Gleb Beliakov | Deakin University (original) (raw)

Papers by Gleb Beliakov

2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013

An important task in multiple-criteria decision making is how to learn the weights and parameters... more An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs.

Studies in Fuzziness and Soft Computing

Several local and global properties of (extended) aggregation functions are discussed and their r... more Several local and global properties of (extended) aggregation functions are discussed and their relationships are examined. Some special classes of averaging, conjunctive and disjunctive aggregation functions are reviewed. A special attention is paid to the weighted aggregation functions, including some construction methods.

Recommender Systems Handbook, 2011

Aggregation of preferences, criteria or similarities happens at various stages in recommender sys... more Aggregation of preferences, criteria or similarities happens at various stages in recommender systems. Typically such aggregation is done by using either the arithmetic mean or maximum/minimum functions. Many other aggregation functions which would deliver flexibility and adaptability towards more relevant recommendations are often overlooked. In this chapter we will review the basics of aggregation functions and their properties, and present the most important families, including generalised means, Choquet and Sugeno integrals, ordered weighted averaging, triangular norms and conorms, as well as bipolar aggregation functions. Such functions can model various interactions between the inputs, conjunctive, disjunctive and mixed behavior. Following, we present different methods of construction of aggregation functions, based either on analytical formulas, algorithms, or empirical data. We discuss how parameters of aggregation functions can be fitted to observed data, while preserving these essential properties. By replacing the arithmetic mean with more sophisticated, adaptable functions, by canceling out redundancies in the inputs, one can improve the quality of automatic recommendations, and tailor recommender systems to specific domains.

Studies in Fuzziness and Soft Computing

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011

We investigate the problem of combining or aggregating several color values given in coding schem... more We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimization of penalty functions on discrete product lattices.

2012 IEEE International Conference on Fuzzy Systems, 2012

The explosion of the Web 2.0 platforms, with massive volume of user generated data, has presented... more The explosion of the Web 2.0 platforms, with massive volume of user generated data, has presented many new opportunities as well as challenges for organizations in understanding consumer's behavior to support for business planning process. Feature based sentiment mining has been an emerging area in providing tools for automated opinion discovery and summarization to help business managers with achieving such goals. However, the current feature based sentiment mining systems were only able to provide some forms of sentiments summary with respect to product features, but impossible to provide insight into the decision making process of consumers. In this paper, we will present a relatively new decision support method based on Choquet Integral aggregation function, Shapley value and Interaction Index which is able to address such requirements of business managers. Using a study case of Hotel industry, we will demonstrate how this technique can be applied to effectively model the user's preference of (hotel) features. The presented method has potential to extend the practical capability of sentiment mining area, while, research findings and analysis are useful in helping business managers to define new target customers and to plan more effective marketing strategies.

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004

This paper treats the problem of fitting general aggregation operators with unfixed number of arg... more This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

Information Fusion, 2014

ABSTRACT a b s t r a c t In this paper we introduce an algorithm to aggregate the preference rela... more ABSTRACT a b s t r a c t In this paper we introduce an algorithm to aggregate the preference relations provided by experts in multi-expert decision making problems. Instead of using a single aggregation function for the whole pro-cess, we start from a set of aggregation functions and select, by means of consensus done through penalty functions, the most suitable aggregation function in order to aggregate the individual preferences for each of the elements. An advantage of the method that we propose is that it allows us to recover the clas-sical methods, just by using a single aggregation function. We also present a generalization of the con-cepts of restricted dissimilarity function and distance between sets for the case where we are working with a Cartesian product of lattices and use such concepts to build penalty functions. Finally, we propose an algorithm that allows us to choose the best combination of aggregation functions for a multi-expert decision making problem.

IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2012

Sleep stage identification is the first step in modern sleep disorder diagnostics process. K-comp... more Sleep stage identification is the first step in modern sleep disorder diagnostics process. K-complex is an indicator for the sleep stage 2. However, due to the ambiguity of the translation of the medical standards into a computer-based procedure, reliability of automated K-complex detection from the EEG wave is still far from expectation. More specifically, there are some significant barriers to the research of automatic K-complex detection. First, there is no adequate description of K-complex that makes it difficult to develop automatic detection algorithm. Second, human experts only provided the label for whether a whole EEG segment contains K-complex or not, rather than individual labels for each subsegment. These barriers render most pattern recognition algorithms inapplicable in detecting K-complex. In this paper, we attempt to address these two challenges, by designing a new feature extraction method that can transform visual features of the EEG wave with any length into mathematical representation and proposing a hybrid-synergic machine learning method to build a K-complex classifier. The tenfold cross-validation results indicate that both the accuracy and the precision of this proposed model are at least as good as a human expert in K-complex detection.

