One of the main tasks in the integration of information systems is to provide relevant retrieval of information consolidated from heterogeneous sources. In the field of inorganic chemistry and materials science, set-theoretic methods of searching for relevant information are known. They ensure the construction of a sufficiently high-quality response to user requests. However, the problem of quantifying evaluation of information search relevance in this subject area remains open. This paper proposes an approach to quantifying evaluation of the relevance of information retrieval in integrated systems on inorganic substances and materials properties.
The development and use of integrated information systems on substances and materials properties that consolidate information from heterogeneous information sources is worldwide common trend. These systems ensure that specialists are capable to quickly find the required information. When developing such systems, the fundamental thing is data representation method that describes corresponding chemical objects and their properties. Furthermore, chemical objects data representation method, in its turn, determines the class of methods for ensuring the search for relevant information and their functionality. The purpose of this paper is to present a new approach for quantifying evaluation of the relevance of information retrieval for integrated information systems (IS) on inorganic substances and materials properties (ISMP) based on information structures describing the qualitative and/or quantitative substance composition.
The information technologies development and the emergence of powerful hardware
and software tools for storing and processing information stimulated works on
information systems development in the field of inorganic materials science. As a result, a
large number of highly specialized information systems have been developed that are
focused on solving problems with due regard for specificity, conditioned by a specific
subject domain and research areas of a specific organization developing IS. An example
is a number of information systems based on databases developed and maintained by
IMET RAS. The IMET RAS information systems core consists of a number of
databases which store data on a variety of properties of substances:
• «Diagram» – database (DB) on the phase diagrams of semiconductor systems;
• «Crystal» – DB on the properties of acoustooptical, electro-optical and
nonlinearoptical substances;
• «Phases» – DB on the general properties of ternary and quaternary compounds;
• «Bandgap» – DB on the band gap of inorganic substances [
These databases are heterogeneous not only by data structures, but also by software
and hardware tools ensuring their operation [
Obviously, to ensure a high-quality information service for materials scientists,
information systems integration in this subject domain is necessary. In Russia, the first
successful attempts in this direction were undertaken at the beginning of the century at
the IMET RAS for the integration of information systems mostly used by Russian users
[
One of the main difficulties in the heterogeneous information system (IS) integration is the diversity of the chemical objects described in them. So, for example, «Diagram» IS contains information at the level of the chemical system, i.e. a set of chemical elements that form a certain phase diagram of a semiconductor system. Other IS on inorganic substances and materials properties (ISMP) describe the properties at a specific quantitative composition level (with a specific ratio of elements in chemical system), taking into account crystalline modifications of substances, i.e. the quantitative composition of the substance and its crystal lattice are described at this level. Such chemical objects descriptions incompatibility in different IS ISMP dictates the need to use a different description of chemical objects in an integrated IS ISMP, at least it’s required to distinguish between several types of chemical objects: chemical systems, substances and their crystal modifications. 2.2
To describe the basic chemical objects of the considered problem domain the set theory is used, taking into account that each subsequent level in the problem domain hierarchy complements the description of the chemical object. The notation is the following: S is the set of chemical systems; C – set of chemical substances, i.e. chemical compounds, solid solutions, heterogeneous mixtures, etc.; M – set of crystal modifications. Then the chemical system is denoted as s (where s ∈ S), the chemical substance is denoted by c (where c ∈ C), and the crystal modifications is m (where m ∈ M).
Having designated second level objects by the «substance» term, we get three-level
chemical objects hierarchy: chemical system, chemical substance and chemical
modification [
Any chemical system s can be represented as a set of chemical elements ei: s = {e1, e2,…, en}. Any chemical substance c is defined not only by the set of atoms (chemical elements), but also by their quantitative incorporation into the composition of the compound, solution or mixture. Therefore, any substance c can be represented by a tuple (s, f), where s ∈ S, and f is a mapping of the set of atoms (chemical elements) that make up the substance, in the set of R* × R* pairs that define the minimum and maximum incorporation of a given chemical element in a compound, solution or mixture c.
That is, f : ei → (R*min, R*max), where R* = R+ ∪ {x}. R+ – is the set of non-negative real numbers, and R* is the set of R+ extended by the element x. The element x is used to denote an unknown number, since in the notation of mixtures where the incorporation of components may vary, it is customary to use x to denote an unknown, for example, Fe1-xSex. R*min and R*max are, respectively, the minimum and maximum concentration of the chemical element ei in the substance c.
