Learning Algorithm For Multivariate Data Analysis Research Articles

Explainability analysis: An in-depth comparison between Fuzzy Cognitive Maps and LAMDA

Currently, it has become very relevant that machine learning techniques can provide an explanation of the results they generate, which is even more relevant in certain domains, called critical, such as health and energy, among others. For this reason, several explainability methods have been generated in the literature. Some of them are Local Interpretable Model-Agnostic Explanations (LIME) and Feature Importance, which have been used in a wide range of problems. The objective of this work is to analyze the explainability capacity of the Learning Algorithm for Multivariate Data Analysis (LAMDA) and Fuzzy Cognitive Maps (FCM), which have been used with great interest due to their interpretability, management of uncertainty during the inference process, simplicity in its use, among other things. For the development of this work, data from two critical domains have been considered, health (COVID-19 and Dengue datasets) and energy (energy price dataset), for which prediction/classification models have been developed using LAMDA and FCM techniques. Afterward, two explainability techniques were used to analyze the explainability provided by each method, one based on the LIME method and the other on the feature importance method, the latter adapted to our work by being based on the permutation of values. Finally, the work proposes two new explainability methods, one based on causal inference and the other on the degrees of membership of the variables to the classes. The latter, in particular, allows doing an explainability analysis by class. The new explainability methods reproduce the results of well-known explainability methods in the literature such as LIME and feature importance, with less execution cost, and also, with an explainability analysis by class. This work opens the doors to new work on class explainability. Furthermore, we see that machine learning approaches based on causal or fuzzy relationships are quite self-explanatory, but specific explainability methods such as those we propose in the work allow us to study particular aspects, such as highly important variables, which general explainability methods do not allow us to do, such as LIME and feature importance.

Acoustic animal identification using unsupervised learning

Abstract Passive acoustic monitoring is usually presented as a complementary approach to monitoring wildlife communities and assessing ecosystem conditions. Automatic species detection methods support biodiversity monitoring and analysis by providing information on the presence–absence of species, which allows understanding the ecosystem structure. Therefore, different alternatives have been proposed to identify species. However, the algorithms are parameterized to identify specific species. Analysing multiple species would help to monitor and quantify biodiversity, as it includes the different taxonomic groups present in the soundscape. We present an unsupervised methodology for multi‐species call recognition from ecological soundscapes. The proposal is based on a clustering algorithm, specifically the learning algorithm for multivariate data analysis (LAMDA) 3pi algorithm, which automatically suggests the number of clusters associated with the sonotypes. Emphasis was made on improving the segmentation of the audio to analyse the whole soundscape without parameterizing the algorithm according to each taxonomic group. To estimate the performance of our proposal, we used four datasets from different locations, years and habitats. These datasets contain sounds from the four major taxonomic groups that dominate terrestrial soundscapes (birds, amphibians, mammals and insects) in audible and ultrasonic spectra. The methodology presents performances between 75% and 96% in presence–absence species recognition. Using the clusters proposed by our methodology, the whole soundscape biodiversity was measured and compared with the estimate of four acoustic indices (ACI, NP, SO and BI). Our approach performs biodiversity assessments similar to acoustic indices with the advantage of providing information about acoustic communities without the need for prior knowledge of the species present in the audio recordings.

Hybrid Approaches-Based Sliding-Mode Control for pH Process Control.

This paper presents two hybrid control topologies; the topologies are designed by combining artificial intelligence approaches and sliding-mode control methodology. The first topology mixes the learning algorithm for multivariable data analysis (LAMDA) approach with sliding-mode control. The second offers a Takagi-Sugeno multimodel approach, internal model, and sliding-mode control. The process under study is a nonlinear pH neutralization process with high nonlinearities and time-varying parameters. The pH process is simulated for multiple reference changes, disturbance rejection, and noise in the transmitter. Performance indices are used to compare the proposed approaches quantitatively. The hybrid control topologies enhance the performance and robustness of the pH process under study.

Approaches based on LAMDA control applied to regulate HVAC systems for buildings

The control of HVAC (Heating Ventilation and Air Conditioning) systems is usually complex because its modeling in certain cases is difficult, since these systems have a large number of components. Heat exchangers, chillers, valves, sensors, and actuators, increase the non-linear characteristics of the complete model, so it is necessary to propose new control strategies that can handle the uncertainty generated by all these elements working together. On the other hand, artificial intelligence is a powerful tool that allows improving the performance of control systems with inexact models and uncertainties. This paper presents new control alternatives for HVAC systems based on LAMDA (Learning Algorithm for Multivariable Data Analysis). This algorithm has been used in the field of machine learning, however, we have taken advantage of its learning characteristics to propose different types of intelligent controllers to improve the performance of the overall control system in tasks of regulation and reference change. In order to perform a comparative analysis in the context of HVAC systems, conventional methods such as PID and Fuzzy-PID are compared with LAMDA-PID, LAMDA-Sliding Mode Control based on Z-numbers (ZLSMC), and Adaptive LAMDA. Specifically, two HVAC systems are implemented by simulations to evaluate the proposals: an MIMO (Multiple-input Multiple-output) HVAC system and an HVAC system with dead time, which are used to compare the results qualitatively and quantitatively. The results show that ZLSMC is the most robust controller, which efficiently controls HVAC systems in cases of reference changes and the presence of disturbances.

