• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
National Research University Higher School of EconomicsStudent ThesesConstruction of Neural Network Frame Based on Formal Concept Lattice

Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Maxim Ushakov
Construction of Neural Network Frame Based on Formal Concept Lattice
Data Science
(Master’s programme)
9
2017
In this paper we consider the problem of constructing a neural network model, in case when we haven’t a priori information about the topology. The selection of optimal network architecture is crucial, as it has high impact on the results of classification. Indeed, if the structure is too small, then we have only few parameters to fit the model, so the resulting accuracy will not be high. On the other hand, with large architecture neural network is more likely to over-fit the training data.

This work attempts to propose an approach based on covering relation on closed subsets in a data set. It is based on the assumption that there is a connection between the complexity of optimal network architecture and the depth of corresponding formal concept lattice. The main advantage of such approach lies in the possibility of eliminating redundant nodes and edges, by choosing only qualitative formal concepts, and thus obtaining straightforward architecture. Another advantage is in the possibility to pre-train the network, using the interpretation of nodes as formal concepts.

There are two main types of architecture models are studied in the research. The first one is based on the ordinary definition of formal concept, and the second one is constructed with use of monotone Galois connections. For every type we have made a comparative empirical analysis of various metrics and algorithms, and as a result we have obtained the optimal structure for further experiments. In addition, the difference between pre-training a neural network and initializing the random weights was studied.

In the final section we have compared the constructed models with other classification methods. In order to make comparison complete, we chose 7 different real datasets with various size, density, and the number of classes. A practical comparison has proven the possibility to use the mentioned models on real datasets, revealed pros and cons of the developed methods.

Student Theses at HSE must be completed in accordance with the University Rules and Regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses