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[Page no. 10] "algorithms for the QoS management in an autonomic IoT platform. Service Oriented Computing and Applications 13, 199–219. Morales, L., Aguilar, J., Garc´es-Jim´enez, A., Gutierrez, De Mesa J., Gomez-Pulido, J., 2020. Advanced fuzzy-logic-based context-driven control for HVAC management systems in buildings. IEEE Access 8, 16111–16126. Mulan. Mulan: A Java Library for Multi-Label Learning. https://mulan.sourceforge.net/ datasets-mlc.html. neuraldesigner Explainable AI Platform. Available from: https://www.neuraldesigner. com/Kaggle. http://kaggle.com. OpenML. A worldwide machine learning lab. https://www.openml.org/. Ouali, Y., Hudelot, C., Tami, M., 2020. An overview of deep semi-supervised learning. arXiv:, 2006, 05278. Paul, J., Jacob, J., Mahmud, M., Vaka, M., Krishnan, S.G., Arifutzzaman, A., Thesiya, D., Xiong, V., Kadirgama, K., Selvaraj, J., 2024. A data mining approach to analyze the role of biomacromolecules-based nanocomposites in sustainable packaging. Int. J. Biol. Macromol. 265, 130850. Quintero, C., Aguilar, J., 2022. LAMDA-HSCC, a semi-supervised learning algorithm based on the multivariate data analysis. Expert System with applications 202. Ray, S., 2019. A quick review of machine learning algorithms. In: 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing, pp. 35–39. Rezgui, A., Ben, N’cir Ch, Essoussi, N., 2014. Overlapping clustering with outliers detection. In: International Conference on Pattern Recognition Applications and Methods, pp. 279–286. Ruiz, F., Isaza, C., Agudelo, A., Agudelo, J., 2017. A new criterion to validate and improve the classification process of LAMDA algorithm applied to diesel engines. Eng. Appl. Artif. Intell. 60, 117–127. Sawant, S., Prabukumar, M., 2021. A review on graph-based semi-supervised learning methods for hyperspectral image classification. The Egyptian Journal of Remote Sensing and Space Science 23 (2), 243–248. Sen, P., Hajra, M., Ghosh, M., 2020. Supervised classification algorithms in machine learning: a survey and review. In: Emerging Technology in Modelling and Graphics. Springer, pp. 99–111. Sinaga, K., Yang, M., 2020. Unsupervised K-means clustering algorithm. IEEE Access 8, 80716–80727. Song, Z., Yang,"

[Page no. 1] "A semi-supervised learning algorithm for multi-label classification and multi-assignment clustering problems based on a Multivariate Data Analysis Carlos Quintero Gull a, Jose Aguilar b,c,d,* a Dpto Cs Aplicadas y Humanísticas, Universidad de Los Andes, M´erida, Venezuela b CEMISID, Facultad de Ingeniería, Universidad de Los Andes, M´erida, Venezuela c GIDITIC, Universidad, EAFIT, Medellín, Colombia d IMDEA Networks Institute, Legan´es, Madrid, Spain A R T I C L E I N F O Keywords: Semi-supervised learning algorithm Multi-label classification Multi-assignment clustering Machine learning A B S T R A C T Classically, in classification and clustering problems, an individual is exclusively assigned to a class (labeled data) or a cluster (unlabeled data). However, the assignment to a single class or cluster may be too strict in several real-world domains. In many cases, an individual may belong to multiple classes or clusters at the same time. On the other hand, we are starting to see machine learning algorithms that solve the problem of multi-label classification and multiple cluster assignment, but there are no algorithms that solve both problems simulta- neously. Classic semi-supervised algorithms can work with labeled and unlabeled data simultaneously, but these types of algorithms assign individuals to a single class or a single cluster. Today, artificial intelligence faces the challenge of developing semi-supervised learning algorithms to work with semi-labeled data that can be assigned to different classes or clusters at the same time. In particular, this paper proposes a semi-supervised learning algorithm to fill this gap, which can solve the problems of multi-label classification and multiple cluster assignment simultaneously, on a semi-labeled dataset. This proposal is based on the LAMDA algorithm (Learning Algorithm for Multivariate Data Analysis), which calculates the degree of membership of a data to a group/class. In this work, a membership threshold is defined, which allows individuals to"