LAMDA Controller Applied to the Trajectory Tracking of an Aerial Manipulator

In this work, a novel LAMDA (Learning Algorithm for Multivariable Data Analysis) control strategy for trajectory tracking for an aerial manipulator is presented. Four control strategies are developed: Kinematic, Inverse Dynamics, Sliding Mode (SMC), and LAMDA. These are compared with each other in order to verify their performance to fulfill the control objective. Experimental tests were also carried out to validate the developed controllers. In addition, a study of stability has been also performed for all the controllers. The results obtained by the LAMDA controller demonstrated the good performance of the controller in the aerial manipulator robot. To the best of our knowledge, this is the first time a LAMDA controller has been applied to an aerial robotic manipulator.

An intelligent sliding mode controller based on LAMDA for a class of SISO uncertain systems

This paper presents a new intelligent sliding mode controller based on LAMDA (Learning Algorithm for Multivariate Data Analysis), a fuzzy method used for supervised and unsupervised learning applicable to the detection of functional systemic states. LAMDA computes the Global Adequacy Degree (GAD) of an object to a class or functional state to determine its degree of similarity. An inference stage has been added to LAMDA to make it work as a controller, in combination with the basic features of a sliding mode control (SMC) and Lyapunov stability theory. The novelty of this proposal is that we have used the LAMDA algorithm to compute the SMC continuous and discontinuous control actions to obtain a chattering-free controller, which can then be applied to a class of SISO systems with variable dynamics and model uncertainties. Simulations on two nonlinear chemical processes have validated the proposal: 1) control of a continuous stirred tank reactor (CSTR) under bounded disturbances and reference changes, and 2) regulation of a mixing tank with variable parameters (variable dynamics). The experiments are compared with other control techniques, demonstrating that the proposed method can accurately control the tanks, improving the results in performance, robustness, and disturbance rejection.

LAMDA Control Approaches Applied to Trajectory Tracking for Mobile Robots

This paper presents the application of different approaches of intelligent controllers based on LAMDA (Learning Algorithm for Multivariate Data Analysis) to perform the trajectory tracking task of a mobile robot Pioneer 3-DX simulated in the Virtual Robot Experimentation Platform V-REP environment. The paper proposes the design of a cascade control strategy composed of two controllers, the external controller based on a feedback linearization for the robot kinematics and the internal controller applied to the robot dynamics where the LAMDA approaches are applied. In this work, it is considered an uncertain dynamic model. Thus, its identification and control are based on a reduced-order model for designing purposes. Finally, the dynamic controller is designed using different controllers based on LAMDA, such as LAMDA-PID, LAMDA-Sliding Mode Control, and Adaptive LAMDA. To perform a comparative analysis between them that includes a conventional PID, SMC, and Fuzzy-PID, different trajectories are examined to evaluate the methods. The obtained results are compared qualitatively and quantitatively to determine which proposal performs the most accurate control and presents the best results in terms of performance.

A Fuzzy Sliding-Mode Control Based on Z-Numbers and LAMDA

Z-Numbers is a recent concept related to fuzzy logic where the restriction and reliability criteria are characterized as fuzzy sets. Due to the potential of Z-numbers, this paper presents the development of a fuzzy controller that combines the fundamentals of LAMDA (Learning Algorithm for Multivariate Data Analysis) with the concepts of the Total Utility of Z-numbers, to establish an inference method to improve the performance in a control system. The controller uses criteria from the sliding mode control (SMC) and the Lyapunov concepts to guarantee robustness and stability respectively. The LAMDA method is applied to compute a chattering-free control action which is applied to systems with model uncertainties and variable dynamics. The fuzzy controller has been tested by simulation in two different tasks: 1) Control of a process that consists of a mixing tank with variable dynamics, and 2) Trajectory tracking of a mobile robot. The proposed approach provides suitable results at runtime and outperforms the results of the other tested controllers in terms of performance, minimizing the deviation between the current system output and the reference. Finally, a complexity analysis is presented to evaluate the feasibility in the implementation of the proposal. The obtained results prove the suitability of using a LAMDA Z-number-based controller in the tested systems.

