh is the “equations of mathematical physics”.
42
According to the relationships of the thesaurus of equations of mathematical phys-
ics, one can easily proceed to search from articles arrays in one subject domain to
another. In the example in Fig. 2 shows how, from the query on the topic “wave equa-
tion”, the transition to the formulation on the topic “transonic gas dynamics” is car-
ried out, where equations from an adjacent subject domain are considered. Another
example: the “Tricomi equation” from the section “equations of mixed type” also has
numerous applications, from the description of the problems of “magneto hydrody-
namic flows” to the problems of “transonic gas dynamics” from one more general
subject area of “equations of mathematical physics”. An unlimited number of these
examples can be found, since the equations of mathematical physics, as a subject area,
appeared for modeling physical and technical processes, i.e., it has many applications
and related fields. Their informational images in search engines can be covered,
thanks to the capabilities of query expansion.
Fig. 3. Scheme of qualifying queries based on the concepts of the thesaurus and their relation-
ships.
In Fig. 5 schematically shows the ways of forming clarifying queries using the con-
cepts of the thesaurus and its main connections in the LibMeta system. Moreover, any
path from the “Search Query” to the “Information Object” may be sufficient to obtain
the necessary response to the query. Keywords can be used not only in the conven-
tional sense, but, as described above, they can be, for example, formulas.
43
3 Benefits of Data Integration to Expand Query
in Mathematical Subject Domains
At first glance, the advantages are obvious: the greater the scope of the request, the
more information as a result the user of the integrated information system will re-
ceive. However, it is also known that the expansion of the query leads to an increase
in information noise, which in no way can be attributed to the advantages of the
search. The combination of these two features should take on some “optimal” values
so that the search query extension service constitutes a useful property of the infor-
mation system.
The optimal properties of the integrated system, ensuring the effective expansion
of the information request, are realized thanks to the following features:
- special data structure;
- functional properties;
- the possibility of “tuning” to the user’s subject domain.
3.1 Structure of Mathematical Data in LibMeta
Ontology describes the resources of the subject domain and their relationship. For
each subject LibMeta's domains, the set of resources may differ both in format and in
the set of resources themselves.
LibMeta uses the semantic content of a specific domain and concepts common to
any domain to describe the library. A set of concepts is proposed that formulate a
description of the content of the library, universal enough to include a specific subject
domain in the system. This approach allows implementing data integration tools with-
in the library, adaptable to the conditions of any subject domain, taking into account
its specificity. Thanks to this, one of the main problems of integrating data from vari-
ous sources is solved, namely, the reconciliation of heterogeneous digital information.
The concepts of ontology in the LibMeta system can be divided according to the
functional purposes as following:
- the description of the content of the subject domain;
- the formation of a thesaurus of any subject domain;
- the description of thematic collections,
- the description of the task of integrating library content with data from external
sources.
Between groups of concepts defined semantically significant relationships.
To support work with mathematical texts in the system, the concept of Formula
was introduced, which allows you to store the original line of the formula from the
source of origin. The formula string can be in the format Content MathML, Presenta-
tion MathML, LaTeX. If necessary, the number of types of presentation of the formu-
la in various notations can be expanded.
The concept of a Formula is connected with relations with information objects that
make up the content of a semantic library and with the concepts of a thesaurus. Thus,
we can always build a network of relations of the formula with the concepts of the
44
thesaurus and with various information objects of the system. Each formula can be
supplemented with keywords, classifier codes, etc. Keywords can be put down by an
expert of the system or added automatically, coming along with the formula from its
source, as well as supplemented with keywords related objects. In Fig. 4 shows a set
of relationships for a formula extracted from the concept of “Cauchy first-order ODE
problem”, automatically constructed from thesaurus links.
Fig. 4. Formula's semantic relationships.
3.2 Configuring a User Subject Domain in LibMeta
Consider the user’s mathematical subject domain. In the LibMeta structure, these are
lists of publications on a certain topic, secondary documents of publications, and for-
mulas as well.
The adaptation of this data of the subject area is interpreted as the “tuning” of the
sources, in which several main stages (i-iii) can be distinguished.
i. Connecting a data source. Each data source is characterized by a unique URL
and some set of parameters necessary for accessing the data. A preliminary analysis
of the information available from the source is carried out; in particular, the types of
its resources and their properties involved in the integration are determined. The result
of this first step is the determination of that part of the source circuit from which data
will be extracted.
ii. Defining LibMeta library resource types corresponding to source resource types.
