Cluster Method of Description of Information System Data Model Based on Multidimensional Approach (часть 3)

We can identify two cases where such approach can be successfully used. The first one takes place when different subdivisions of the dimensions onto the layers occur during the analysis of different semantic components, and the second one – when there is a simple way of building a subset describing the SPMC redundantly, and the efficient way to describe the combinations which are to be excluded from this subset to reduce it to the SPMC. Let’s consider these cases in more detail.

In the first case, the decomposition of the observed phenomenon on l semantic components corresponds to the union of member combinations subsets:
SPMC(H) = Q1 ∪ Q2 ∪.. ∪ Ql.
Set of analytical space dimensions can be divided into layers in different ways due to differences in semantics of the observed phenomenon components:
D(H) = L1i ∪ L2i ∪.. ∪ Qmii,
there i = 1, …, l – number of component, and mi – the quantity of layers in i component. Each subset Qi is formed according to its split of set of the dimensions can into layers.

In the second case, set of possible member combinations is represented as the difference of two subsets:
SPMC(H) = R Q,
there R – set of member combinations, described with an excess (set to reduce), and Q – set of combinations to be excluded. Set to reduce may be formed using the following rules. It should include member combinations obtained by the Cartesian product of all members of all dimensions. It must be supplemented with a set of combinations that contain the special value “Not in use” for some dimensions, for which this value is acceptable. From this set it should be excluded those combinations which can be obtained by replacing the special value “Not in use” by the member. This approach can be used in case the set SPMC(H) has a complex structure and it may be offered a simple algorithm of forming a subset Q.

4 Method of construction of set of possible member combinations

We can propose the algorithm of SPMC description basing on the cluster approach and consisting of the following steps:

1. Allocate the n semantic components (n≥1) within the observed phenomenon and juxtapose these components with the subsets of combinations Qi, i = 1, …, n;
2. Construct a formula for SPMC(H) using Qi and operations of set theory according to the revealed relationships between the components of the observed phenomenon;
3. Form a subset of combinations for each Qi:
   (a) perform the analysis of pairwise relations between the dimensions corresponding to Qi semantics, and form the groups of members expressing these relations;
   (b) allocate the layers of dimensions in a set of dimensions and build the dimensions connectivity diagram for each layer;
   (c) make the subdivision of the groups of members specified in layers according to the relations available from the diagrams of layers connectivity;
   (d) realize the formation of clusters of member combinations and consolidation of these clusters in subsets of combinations for layers;
   (e) execute the formation of a subset of Qi combinations by the Cartesian product of subsets of combinations for the dimensional layers;
4. Calculate the SPMC(H) using the constructed formula.

5 Conclusion

In case of the development of large multiple-aspect multidimensional information system the use of the cluster approach for describing the set of possible member combinations allows to provide the compactness while specifying the metadata and to express the semantics of the analyzed phenomenon observed. The proposed approach is based on the identification of relations between the dimensions which reflect the properties of the observed phenomenon, and on the formation of the groups of members which elements are united by the similar behavior towards these relations.

Acknowledments
The work is partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008).

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