In information systems based on a multidimensional approach, a data model is a multidimensional data cube. If one uses a large set of aspects for the analysis of data domain the data cubes are characterized by substantial sparseness. This makes it dificult to describe the metadata of the information system and complicates the organization of data storage. To describe the structure of a sparse data cube, a cluster method can be used. This method is based on the construction of groups of members which are semantically connected with other groups of members. Connected groups related to diferent dimensions describe the cluster of cells. Classification schemes that correspond to the structural components of the observed phenomenon can be used to describe it's semantics. Every classification scheme is a graph describing the hierarchy of members that are associated with a separate structural component of the observed phenomenon. The coupling between several classification schemes related to diferent structural components helps to describe the metadata of the multidimensional information system. Classification schemes are a source of classification of information objects of a multidimensional cube related to the structural components of the observed phenomenon.
Copyright © 2018 for the individual papers by the papers’ authors. Copying permitted for private and academic purposes. This volume is published and copyrighted by its editors. In: K. E. Samouylov, L. A. Sevastianov, D. S. Kulyabov (eds.): Selected Papers of the 1st Workshop (Summer Session) in the framework of the Conference “Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems”, Tampere, Finland, 20–23 August, 2018, published at http://ceur-ws.org solved: data.
Multidimensional information systems based on the principles of OLAP are used for the operational analysis of large datasets.
Analytical space in a system
of this
type is a multidimensional data cube. The role of the cube dimensionalities is played
by the dimensions corresponding to various aspects of the observed phenomenon for
which description the system is developed. If we use a large amount of semantically
heterogeneous data for the description of the observed phenomenon the multidimensional
cube is characterized by high sparseness and irregular filling [
The cluster method can be used for the efective description of the multidimensional cube structure. This method is based on the semantic analysis of diferent dimensions’ members’ compatibility in possible cube cells. It allows describing the metadata of the information system
as a set of possible member combinations. Possible combinations comply with possible cells of the multidimensional cube.
complies with some fact.
Dificulties in describing the structure of the analytical space may arise in case if, in the process of forming the metadata of the information system, the analysis of the semantic aspects of the observed phenomenon is subject to technological aspects. The observed phenomenon is a set of interrelated processes related to the subject domain. Data describing the observed phenomenon can form one or more multidimensional data cubes. In describing the structure of an analytic space, the following problems must be –
the problem of classification of data describing the observed phenomenon; – the problem of accounting for the semantics of the observed phenomenon in these 2.
( ) = {︀
1, 2, .., }︀ , there is -dimension, and
The structure of multidimensional data model should reflect the aspects of subject domain which are used in the data analysis process.
A full set of dimensions forms a set
= dim( ) – dimensionality
of multidimensional cube [
, there is a number of dimension, – the quantity of members. a combination of members = 1 , 22 , .., ︁) ︁(
1 to an aspect of the observed phenomenon associated with .
Members of are drawn from a set of positions of the basic classifier which corresponds The multidimensional data cube is a structured set of cells. Each cell is defined by . The combination includes one member each other and generates sparseness in the cube. for each of the dimensions. If the analysis of the observed phenomenon is performed using a large set of diverse aspects, not all members combinations define the possible cells of multidimensional cube, i.e. the cells corresponding to a certain fact. This efect occurs due to semantic inconsistencies of some members from diferent dimensions to
The complex structure of the compatibility of members may lead to a situation where a certain dimension becomes semantically uncertain if combined with a set of members from other dimensions. In this situation, while describing the possible cell of multidimensional cube the special value “Not in use” can be used to set the member of semantically unspecified dimension. The structure of the multidimensional data cube in the information system can be described as the set of possible members combinations. Diferent values from the classifiers, which comply with the dimensions, and the special value “Not in use” can be applied in the combinations of this set. To refer to the set of possible members combinations we will use the abbreviation “SPMC”.
The subject domain is characterized by the measure values defined in possible cells of the multidimensional cube.