For each source resource defined by its schema extracted at this stage, the LibMeta
library resource is mapped. The result of this step is the establishment of a link be-
tween the library resource and the source resource. Relationships are established us-
ing the appropriate operation, which declares that there are resource instances corre-
45
sponding to the same real-world object. Based on certain (identified) relationships, the
next step is the mapping of attributes.
iii. For each LibMeta resource, the mapping of attributes to the corresponding
properties of the data source resource is determined. First of all, a mapping is con-
structed for identifying attributes that are mandatory, then for the rest. For each such
pair, the type of connection and the set of operations are determined.
Thanks to this construction of mappings, we obtain a set of rules by which one can
represent each object found in the source within the framework of the concepts of the
LibMeta library. Next, save the metadata of objects in local storage at the request of
the user, or simply save the connection between the found object in the source and the
object in the library.
3.3 Data Integration of Different Subject Domains
A formal model of the process of integrating data from various subject areas can be
represented as follows.
Based on the basic concepts of LibMeta, the content model of the G library is a
few sets:
- the set of resources R = {rj},
- the set of attributes A = {ai},
- the set of attributes N(r)A,, i.e., rj(a1,.., an), anN(r), defined for each resource.
Each set of attributes includes identifying attributes, I(r)N(r)A, used to uniquely
identify the information objects of this resource.
Formally, the integration subsystem IT is represented by a triple ,
where G is a predefined content model consisting of a set of resources R and their
descriptions in the form of a set of attributes N (r), Si is an i-th source connected to
the system, Mi is the display of the i-th source, 1≤i≤n, where n is the number of data
sources.
Using a data source can occur in two scenarios:
- in the mode of affixing relations with objects available in the library;
- in the attribute search mode by the data source within the specified by the presen-
tation (information image).
At the same time, data on objects from sources can be saved in two ways:
- “linking” – this method is identical to establishing a “see also” connection and
means that at one end there is more complete and extensive information on the re-
source;
- “identification” – this method is identical in meaning to establishing a connection
"the same as" and means that at one end contains exactly the same quality of infor-
mation object, as with the other.
Due to the flexibility of the library content model, a scenario is possible for creat-
ing additional types of resources for plug-in sources, the information from which can
be used as the values of some attributes of the main resources.
The library resource scheme G, both the data source S and the content, can be rep-
resented in the form of a graph (Fig. 5), which includes objects and relationships.
46
Fig. 5. The scheme of the examples of the formation of clarifying queries based on the concepts
of the thesaurus and their relationships.
Integration of data of various origin allows you to implement the pre-property of que-
ry expansion when searching for mathematical texts. For example, if similar formulas
are found in publications, then expanding the query through formulas will help to
increase the search coverage and obtain a more complete amount of relevant infor-
mation.
In Fig. 6, an example of a user request “Riccati equation” is given. This concept is
found both in the thesaurus in the subject field "ordinary differential equations"
(ODE), and in the mathematical encyclopedia. Information from both sources was
presented to the user in an integrated form so that he could select clarifying infor-
mation. As can be seen from the diagram, for accessing Russian-language objects (2)
and (3) as a result, there are several ways for them to relate to the concepts of the
thesaurus. Without taking into account relations with formulas that act as independent
information objects, inclusion of object (1) in the result set is not possible.
Fig. 6. The diagram of the ways of forming clarifying queries based on the concepts of various
thesauruses and their relationships.
47
4 Conclusions and Outlook
The ontological approach to presenting information in a digital environment allows
the use of subject area semantics for search query extensions. New technologies for
data recognition and analysis make it possible to include symbolic information and
formulas in articles of subject thesauri, thereby expanding the possibilities of their use
for indexing and searching publications. This allows a new perspective on the repre-
sentation of mathematical knowledge in digital space. Taking into account the associ-
ative relations of terms and formulas in the thesaurus allows you to search not only in
related fields, but in digital arrays of various fields of knowledge, without increasing
search noise. These conclusions are quite expected, and the problems discussed in the
work are relevant from the point of view of combining ontologies of individual areas
of knowledge without increasing the search time.
In the given examples, the data of mathematical subject areas are used as typical
for query expansion due to formulas in adjacent domains, which, of course, does not
limit the query extension to other subject areas integrated in LibMeta. The LibMeta
project implements links with any sources that meet the requirements of LOD, as well
as content, and testing links with a linguistic database and mathematical encyclopedia.
Research in this direction is the subject of further work.
This work was supported in part by the Russian Foundation for Basic Research,
projects #18-00-00297komfi, #20-07-00324.
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