Classical Averaging Functions

Hsieh

et al. 2021

Preprint

Recently, decoding human electroencephalographic (EEG) data using convolutional neural network (CNN) has driven the state-of-the-art recognition of motor-imagery EEG patterns for brain-computer interfacing (BCI). While a variety of CNN models have been used to classify motor-imagery EEG data, it is unclear if aggregating an ensemble of heterogeneous CNN models could further enhance the classification performance. To integrate the outputs of ensemble classifiers, this work utilizes fuzzy integral with particle swarm optimization (PSO) to estimate optimal confidence levels assigned to classifiers. The proposed framework aggregates CNN classifiers and fuzzy integral with PSO, achieving robust performance in single-trial classification of motor-imagery EEG data across various CNN model training schemes depending on the scenarios of BCI usage. This proof-of-concept study demonstrates the feasibility of applying fuzzy fusion techniques to enhance CNN-based EEG decoding and benefit practical applications of BCI.

Section: Methodsmentioning

confidence: 99%

Fuzzy Integral With Particle Swarm Optimization for CNN-Based Motor-Imagery EEG Classification

Hsieh

et al. 2021

Preprint

“…Aggregation function

(cf. [ 41 ]) is increasing with respect to each variable:

and satisfies the boundary conditions

…”

Section: Interval Modelingmentioning

confidence: 99%

Ensemble Classifier Based on Interval Modeling for Microarray Datasets

Bentkowska,

Gałka,

Mrukowicz

et al. 2024

Entropy

The purpose of the study is to propose a multi-class ensemble classifier using interval modeling dedicated to microarray datasets. An approach of creating the uncertainty intervals for the single prediction values of constituent classifiers and then aggregating the obtained intervals with the use of interval-valued aggregation functions is used. The proposed heterogeneous classification employs Random Forest, Support Vector Machines, and Multilayer Perceptron as component classifiers, utilizing cross-entropy to select the optimal classifier. Moreover, orders for intervals are applied to determine the decision class of an object. The applied interval-valued aggregation functions are tested in terms of optimizing the performance of the considered ensemble classifier. The proposed model’s quality, superior to other well-known and component classifiers, is validated through comparison, demonstrating the efficacy of cross-entropy in ensemble model construction.

“…On the other hand, being a generalization of the power mean function and having connections to other important classes of means, more attention has recently been geared towards the Lehmer mean function and its characterization. For instance, the function's elementary properties like homogeneity, monotonicity and differentiability have been discussed in 1,3 , whereas its more advanced properties like Schur-convexity, Schur harmonic convexity and Schur power convexity have been the focus of more recent studies, e.g., see [8][9][10]23,24 and references therein. Also, the inflection points of the function have been studied in 18 , and the results concerning its possible connections to Gini and Toader means have been provided in [5][6][7]12,22,25 .…”

Section: Openmentioning

confidence: 99%

Theory of Lehmer transform and its applications in identifying the electroencephalographic signature of major depressive disorder

Ataei

Wang

2022

Sci Rep

We propose a novel transformation called Lehmer transform and establish a theoretical framework used to compress and characterize large volumes of highly volatile time series data. The proposed method is a powerful data-driven approach for analyzing extreme events in non-stationary and highly oscillatory stochastic processes like biological signals. The proposed Lehmer transform decomposes the information contained in a function of the data sample into a domain of some statistical moments. The mentioned statistical moments, referred to as suddencies, can be perceived as the moments that generate all possible statistics when used as inputs of the transformation. Besides, the appealing analytical properties of Lehmer transform makes it a natural candidate to take on the role of a statistic-generating function, a notion that we define in this work for the first time. Possible connections of the proposed transformation to the frequency domain will be briefly discussed, while we extensively study various aspects of developing methodologies based on the time-suddency decomposition framework. In particular, we demonstrate several superior features of the Lehmer transform over the traditional time-frequency methods such as Fourier and Wavelet transforms by analyzing the challenging electroencephalogram signals of the patients suffering from the major depressive disorder. It is shown that our proposed transformation can successfully lead to more robust and accurate classifiers developed for discerning patients from healthy controls.