) = { 1, 2, .., }
, where is -measure, – the quantity of measures in the hypercube. Not all the measures from the ( ) can be defined in the possible cell. This situation can appear in case of semantic inconsistency between the members defining the cell and some measures.
While describing multidimensional data cube structure for every possible sell it is necessary to define its own set ( ) = { 1, , .., } the description of c measures, which are not included in the set ( ). certain measures for this cell, 1 ≤ ≤ . We can use the special value “Not in use” for , which consists of
The description of the SPMC can be obtained with the help of the cluster method
based on the analysis of links between members [
identifying the groups of members. The group = -dimension includes members (1 ≤ ≤ ), where is a group number and contains members, which equally coincide in the SPMC with the members from some groups of members of other dimensions.
It is possible to define connected groups of member in diferent dimensions with the help of the semantic analysis. The cluster of members combinations is the set of member combinations, which can be obtained with the help of Cartesian product where operands are groups of members or special value “Not in use”; one operand stands for every dimension used in the cluster SPMC( members combinations can be used for the description of the SPMC. ) = 1 × 2 × .. × . Clusters of ︁{ 1, 2, .., ︁} of members in
From the position of semantic the description of the observed pattern characteristics
within the multidimensional data model consists of the classification attributes detecting
(dimensions of the multidimensional cube) and establishing the links between them. It
can be rather dificult if there are a great number of dimensions. Classification schemes
(SC) can be used to solve the problem of classification of data describing the observed
phenomenon. For CS it is possible to formulate a number of requirements [
It is necessary to take into account the component structure of the observed pattern while defining CS. If the observed pattern can be semantically divided into separate structural components for which is possible to choose their own sets of aspects for analysis every component should be compared with CS. The procedure of CS formation is based on defining and analysis of the attributes relevant to the chosen aspects of the analysis. The dimensions of the multidimensional cube should be compared with the characteristics.
CS of the attributes for the observed patterns should be formed on the hierarchical principle. Ranking should be established among the attributes related to CS. This ranking allocates the dimensions which to some extent convey the essence of the structural component for the observed pattern.
with
CS. It is necessary to define the major dimension which is more likely to reflect the semantic of the structural component relevant to CS. The hierarchy of attributes should be formed from other dimensions included into CS which are semantically subordinate to the major dimension and express some particular properties of the structural component for the observed pattern.
The following principle should be observed: the members of the major dimension convey the most important attributes of the observed pattern, the members of other dimensions which come hierarchically below the major one convey some subordinate attributes specifying the essence of the major dimension.
While forming the hierarchy of the attributes for the observed pattern in CS it should be possible to describe the members of the major dimension separately or in groups of members as diferent members can be connected with diferent semantic aspects of the structural component for the observed pattern. Diferent hierarchies of attributes should be formed for the members of the major dimension which are semantically diferent.
In the hierarchy of the attributes in CS there must be the information about the set of measures describing the observed pattern in case of choosing some particular members from the hierarchy.
The classification scheme of the attributes for the observed pattern is an object of the multidimensional information system which describes the structural component of the observed pattern and contains the following information: – the set of dimensions included into the classification scheme; – the set of members of these dimensions included into the classification scheme; – the major dimension chosen in the set of dimensions CS; – the set of measures included into the classification scheme; – the tree of member combinations CS which form the hierarchy of the attributes included into CS.
The hierarchy principal of CS forming is realized in the structure of a tree which presents the member combinations in CS. The tree of combinations can be formed as a result of the semantic analysis of the structural component for the observed pattern. The tree can be defined while describing the process of its formation. One should start the formation of the tree from its roots where the groups of members of the major dimension are placed. Then it is necessary to go down passing the hierarchical levels and adding a group of members to each of them. Thus every group reveals the essence of every previous member on the previous level. What is more it is necessary to add the group related to the dimension which is mostly connected with the members of the previous level. As a result diferent sequences of CS measures can appear in tree brunches on the way from the roots to leaves.
