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We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the…
Within the framework proposed in this paper, we address the issue of extending the certain networks to a fuzzy certain networks in order to cope with a vagueness and limitations of existing models for decision under imprecise and uncertain…
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…
One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…
Interaction nets are a graphical model of computation, which has been used to define efficient evaluators for functional calculi, and specifically lambda calculi with patterns. However, the flat structure of interaction nets forces pattern…
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
An appropriate visualization of multiobjective non-dominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their…
Bigraphs are a versatile modelling formalism that allows easy expression of placement and connectivity relations in a graphical format. System evolution is user defined as a set of rewrite rules. This paper presents a practical, yet…
Network graphs have become a popular tool to represent complex systems composed of many interacting subunits; especially in neuroscience, network graphs are increasingly used to represent and analyze functional interactions between neural…
Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices. We show that…
Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…
This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
The concepts of calibrating Function Points are discussed, whose aims are to fit specific software application, to reflect software industry trend, and to improve cost estimation. Neuro-Fuzzy is a technique which incorporates the learning…
In dealing with veracity of data analytics, fuzzy methods are more and more relying on probabilistic and statistical techniques to underpin their applicability. Conversely, standard statistical models usually disregard to take into account…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
This study leverages the data representation capability of fuzzy based membership-mappings for practical secure distributed deep learning using fully homomorphic encryption. The impracticality issue of secure machine (deep) learning with…
Over the past 15 years, hundreds of bias mitigation methods have been proposed in the pursuit of fairness in machine learning (ML). However, algorithmic biases are domain-, task-, and model-specific, leading to a `portability trap': bias…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…