Modeling and control of nonlinear systems using an Adaptive LAMDA approach

This paper presents a soft computing technique for modeling and control of nonlinear systems using the online learning criteria. In order to obtain an accurate modeling, and therefore a controller with good performance, a method based on the fundamentals of the artificial intelligence algorithm, called LAMDA (Learning Algorithm for Multivariate Data Analysis), is proposed, with a modification of its structure and learning method that allows the creation of an adaptive approach. The novelty of this proposal is that for the first time LAMDA is used for fuzzy modeling and control of complex systems, which is a great advantage if the mathematical model is not available, partially known, or variable. The adaptive LAMDA consists of a training stage to establish initial parameters for the controller, and the application stage in which the control strategy is computed and updated using an online learning that evaluates the closed-loop system. We validate the method in several control tasks: (1) Regulation of mixing tank with variable dead-time (slow variable dynamics), (2) Regulation of a Heating, Ventilation and Air-Conditioning (HVAC) system (multivariable slow nonlinear dynamics), and (3) trajectory tracking of a mobile robot (multivariable fast nonlinear dynamics). The results of these experiments are analyzed and compared with other soft computing control techniques, demonstrating that the proposed method is able to perform an accurate control through the proposed learning technique.

LAMDA-HAD, an Extension to the LAMDA Classifier in the Context of Supervised Learning

This paper proposes a new approach to improve the performance of Learning Algorithm for Multivariable Data Analysis (LAMDA). This algorithm can be used for supervised and unsupervised learning, based on the calculation of the Global Adequacy Degree (GAD) of one individual to a class, through the contributions of all its descriptors. LAMDA has the capability of creating new classes after the training stage. If an individual does not have enough similarity to the preexisting classes, it is evaluated with respect to a threshold called the Non-Informative Class (NIC), this being the novelty of the algorithm. However, LAMDA has problems making good classifications, either because the NIC is constant for all classes, or because the GAD calculation is unreliable. In this work, its efficiency is improved by two strategies, the first one, by the calculation of adaptable NICs for each class, which prevents that correctly classified individuals create new classes; and the second one, by computing the Higher Adequacy Degree (HAD), which grants more robustness to the algorithm. LAMDA-HAD is validated by applying it in different benchmarks and comparing it with LAMDA and other classifiers, through a statistical analysis to determinate the cases in which our algorithm presents a better performance.

Advanced Fuzzy-Logic-Based Context-Driven Control for HVAC Management Systems in Buildings

Control in HVAC (heating, ventilation and air-conditioning) systems of buildings is not trivial, and its design is considered challenging due to the complexity in the analysis of the dynamics of its nonlinear characteristics for the identification of its mathematical model. HVAC systems are complex since they consist of several elements, such as heat pumps, chillers, valves, heating/cooling coils, boilers, air-handling units, fans, liquid/air distribution systems, and thermal storage systems. This article proposes the application of LAMDA (learning algorithm for multivariable data analysis) for advanced control in HVAC systems for buildings. LAMDA addresses the control problem using a fuzzy classification approach without requiring a mathematical model of the plant/system. The method determines the degree of adequacy of a system for every class and subsequently determines its similarity degree, and it is used to identify the functional state or class of the system. Then, based on a novel inference method that has been added to LAMDA, a control action is computed that brings the system to a zero-error state. The LAMDA controller performance is analyzed via evaluation on a regulation problem of an HVAC system of a building, and it is compared with other similar approaches. According to the results, our method performs impressively in these systems, thereby leading to a trustable model for the implementation of improved building management systems. The LAMDA control performs very well for disturbances by proposing control actions that are not abrupt, and it outperforms the compared approaches.

On LAMDA clustering method based on typicality degree and intuitionistic fuzzy sets

The learning algorithm for multivariable data analysis (LAMDA) is a learning method to group or classify quantitative and qualitative historical data. LAMDA can be applied for self-learning and directed learning. Considering self-learning, LAMDA groups historical data through the global membership degrees of a sample with respect to a class, considering the contribution of all features for each sample. Such contribution is called marginal adequacy degree (MAD). To mix all MADs, several aggregation functions such as linear and geometrical connectives are used. The aggregation function calculates the global adequacy degree (GAD) of a sample with respect to a class. This procedure avoids assigning the class number as initial parameter due to that LAMDA applies an automatic threshold called non-informative class (NIC) which finds the best assignment of a portion of data to one class. One improvement for the LAMDA algorithm is the use of a full reinforcement operator called Yager–Rybalov Triple Pi, which can reduce the number of classes. However, this kind of solution ignores the degree to which one sample belongs to one class relative to all samples. Another limitation is that the classes reduction is not controlled by a parameter or an algorithm, which removes some classes required by a human expert. Such removed classes can be useful for the human expert in the data analysis of complex processes or for intelligent systems when the searching of additional information is required in decision-making. In this paper, the typicality degree and the intuitionistic fuzzy sets (IFSs) are used to propose one improvement of the LAMDA method in order to develop a strategy that avoids the loss of significant classes. This paper shows two functions: global typicality degree (GTD) and intuitionistic global adequacy degree (IGAD). By integrating both functions, a new function called typicality and intuitionistic global adequacy degree (TIGAD) is proposed. The proposal is applied in three study cases. The results show an improvement of clustering which were validated by the human expert and the information of data. Furthermore, the impact of the research is focused on data analysis, where the expert should make the best decision.