Relationships between the members of diferent dimensions can be established
using approaches of non-parametric methods of statistical analysis [
For the tree structure of classification scheme, the following rules must be followed: 1. The root of the tree is the unit “Major dimension”. 2. The tree itself is a hierarchical structure where the levels are set through alternating such units as “Group of members” and units “Dimension”. At the same time groups of members should be formed in the dimensions relevant to the units hierarchically placed one level higher. 3. Leaves of the tree are units “Group of members”. 4. The unit “Group of members” (except the unit which is a tree leaf) should be relevant to the unit “Dimension” hierarchically placed on a lower level. Only one unit or several units “Group of members” placed on a lower level can be relevant to the unit “Dimension”. 5. Moving from the root to a leaf you can see every dimension only once.
The analysis of the observed phenomenon reveals the qualification characteristics that are included in the metadata of the information system. In the structure of a multidimensional data cube, these characteristics are divided into subject of analysis (measures) and aspect of analysis (dimensions). Semantic analysis allows to establish connections between these characteristics. As a result, the structure of a multidimensional cube can be revealed, that is, significant cells of a multidimensional cube corresponding to the facts are described.
Dificulties in the application of the described technique are due to the fact that the complex observed phenomenon is characterized by a large number of aspects. A complete set of these aspects allows us to construct many multidimensional data cubes corresponding to diferent structural components of the observed phenomenon. The pairwise analysis of the characteristics does not make it possible to separate them in accordance with the structural components, since they are mixed in the observed phenomenon and there are no hierarchical relationships between them.
Construction of classification schemes related to the observed phenomenon as a result of semantic analysis allows to achieve the following result: – semantic separation of the characteristics of the observed phenomenon, their binding to the structural components of the observed phenomenon; – ranking of characteristics, building a hierarchy of characteristics in accordance with their significance in the description of the properties of the structural component of the observed phenomenon.
The described properties of classification schemes allow us to consider them as the main objects that describe and systematize information about the structural components of the observed phenomena. The interaction of information objects included in the multidimensional data cube and the classification scheme can be represented by a diagram (see figure 1). The links in the diagram represent semantic and technological dependencies. The use of classification schemes alters the relationship between the observed phenomenon and the multidimensional data cube. Classification schemes are a source of classification of information objects of a multidimensional cube related to the structural components of the observed phenomenon.
Members belonging to diferent dimensions and measures form a classification scheme. The process of such formation is influenced by the semantic relationship between the observed phenomenon on the one hand and the dimensions and measures on the other hand. Due to the fact that the classification scheme expresses the properties of the structural component of the observed phenomenon, there is an implicit semantic relationship between the classification scheme and the observed phenomenon, which forms the composition of dimensions, members and measures of the classification scheme. The same relationship allows us to determine which classification schemes can underlie multidimensional data cubes related to the observed phenomenon. The insertion of classification schemes changes the nature of the relationship between the observed phenomenon and the multidimensional data cube. The observed phenomenon loses its role as a source of classification, while the multidimensional cube plays the role of a technological component. 5.
The paper considers the method of designing information systems using a multidimensional approach. This approach allows us to develop a system based on a metamodel, which is semantically related to the subject domain of the system. The method is based on the construction of groups of members which are semantically connected with other groups of members. Connected groups related to diferent dimensions describe the cluster of cells.
Classification schemes that correspond to the structural components of the observed phenomenon can be used to describe it’s semantics. Every classification scheme is a graph describing the hierarchy of members that are associated with a separate structural component of the observed phenomenon. Classification schemes can be used to solve the problem of classification of data describing the observed phenomenon. The coupling between several classification schemes related to diferent structural components helps to describe the metadata of the multidimensional information system. It is formed on the hierarchical principle and establishes a ranking between the characteristics of structural component of observed phenomenon. The classification scheme is a technological component in relation to multidimensional data cube, while the multidimensional cube plays the technological role in relation to the observed phenomenon.
The publication has been prepared with the support of the “RUDN University Program 5–100”.