[Page no. 3] "Finally (Hu et al., 2018), present a review of MAC techniques, assuming that a single clustering for a dataset can be too strict and cannot capture the diversity in some applications. In this work, the re- view is categorized into two perspectives, coupled and de-coupled methods. Also, the methods described in this work are compared based on a series of properties specifics like input parameters and the kind of subspaces considered, among other aspects. As can be seen from the reviewed literature, there are no algorithms that simultaneously consider the problem of multi-labels or MAC. 2.3. Semi-supervised learning methods (Ouali et al., 2020) present a review of the different deep semi-supervised approaches. They analyze semi-supervised learning and its applications in image classification to deep neural networks to reduce the amount of labeled data required. In the paper (van Engelen and Hoos, 2020), the authors propose a taxonomy of semi-supervised clas- sification algorithms and describe the fundamentals of the different semi-supervised learning algorithms. On the other hand (Yang et al., 2023), present a taxonomy for deep semi-supervised learning that cat- egorizes existing methods. Then they provide a review of 60 represen- tative methods and present a comparison of these methods in terms of the type of losses, architecture differences, and test performance results (Zhai et al., 2021). define a self-supervised semi-supervised learning framework for image classification. In the previous works, we can see that some are based on deep learning or are for image processing, with a high computational cost. (Huang et al., 2021) define the CAFA framework for the processing of labeled and unlabeled datasets. Particularly, CAFA uses a scoring strategy to determine the relationship between the labeled and unla- beled data to improve the semi-supervised training (Zheng et al., 2022). define SimMatch, a semi-supervised learning framework that simulta- neously"

[Page no. 4] "between EI and GADNICEI : index = max ( HADEIO, GADNICEI ) (11) The output of the LAMDA-HAD algorithm is the class to which the individual is allocated. Table 1 presents the LAMDA-HAD Algorithm. 3.2. LAMDA –RD LAMDA-RD has been defined by (Morales and Aguilar, 2020) to enhance LAMDA in clustering tasks due to LAMDA tends to generate numerous groups. To solve this problem (Morales and Aguilar, 2020), determined a new measure of grouping, and additionally, developed a procedure for automatic group merger. The concepts of LAMDA-RD are defined below. Definition 8. Cauchy Marginal Adequacy Degree (CMAD). It de- fines the Marginal Adequacy Degree based on the Function of Fuzzy Cauchy: CMADk,j ( xj ⃒⃒ρkj ) = 1 1 + dist ( xj, ρkj ) (12) Where: dist ( xj, ρkj ) is the length between the feature j of the data X and the variable j of the centroid of the group kρkj. Definition 9. Robust Marginal Adequacy Degree (RMAD). It re- defines the MAD by multiplying it by a penalty factor Kk,X calculated for each group k: RMADk,j ( xj ⃒⃒ρkj ) = KkX × CMADkj ( xj ⃒⃒ρkj ) (13) Two parameters are required to determine kkX. The first is the mean distance of the individual between the groups, which is: dkX = 1 n ∑ j=n j=1 ⃒⃒xj − ρkj ⃒⃒ (14) The second is the mean distance between neighbor groups (dnb; ∈ [0, 1]), which is a parameter that is defined via calibration. Definition 10. Penalty factor (KkX). It is computed using Equation (15) when the distance dkX is greater than dnb: kkX = dnb dnb + dist(dkX, dnb) (15) According to Eq. (15), the distance dk,X penalizes the unlikeness between the observations and the groups, and is named Robust Distance C.Q. Gull and J."

[Page no. 4] "high values, it is very strict (Morales et al., 2018). T and S are linear inter- polation functions based on MAD. For categorization problems can be used the next operators: Minimum-Maximum, Hammacher or Product-Sum. In the clustering problems can be used the Dombi Generally operator (Morales and Aguilar, 2020). In this work, we use the next Min-Max functions for T and S: T(a, b) = Min(a, b) and S (a,b) = Max(a, b). The maximum value of GAD for all categories/clusters defines the assignment of a data to a group/category. Thus, the index in Equation (5) is the class/cluster where the individual will be allocated. index = max(GAD1X, GADkX, ….., GADmX, GADNICX ) (5) Where: GADNICX is the GAD of the NIC, calculated using a probability of 0.5. Thus, data is allocated to the cluster/category with the maximum value of GAD, including the NIC’s GAD in the calculation. So, in that case, a new cluster/class is generated. In the literature, there are several improvements to LAMDA, both in the case of classification and clus- tering. In classification tasks, some of the approaches are LAMDA-HAD (Highest Adequacy Degree) (Morales et al., 2018, 2019) and LAMDA-FAR (Ruiz et al., 2017). For clustering tasks, some of the im- provements are the LAMDA Triple π operator (Bedoya et al., 2014) LAMDA-RD (Robust Distance) (Morales and Aguilar, 2020), and the LAMDA clustering method founded on intuitionistic fuzzy sets (Botía and Botía, 2018). The LAMDA algorithm has been used in multiple contexts for different tasks (Aguilar-Martín and L´opez De Mantaras, 1982; Bedoya et al., 2014; Kempowsky et al., 2006; Morales et al., 2019; Morales et al., 2020; Ruiz et al., 2017; Aguilar et al., 2019): supervision, diagnosis, control, among others. 3.1. LAMDA –HAD algorithm LAMDA-HAD (Highest Adequacy Degree) has been defined in (Morales et al., 2018,"

Query: Describe LAMDA –RD algorithm
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