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In real time evaluation systems the decision should be made in time to avoid the serious consequences. In the literature there are several techniques which aim to reduce the computational complexity of these kinds of systems. Among others the Higher Order Singular Value Decomposition (HOSVD) based reduction method is a useful tool for handling this problem. In the case when only non-exact reduction can be performed, the error calculation is also essential, because the reduction degree is based on the calculated error in these systems. In this paper the authors present the HOSVD reduction error calculation in hierarchical fuzzy systems using Mamdani-type inference and define a general formula which includes the propagated error from the previous levels of the hierarchy; in which the error bound, calculated by different ways, can be used and takes into account the case when not all the inputs contain a propagated error but only a few of them. Furthermore a greedy algorithm is presented for reduction optimization.

This paper describes the relation of the higher order singular value decomposition (HOSVD) based canonical form to the Hilbert-Schmidt type integral operators. This connection between the canonical form of f(x) and the integral operators determined by function f(x) is important; on the one hand it gives a new aspect for the consideration of LPV models, and on the other hand it allows for the approximation of eigenfunctions and integral operators based on a numerical reconstruction of the canonical form.

In the paper the authors proposed a HOSVD based approach to enhance the reconstruction of inner structures based on projections from different angles which is strongly related to the well known Radon transform. It is shown that in case of less number of projections the HOSVD based approximation applied in the projection space can significantly enhance the output obtained by the inverse Radon transform.

Complexity reduction techniques should be used in those kinds of complex systems in which the evaluation time has a critical importance. Although the hierarchical clustered structure can reduce the number of the rules in contrast to the single-staged models, a further reduction technique is recommended to use in the subsystems to improve the evaluation time. A possible method among the several available ones is the widely used Higher Order Singular Value Decomposition (HOSVD), which is used to reduce the number of the rules in fuzzy logic-based systems. The authors studied this method and a novel pre-processing procedure was developed. This procedure can be used in HOSVD rule base reduction as an offline process to calculate the new membership function values belongs to crisp inputs. Due to offline processing the operation needs are reduced at all levels and all groups of the hierarchy where the reduction is performed separately. The novel method is based on the equidistant division of the input's domain, where the division is based on the accuracy of the input factor.

The representation of data plays significant role in many applications, as for instance when performing data compression, feature extraction or enhancement, etc. In this paper we briefly mention some well known data representation forms and propose a new domain based on the so called higher order singular value decomposition (HOSVD) and wavelet transformation. It will be shown how the data can be processed by manipulating its components in this domain. Furthermore, the properties of the components as well as the applicability of the proposed approach in the field of image processing and system identification will be shown.

The paper describes an approach for data representation and processing in the so called HOSVD-DCT based domain which combines the higher order singular value decomposition (HOSVD) with the discrete cosine transformation (DCT). The key idea is to express the multivariate function by an orthonormal set of one variable specific functions and perform DCT on those components which are less significant from the application point of view in order to ensure finer grained processing. It is advantageous also in case of system identification, where the behaviour of the system can be approximated by blending locally identified models. In this case the proposed method can efficiently be applied.

Data compression and enhancement represent an important consideration in many application areas. The transmission bandwidth and storage capacity are often crucial factors. The efficiency of the processing of data in numerous cases strongly depends on the form of data representation. In the present paper a method, based on the so called higher order singular value decomposition and tensor-product transformation, is introduced for multidimensional scaling and compression of thermal images sequences. The proposed approach operates with smooth functions forming an orthonormal basis. Because of the smoothness property of these orthonormal components, the method can advantageously be utilized for the efficient compression of thermal image sequences.

The approximation methods of mathematics are widely used in theory and practice for several problems. In the framework of the paper a novel tensor-product based approach for representation of neural networks (NNs) is proposed. The NNs in this case stand for local models based on which a more complex parameter varying model can numerically be reconstructed and reduced using the higher order singular value decomposition (HOSVD). The HOSVD as well as the tensor-product based representation of NNs will be discussed in detail.

The paper discusses formulas and interpretations of the fine structure constant (FSC) and the Number Archetype 137 taking into account of our earlier results and the concept of the “undetached observer” of Pauli. A new “controlling-.observing equation” is proposed for the reinterpretation of FSC and other Number Archetypes on the basis of Hermeneutics found in W. Pauli and C. G. Jung “Correspondence”.

The main aim of this paper is to introduce a method for approximating surfaces given by a set of discrete points with possible additional parameters. The method uses the higher order singular value decomposition based on canonical form of two-variable TP (tensor product) functions. Except of approximation abilities of this principle, the paper focuses on the compression properties of the method, as well. The method is able to achieve high compression rate in the input data by keeping the error at remarkable lower level.