IEEE Transactions on Image Processing, 2012

We investigate the problem of averaging values on lattices, and in particular on discrete product... more We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

IEEE Transactions on Fuzzy Systems, 2011

We consider an application of fuzzy measures to the problem of metric learning in semisupervised ... more We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain the analogous conditions for the ordered-weighted-averaging (OWA) operators, which constitute a special case. We then generalize these results for power-based Choquet and OWA operators. We show that this metric-learning problem can be formulated as a linearprogramming problem and specify the required sets of linear constraints. We present the results of numerical experiments on artificial-and real-world datasets, which illustrate the potential, usefulness, and limitations of this construction.

IEEE Transactions on Fuzzy Systems, 2007

Fuzzy Sets and Systems, 2011

We review various representations of the median and related aggregation functions. An advantage o... more We review various representations of the median and related aggregation functions. An advantage of the median is that it discards extreme values of the inputs, and hence exhibits a better central tendency than the arithmetic mean. However, the value of the median depends on only one or two central inputs. Our aim is to design median-like aggregation functions whose value

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction an... more Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and averaging. Recently double aggregation operators have been introduced; they model multistep aggregation process. The choice of aggregation operators depends on the particular problem, and can be done by fitting the operator to empirical data. We examine fitting general aggregation operators by using a new method of monotone Lipschitz smoothing. We study various boundary conditions and constraints which determine specific types of aggregation.

Beliakov, Gleb, Calvo, T., Barriocanal, E. and Sicilia, M. 2004, Choquet integral-based aggregati... more Beliakov, Gleb, Calvo, T., Barriocanal, E. and Sicilia, M. 2004, Choquet integral-based aggregation of interface usability parameters: identification of fuzzy measure, in ICOTA 2004 : Proceedings of the 6th International Conference on Optimization Techniques and Applications, [University of Ballarat], [Ballarat, Vic.]. ... Beliakov, Gleb Calvo, T. Barriocanal, E. Sicilia, M. ... Unless expressly stated otherwise, the copyright for items in Deakin Research Online is owned by the author, with all rights reserved. ... Deakin University acknowledges the traditional land owners of ...

2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013

An important task in multiple-criteria decision making is how to learn the weights and parameters... more An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs.

Studies in Fuzziness and Soft Computing

Several local and global properties of (extended) aggregation functions are discussed and their r... more Several local and global properties of (extended) aggregation functions are discussed and their relationships are examined. Some special classes of averaging, conjunctive and disjunctive aggregation functions are reviewed. A special attention is paid to the weighted aggregation functions, including some construction methods.

Recommender Systems Handbook, 2011

Aggregation of preferences, criteria or similarities happens at various stages in recommender sys... more Aggregation of preferences, criteria or similarities happens at various stages in recommender systems. Typically such aggregation is done by using either the arithmetic mean or maximum/minimum functions. Many other aggregation functions which would deliver flexibility and adaptability towards more relevant recommendations are often overlooked. In this chapter we will review the basics of aggregation functions and their properties, and present the most important families, including generalised means, Choquet and Sugeno integrals, ordered weighted averaging, triangular norms and conorms, as well as bipolar aggregation functions. Such functions can model various interactions between the inputs, conjunctive, disjunctive and mixed behavior. Following, we present different methods of construction of aggregation functions, based either on analytical formulas, algorithms, or empirical data. We discuss how parameters of aggregation functions can be fitted to observed data, while preserving these essential properties. By replacing the arithmetic mean with more sophisticated, adaptable functions, by canceling out redundancies in the inputs, one can improve the quality of automatic recommendations, and tailor recommender systems to specific domains.

Studies in Fuzziness and Soft Computing

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011

We investigate the problem of combining or aggregating several color values given in coding schem... more We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimization of penalty functions on discrete product lattices.

2012 IEEE International Conference on Fuzzy Systems, 2012

The explosion of the Web 2.0 platforms, with massive volume of user generated data, has presented... more The explosion of the Web 2.0 platforms, with massive volume of user generated data, has presented many new opportunities as well as challenges for organizations in understanding consumer's behavior to support for business planning process. Feature based sentiment mining has been an emerging area in providing tools for automated opinion discovery and summarization to help business managers with achieving such goals. However, the current feature based sentiment mining systems were only able to provide some forms of sentiments summary with respect to product features, but impossible to provide insight into the decision making process of consumers. In this paper, we will present a relatively new decision support method based on Choquet Integral aggregation function, Shapley value and Interaction Index which is able to address such requirements of business managers. Using a study case of Hotel industry, we will demonstrate how this technique can be applied to effectively model the user's preference of (hotel) features. The presented method has potential to extend the practical capability of sentiment mining area, while, research findings and analysis are useful in helping business managers to define new target customers and to plan more effective marketing strategies.