In the case when the concentration of a particular chemical element ei in the substance c is fixed, then R*min = R*max. Chemical modification m can be represented by a tuple (s, f, mod), where s ∈ S, f : ei → (R*min, R*max), and mod is the string notation for the crystal modification of a substance – common for integrated IS ISMP (one of the singony enumeration values: {Triclinic, Monoclinic, Orthorhombic, Tetragonal, Trigonal, Hexagonal, Cubic}). 2.3
Quite reasonably, when designing integrated IS ISMP, it’s required to provide search facilities for relevant information contained in other IS ISMP of distributed system. Therefore, it’s required to develop some active data store that should “know” what information is contained in every integrated IS ISMP. Considering chemical objects hierarchy, some database should exist that describes information contained in integrated resources in terms of chemical systems, substances and crystal modifications. Here we come to the metabase concept – a special database that contains metadata that describe integrated IS ISMP contents in terms of chemical objects hierarchy as well as some additional information on users and their permissions together with information required to integrate distributed IS ISMP (Fig. 2).
The metabase defines integrated IS capabilities. Its structure should be flexible enough to represent metadata on integrated ISs ISMP contents and at the same time the metabase structure should be simple and versatile to describe arbitrary data source on inorganic substances properties without exhaustive additional payload currently offered by numerous materials ontologies. Taking into consideration the fact that chemical objects and their corresponding properties description is given at different detail level in different ISs ISMP, it’s important to develop metabase structure that would be suitable for description of information residing in different ISs ISMP. For example, some integrated DBs contain information on particular crystal modifications properties while others contain properties description at chemical system level. Thus, integrated ISs ISMP deal with different chemical objects situated at different chemical objects hierarchy levels. For simplicity in current paper we consider only a part of metabase structure that is devoted to chemical systems and their properties (Fig. 2). The amount of this metainformation should be enough to perform search for relevant information on systems and corresponding properties.
All tables (Fig. 2) can be logically separated into several groups according to their purpose: • DBInfo – root table, that contains information on integrated database systems; • DBExcludeCompatibility – table that stores exception list of ISs for relevant information search; • UsersInfo, UsersAccess – tables that contain information on integrated system users and their access rights to integrated IS ISMP; • SystemInfo, PropertiesInfo, DBContent – tables that describe contents of integrated
IS ISMP;
• CompatibilityClasses, Compatibility, Systems2ConsiderInCompatibility – tables
that contain information on accessible relevance classes and their contents (currently
3 relevance classes are used [
Taking into account chemical objects hierarchy description, a special method was
developed to search for relevant information in the context of an integrated information
system, based on a set-theoretic approach [
Relevance itself and its notion to information search is a philosophic term, covered in
numerous publications. A comprehensive review of relevance itself is given by Tefko
Saracevic [
Thus, according to accepted notation the search for relevant information on a
particular chemical system s can be reduced to proper definition of an R relation, which is a
subset of the S × S Cartesian product (in other words, R ⸦ S2). Thus, for any pair (s1,
s2) ∈ R, we can state that the s2 system is relevant to the s1 system. For the practical
solution of the problems of searching for relevant information in integrable information
systems, the following rules are often used to construct R [
It should be noted that abovementioned automatic variant of R relation generation is
just one of the simplest and most obvious variants of such rules, and in fact more
complex mechanisms can be used to get R relation. Other alternatives are used to build the
R relation, called relevance classes. For example, browsing information on a particular
property of a compound in one of integrated IS ISMP (in fact, it is information defined
by (d1, s1, p1) triplet), we consider (d2, s2, p2) triplet to be relevant information. (d2, s2,
p2) triplet characterizes information on some other property of a chemical system from
another integrated IS ISMP. This enables us to define relevant information more
precisely, e.g. if we consider the R relations in the form: R ⸦ (d1, s1, p1) × (d2, s2, p2), where
d1, d2 ∈ D, s1, s2 ∈ S, p1, p2 ∈ P. Actually, it’s possible to even define a set of several R
relations (R1, R2, …, Rn) by applying different rules to enable users to perform search
for relevant information based on wide variety of R interpretations. However complex
interpretations of R (R ⸦ (d1, s1, p1) × (d2, s2, p2)) are not being currently used in IMET
RAS, since metabase structure would be more complex to store such relations however
its reasonability is not so clear. In IMET RAS simple relevancy relations of R ⸦ S2 are
used. More rules to form relevance classes are given in [
Improvement of the search relevance can also be achieved by using the ci level, i.e.
