The plethora of ways of data representation and their applications to system modeling is inherently associated with dimensionality reduction. In a nutshell, the result of dimensionality reduction should support efficient ways of constructing ensuing models (classifiers and predictors) as well as an interpretation of the data themselves. Furthermore, there should be a suitable measure quantifying the quality of data positioned in the reduced space. We advocate that what makes the reduced data interpretable goes hand in hand with revealing a logic fabric of the data, suppressing redundancy, and finally arriving at a logic description of data. The anticipation is that the reduced data can be described in the form of logic expressions formed over the original highly dimensional data. Evidently, having these above-stated points in mind, the aim of this article is twofold: 1) to develop a logic-oriented data representation with the aid of autoencoders; and 2) to quantify the quality of results of this dimensionality reduction by incorporating a facet of information granularity. In other words, we argue that the result of dimensionality reduction gives rise to information granules whose level of granularity associates with the quality of processing completed by the autoencoder. In light of the recent surge of architectures of deep learning, the study is focused on the construction and analysis of logic-oriented autoencoders. We propose a two-level architecture composed of the logic-oriented processing units organized in two layers of logic processing units. As data representation provided by the autoencoder is not ideal, we augment the original architecture by granular parameters, which give rise to granular logic-oriented autoencoders. A suite of experiments is also reported.
Evolutionary optimizers (EOs) have assumed a visible position as important problem solvers because of their flexibility, versatility, and ability to optimize in complex multimodal search spaces. This paper discusses a problem of sparse optimization with a special emphasis placed on mixed genetic algorithm-particle swarm optimization (GA-PSO) techniques.
In this article, we are concerned with a problem of aggregation of order-2 information granules, and fuzzy sets, in particular. When processing order-1 fuzzy sets, the structural information about the space over which fuzzy sets are defined is not taken into account at all. In contrast, the aggregation of order-2 fuzzy sets requires a careful attention that needs to be paid both to the closeness determined in the space of membership degrees and the collection of information granules over which such fuzzy sets are defined. We formulate an original optimization problem that simultaneously involves considerations of distances in the membership space (space of membership grades) and some measure of resemblance formed in the space of relationships of reference information granules. The gradient-based learning scheme is constructed. Some illustrative examples are included.
The study is focused on a problem of accumulating information with finite automata. Potentially infinite input data with a given structure and exhibiting possible irregularities and abnormalities are considered. Irregularities are acceptable exceptions of the given structure while abnormalities are unacceptable exceptions of this structure. In the paper, analysis of irregularities and abnormalities with usage of different types of finite automata are illustrated. We start with classical deterministic and nondeterministic finite automata. Then, a description of classical finite automata are generalized in terms of imperfectness of transition function and input data. The aim of this "work in progress" paper is just examples based illustration of different types of finite automata applied to potentially infinite time series like input data. Presented examples offer some illustrative proposals of farther research.
In this paper, we propose a new design methodology that supports the development of hybrid incremental models. These models result through an iterative process in which a parametric model and a nonparametric model are combined so that their underlying and complementary functionalities become fully exploited. The parametric component of the hybrid model captures some global relationships between the input variables and the output variable. The nonparametric model focuses on capturing local input-output relationships and thus augments the behavior of the model being formed at the global level. In the underlying design, we consider linear and quadratic regression to be a parametric model, whereas a fuzzy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbors model serves as the nonparametric counterpart of the overall model. Numeric results come from experiments that were carried out on some low-dimensional synthetic data sets and several machine learning data sets from the University of California-Irvine Machine Learning Repository.