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004

This paper treats the problem of fitting general aggregation operators with unfixed number of arg... more This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

Information Fusion, 2014

ABSTRACT a b s t r a c t In this paper we introduce an algorithm to aggregate the preference rela... more ABSTRACT a b s t r a c t In this paper we introduce an algorithm to aggregate the preference relations provided by experts in multi-expert decision making problems. Instead of using a single aggregation function for the whole pro-cess, we start from a set of aggregation functions and select, by means of consensus done through penalty functions, the most suitable aggregation function in order to aggregate the individual preferences for each of the elements. An advantage of the method that we propose is that it allows us to recover the clas-sical methods, just by using a single aggregation function. We also present a generalization of the con-cepts of restricted dissimilarity function and distance between sets for the case where we are working with a Cartesian product of lattices and use such concepts to build penalty functions. Finally, we propose an algorithm that allows us to choose the best combination of aggregation functions for a multi-expert decision making problem.

IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2012

Sleep stage identification is the first step in modern sleep disorder diagnostics process. K-comp... more Sleep stage identification is the first step in modern sleep disorder diagnostics process. K-complex is an indicator for the sleep stage 2. However, due to the ambiguity of the translation of the medical standards into a computer-based procedure, reliability of automated K-complex detection from the EEG wave is still far from expectation. More specifically, there are some significant barriers to the research of automatic K-complex detection. First, there is no adequate description of K-complex that makes it difficult to develop automatic detection algorithm. Second, human experts only provided the label for whether a whole EEG segment contains K-complex or not, rather than individual labels for each subsegment. These barriers render most pattern recognition algorithms inapplicable in detecting K-complex. In this paper, we attempt to address these two challenges, by designing a new feature extraction method that can transform visual features of the EEG wave with any length into mathematical representation and proposing a hybrid-synergic machine learning method to build a K-complex classifier. The tenfold cross-validation results indicate that both the accuracy and the precision of this proposed model are at least as good as a human expert in K-complex detection.

IEEE Transactions on Image Processing, 2012

We investigate the problem of averaging values on lattices, and in particular on discrete product... more We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

IEEE Transactions on Fuzzy Systems, 2011

We consider an application of fuzzy measures to the problem of metric learning in semisupervised ... more We consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering. We investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete Choquet integral suitable for defining a metric. As a byproduct, we can obtain the analogous conditions for the ordered-weighted-averaging (OWA) operators, which constitute a special case. We then generalize these results for power-based Choquet and OWA operators. We show that this metric-learning problem can be formulated as a linearprogramming problem and specify the required sets of linear constraints. We present the results of numerical experiments on artificial-and real-world datasets, which illustrate the potential, usefulness, and limitations of this construction.

IEEE Transactions on Fuzzy Systems, 2007

Fuzzy Sets and Systems, 2011

We review various representations of the median and related aggregation functions. An advantage o... more We review various representations of the median and related aggregation functions. An advantage of the median is that it discards extreme values of the inputs, and hence exhibits a better central tendency than the arithmetic mean. However, the value of the median depends on only one or two central inputs. Our aim is to design median-like aggregation functions whose value

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction an... more Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and averaging. Recently double aggregation operators have been introduced; they model multistep aggregation process. The choice of aggregation operators depends on the particular problem, and can be done by fitting the operator to empirical data. We examine fitting general aggregation operators by using a new method of monotone Lipschitz smoothing. We study various boundary conditions and constraints which determine specific types of aggregation.

Beliakov, Gleb, Calvo, T., Barriocanal, E. and Sicilia, M. 2004, Choquet integral-based aggregati... more Beliakov, Gleb, Calvo, T., Barriocanal, E. and Sicilia, M. 2004, Choquet integral-based aggregation of interface usability parameters: identification of fuzzy measure, in ICOTA 2004 : Proceedings of the 6th International Conference on Optimization Techniques and Applications, [University of Ballarat], [Ballarat, Vic.]. ... Beliakov, Gleb Calvo, T. Barriocanal, E. Sicilia, M. ... Unless expressly stated otherwise, the copyright for items in Deakin Research Online is owned by the author, with all rights reserved. ... Deakin University acknowledges the traditional land owners of ...