taking into account the quantitative composition of a substance, or crystal modifications
of a specific substance mi instead of chemical system designations si in cases when a
user requests relevant information, being at the level of inorganic substances or their
modifications in the system-substance-modification hierarchy concepts [
When searching at the substance level, the quantitative compound composition is taken into account. The pair (aimin, aimax) denotes the quantitative inclusion of chemical element ei ∈ s into the composition, aimin, aimax ∈ R+, aimin ≤ aimax. If aimin = aimax, then the substance has a constant composition by the element ei ∈ s. For each element of the chemical system ei ∈ s, user during the search could specify a pair (rimin, rimax), where rimin, rimax ∈ R+, denoting the allowable interval of the i-th element in the substance (R+ is the set of non-negative real numbers). Then all substances belonging to the same chemical system are considered relevant, if for each pair (rimin, rimax) the following is correct: aimin ∈ [rimin, rimax] or aimax ∈ [rimin, rimax]. In other words, if the logical disjunction [rimin ≤ aimin & aimin ≤ rimax] + [rimin ≤ aimax & aimax ≤ rimax] = true for all ei ∈ s, then the data on the substance are considered relevant.
When searching for relevant information taking into account the crystal modifications of mi, crystal systems are taken into account, since often information on crystal structures is shown in different ways. For example, for lithium niobate (LiNbO3) a hexagonal or trigonal crystallographic system is indicated in different information sources of the IS ISMP, which, in fact, corresponds to the same crystal modification.
However, it should be noted that despite the fact that the described approach, in
general, provides an acceptable level of search relevance for inorganic compounds, it
suffers from the inability to obtain a quantitative assessment of the search relevance and,
as a consequence, the fundamental inability of search results changes by adjusting some
parameters or corresponding metrics. Note that such an adjustment is useful in some
cases, in particular when preparing training data sets for machine learning tasks in
computer-aided construction of inorganic compounds [
To search for relevant information and obtain a quantitative measure of relevance assessment within an integrated information system based on the properties of inorganic substances and materials, we propose to use a graph model based on the weighted graph G = (V, E), built on chemical objects described as part of an integrated information system.
Let’s define a set of vertices V for graph G. In accordance with the accepted threelevel description of chemical objects in an integrated information system, the set of vertices consists of three disjoint subsets V = {S, C, M}, where S is the set of chemical systems si (qualitative compound composition), C is the set of chemical compounds ci ( the quantitative compound composition or the substance formula), M is the set of crystal modifications mi of specific substances.
Define a set of edges E for graph G, as the union of non-intersecting subsets E = Es Ec Em Esc Ecm, where Es – edges that are incidental only to the set of vertices S; Ec – edges that are incidental only to the set of substances C; Em – the edges that are incidental only to modifications set M. The vertices connectivity for the classes of S, C, M is achieved by two sets of edges: Esc edges to connect vertices from S and C sets; and Ecm edges to connect vertices from C and M. Please note, that the edges connecting vertices from S and M sets, are absent.
To define the elements of the E subsets we need to introduce a couple of trivial functions: Fs(c) and Fc(m). The Fs(c) function returns the chemical system for a given compound c, i.e. it allows to get qualitative composition from quantitative composition. The Fc(m) function returns quantitative composition of a particular crystal modification of the substance, i.e. it allows to get quantitative composition from a particular crystal structure of the compound. Then, given that the chemical system is a set of chemical elements s = {e1, e2, ..., en} we get the following set of edges:
Es = {(si, sj)}, where si = {ei1, ei2, ..., ein}, sj = {ej1, ej2, ..., ejm}, | si | = n, | sj | = m, m – n = 1, si ⸦ sj;
Ec = {(ci, cj)}, where Fs(ci) = Fs(cj); Em = {(mi, mj)}, where Fc(mi) = Fc(mj); Esc = {(si, cj)}, where Fs(cj) = si; Ecm = {(ci, mj)}, where Fc(mj) = ci.