Fault Location in Power Distribution Systems Using a Learning Algorithm for Multivariable Data Analysis

This paper proposes alternatives to improve the electric power service continuity using the learning algorithm for multivariable data analysis (LAMDA) classification technique to locate faults in power distribution systems. In this paper, the current and voltage waveforms measured during fault events are characterized to obtain a set of descriptors. These sets are analyzed by using the projection pursuit exploratory data analysis to obtain the best projection in the alpha* and beta* axes. Next, these projections are used as input data of five LAMDA nets which locate the fault in a power distribution system. The proposed methodology demands a minimum of investment from utilities since it only requires measurements at the distribution substation. The information used to estimate the fault location is the system configuration, line parameters, and data from recorders installed at the distribution substation.

A new support methodology for the placement of sensors used for fault detection and diagnosis

The principal objective of this work is the identification and the location of sensors on a complex chemical plant needed for online process situation monitoring, fault detection and diagnosis of malfunctions. This identification is based on the use of a classification technique and a measure of the quantity of information provided by the process variables, the entropy. Any classification method providing an interpretable description of the classes describing the process situations can be applied. In this work, the LAMDA (Learning Algorithm for Multivariate Data Analysis) classification method was employed for the design of the support tool. LAMDA combines Fuzzy Logic concepts, such as the adequacy of an element to a class, and the neural model representation. It allows, without changing of algorithm, to carry out classifications using a supervised (directed) or unsupervised (automatic) learning stage. The illustration of such a methodology is shown on a classical chemical plant: the propylene glycol production plant. This chemical process is composed of a mixer, a chemical reactor (CSTR) and a rectification column. This plant has been designed and simulated (dynamic simulation) using the well-known HYSYS simulation package. This simulation model has been used to generate scenarios of the various faults and malfunctions generally encountered in this type of plant. In particular, faults affecting the production quality have been simulated. After a short presentation of the most popular classification methods and the Entropy concept, the steps for the development of the proposed support tool are explained. This methodology is then applied to the example of the propylene glycol production plant. The present results highlight the contribution of both the methodology to select the “right” sensors and the classification technique to the design of a behavioral model used for monitoring and fault detection.

06/00789 Sensor-fault detection, diagnosis and estimation for centrifugal chiller systems using principal-component analysis method: Wang, S. and Cui, J. Applied Energy, 2005, 82, (3), 197–213.

The principal objective of this work is the identification and the location of sensors on a complex chemical plant needed for online process situation monitoring, fault detection and diagnosis of malfunctions. This identification is based on the use of a classification technique and a measure of the quantity of information provided by the process variables, the entropy. Any classification method providing an interpretable description of the classes describing the process situations can be applied. In this work, the LAMDA (Learning Algorithm for Multivariate Data Analysis) classification method was employed for the design of the support tool. LAMDA combines Fuzzy Logic concepts, such as the adequacy of an element to a class, and the neural model representation. It allows, without changing of algorithm, to carry out classifications using a supervised (directed) or unsupervised (automatic) learning stage.The illustration of such a methodology is shown on a classical chemical plant: the propylene glycol production plant. This chemical process is composed of a mixer, a chemical reactor (CSTR) and a rectification column. This plant has been designed and simulated (dynamic simulation) using the well-known HYSYS simulation package. This simulation model has been used to generate scenarios of the various faults and malfunctions generally encountered in this type of plant. In particular, faults affecting the production quality have been simulated. After a short presentation of the most popular classification methods and the Entropy concept, the steps for the development of the proposed support tool are explained. This methodology is then applied to the example of the propylene glycol production plant. The present results highlight the contribution of both the methodology to select the “right” sensors and the classification technique to the design of a behavioral model used for monitoring and fault detection.

Detection of functional states by the ‘LAMDA’ classification technique: application to a coagulation process in drinking water treatment

The present Note proposes a learning classification methodology to identify functional states on a coagulation process involved in drinking water treatment. In this work, we chose to carry out the supervised control of this process while using the LAMDA (Learning Algorithm for Multivariate Data Analysis) classification technique. The LAMDA classification technique proposes the interactive participation of the expert operator during the learning phase and in the optimisation of the classification. In this work, all information stemming from the environment process as well as expert knowledge has been aggregated and exploited. The application chosen for state identification is the Rocade drinking water treatment plant located at Marrakech, Morocco. To cite this article: B. Lamrini et al., C. R. Physique 6 (2005).