When searching for relevant information for a chemical object, it is necessary that a path should exist in graph between the corresponding object and a relevant one, and it is easy to calculate the measure of relevance by adding the weights of the edges on the corresponding path. Thus, we come to the necessity of introducing a real-valued function W defined on the set of graph edges:
W(Es) = 1000;
W(Ec) = W((ci, cj)) = min(∑ =0 10 ∗ | − |) ; where n = | Fs(ci) | = | Fs(cj) | , qik and qjk – quantitative occurrence of k-th element at ci and cj compositions, i.e. Q: ek → R+ (respectively Q(elik) = qik, Q(ejk) = qjk), and the order of elements in substances is selected so to ensure the minimum value of the W(Ec) objective function.
W(Em) = 0.1; W(Esc) = 100; W(Ecm) = 1. (1) (2) (3) (4) (5) (2.1) (2.2) (2.3) (2.4) (2.5)
As an example, we give a fragment of the relevance graph for chemical systems CuIn-S and In-S (Fig. 3). On this example we emphasize its properties and justify the role of edge weights for quantitative assessment of the chemical objects’ relevance. Based on the definition of the set of edges E, it can be seen that the relevance graph is partitioned into subgraphs based on the vertices of a set S (chemical systems). Moreover, there is no path in the graph between substances from different chemical systems, bypassing the vertices of chemical systems. The vertices of the systems themselves are connected by an edge only if the set of elements of one of the systems is an own subset of the other system and their powers (i.e. a number of chemical elements that built up a system) differ by one.
Consider a subgraph constructed on the basis of the In-S chemical system vertex and consisting of substances and their corresponding modifications related to this system. It should be noted that the subgraph composed of vertices of a C set (compounds, i.e. qualitative formula) is complete, as all the vertices (InS, In2S3, In4S5, In6S7) are connected to each other and form a clique. Note, however, that the weights of the ribs connecting the vertex substances are different. Edge weight is a quantity characterizing the degree of closeness of corresponding quantitative compositions: the smaller the difference, the lower the weight («cost») of transition along the edge, and the corresponding substance is considered more relevant than other with greater weight of transition.
Similarly, modifications subgraph constructed on the basis of the vertex designating a particular compound is complete, and the weights of all edges are equal to 0.1. In Fig. 3 such edges are connected to each other, e.g. α-In2S3 and β-In2S3 vertices. Note, that the transition from modification to the corresponding substance has a cost of 1, and the transition from substance to the system – 100, which makes more relevant data on other modifications (including crystal structure) than the transition to the level of substances to choose another qualitative composition. 5
The proposed graph model is an attempt to reflect the similarity degree of various chemical objects even at different representation level (system, compound, modification). In this sense, the path cost is a measure of the difference between the corresponding chemical objects, which are the vertices of the graph. The more similar the objects, the «closer» they are, meaning the path cost in the graph is less. It is worth noting that, in a broad sense, according to the definitions given in the paper, the overall relevance graph is disconnected due to the absence of a path between the vertices of chemical systems, that have no common chemical elements (i.e. s1 ∈ S, s2 ∈ S such that s1 ∩ s2 = ∅). For example, in the current model, there is no connectivity between In-S and Ga-As chemical systems, although In and Ga are similar in many ways, as far as In and Ga are elements from the same subgroup of the periodic system. In this sense, it is advisable to introduce rules for the formation of edges between similar substances and systems (in which an element from the same periodic system subgroup changes), although such an edge should have an appropriate (sufficiently large) weight comparing with analogues with common chemical elements.
As possible ways of further graph model development, one can offer the transformation of edges from the sets Esc and Ecm in pairs of arcs. In this case, the weight of the arc in the direction from the modification to the substance and from the substance to the system should be made much less than the weight of the original edge, and the reverse arc should preserve the original edge weight. This measure will allow to obtain relevant information, described one or two levels above, which is a common way of information search in chemistry. 6
In the paper by means of the graph model, the concept of relevant information search was extended regarding to integrated IS ISMP. The new model allows to obtain quantitative relevance assessment of information retrieval based on the path calculation in a weighted graph, which allows ranking of chemical information found in consolidated data sources. The proposed approach is applicable not only to improve information retrieval for end users – material chemists, but also for application to computer aided design of inorganic compounds at the stage of training samples formation based on the quantitative relevance assessment.
This work was partially supported by the Russian Foundation for Basic Research (project no. 18-07-00080) and the State task № 075-00746-19-00.