A Survey on Internal Validity Measure for Cluster Validation

Predictive maintenance in Industry 4.0: a survey of planning models and machine learning techniques

Equipment downtime resulting from maintenance in various sectors around the globe has become a major concern. The effectiveness of conventional reactive maintenance methods in addressing interruptions and enhancing operational efficiency has become inadequate. Therefore, acknowledging the constraints associated with reactive maintenance and the growing need for proactive approaches to proactively detect possible breakdowns is necessary. The need for optimisation of asset management and reduction of costly downtime emerges from the demand for industries. The work highlights the use of Internet of Things (IoT)-enabled Predictive Maintenance (PdM) as a revolutionary strategy across many sectors. This article presents a picture of a future in which the use of IoT technology and sophisticated analytics will enable the prediction and proactive mitigation of probable equipment failures. This literature study has great importance as it thoroughly explores the complex steps and techniques necessary for the development and implementation of efficient PdM solutions. The study offers useful insights into the optimisation of maintenance methods and the enhancement of operational efficiency by analysing current information and approaches. The article outlines essential stages in the application of PdM, encompassing underlying design factors, data preparation, feature selection, and decision modelling. Additionally, the study discusses a range of ML models and methodologies for monitoring conditions. In order to enhance maintenance plans, it is necessary to prioritise ongoing study and improvement in the field of PdM. The potential for boosting PdM skills and guaranteeing the competitiveness of companies in the global economy is significant through the incorporation of IoT, Artificial Intelligence (AI), and advanced analytics.

clusterBMA: Bayesian model averaging for clustering

Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one 'best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a combined posterior similarity matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name. We use simulated datasets to explore the ability of the proposed technique to identify robust integrated clusters with varying levels of separation between subgroups, and with varying numbers of clusters between models. Benchmarking accuracy against four other ensemble methods previously demonstrated to be highly effective in the literature, clusterBMA matches or exceeds the performance of competing approaches under various conditions of dimensionality and cluster separation. clusterBMA substantially outperformed other ensemble methods for high dimensional simulated data with low cluster separation, with 1.16 to 7.12 times better performance as measured by the Adjusted Rand Index. We also explore the performance of this approach through a case study that aims to identify probabilistic clusters of individuals based on electroencephalography (EEG) data. In applied settings for clustering individuals based on health data, the features of probabilistic allocation and measurement of model-based uncertainty in averaged clusters are useful for clinical relevance and statistical communication.

Comparison of univariate and multivariate anthropometric accommodation of the northwest Mexico population

ABSTRCTErgonomic workstation design is crucial to prevent work-related musculoskeletal disorders. Many researchers have proposed multivariate analysis for human accommodation. However, no multivariate anthropometric analysis exists for the Mexican population. This study compares common multivariate human accommodation approaches (e.g. principal component and archetypal analyses) and clustering techniques (e.g. k-means and Ward's algorithm) with the classical percentile-based univariate accommodation approach, using the Chi-squared goodness-of-fit test and the McNemar's test. The theoretical accommodation percentage obtained by multivariate approaches was higher than those obtained by the percentile univariate approach considering the central 98% data. k-means and archetypal analysis obtained similar and the highest accommodation values, followed by Ward's algorithm and principal component analysis. The study findings can be deployed to assess the design of workstations in Mexico, such as electronic components assembly and crew designs, and the effects of different anthropometric measurements in human accommodation. Practitioner summary: Products and workplaces design are commonly based on the classical univariate approach, using the extreme percentiles. In this study, multivariate approaches were tested on dimensions for sitting workstations, and results showed a bigger accommodation level in comparison to the univariate 1%-99% approaches. Abbreviations: RHM: representative human model; DHM: digital human model; PCA: principal component analysis; AA: archetypal analysis (AA); PCs: principal components; FA: factor analysis; RSS: residual sum of squares; SSE: sum of squared estimated errors; WA: Ward's algorithm; DBI: Davies-Bouldin index; CHI: Calinski-Harabaz index; SI: silhouette index; SH: sitting height; EHS: eye height, sitting; AHS: acromial height, sitting; PH: popliteal height; KHS: knee height, sitting; BPL: buttock-popliteal length; BKL: buttock-knee length; FGR: functional grip reach; AD: anthropometric dimension; E: expected; A: achieved.

College Students' Perception of Current and Projected 30-Year Cardiovascular Disease Risk Using Cluster Analysis with Internal Validation

Cardiovascular risk factors in young adults at a national level are less than ideal specifically for hypercholesterolemia, hypertension, and diabetes. Explore college students' perception of their 30-year cardiovascular disease (CVD) risk using cluster analysis technique with internal validation. This is a descriptive and cross-sectional study. A total of 133 college students, aged 20-36 with no known history of CVD, were recruited and used to perform cluster analysis with internal validation. The mean age of the sample was 24.85 and predominately female (59.5%). The mean score for perception of cardiovascular risk factors was 21.20 ranging from 12 to 34 points on a Likert scale. The mean score for the 30-year CVD risk assessment was 5.23 ranging from 1 to 22%. Five clusters emerged from the cluster analysis. However, two of the clusters, the highest risk with moderate perception and low risk and lowest perception, were identified as areas for potential intervention as there were discrepancies between subjects' perceived risk and their actual 30-year risk. The national data and literature has indicated a lack of awareness of CVD risk among this population which our study also concurred. Identifying the discrepancies between the perceived and projected CVD risk are useful for researchers and clinicians such as nurses to take the initiative to focus on and begin to intervene in this population to reduce potential adverse events of CVD.

Comparison of five cluster validity indices performance in brain [18 F]FET-PET image segmentation using k-means

PURPOSE

Dynamic [¹⁸ F]fluoro-ethyl-L-tyrosine positron emission tomography ([¹⁸ F]FET-PET) is used to identify tumor lesions for radiotherapy treatment planning, to differentiate glioma recurrence from radiation necrosis and to classify gliomas grading. To segment different regions in the brain k-means cluster analysis can be used. The main disadvantage of k-means is that the number of clusters must be pre-defined. In this study, we therefore compared different cluster validity indices for automated and reproducible determination of the optimal number of clusters based on the dynamic PET data.

METHODS

The k-means algorithm was applied to dynamic [¹⁸ F]FET-PET images of 8 patients. Akaike information criterion (AIC), WB, I, modified Dunn's and Silhouette indices were compared on their ability to determine the optimal number of clusters based on requirements for an adequate cluster validity index. To check the reproducibility of k-means, the coefficients of variation CVs of the objective function values OFVs (sum of squared Euclidean distances within each cluster) were calculated using 100 random centroid initialization replications RCI₁₀₀ for 2 to 50 clusters. k-means was performed independently on three neighboring slices containing tumor for each patient to investigate the stability of the optimal number of clusters within them. To check the independence of the validity indices on the number of voxels, cluster analysis was applied after duplication of a slice selected from each patient. CVs of index values were calculated at the optimal number of clusters using RCI₁₀₀ to investigate the reproducibility of the validity indices. To check if the indices have a single extremum, visual inspection was performed on the replication with minimum OFV from RCI₁₀₀ .

RESULTS

The maximum CV of OFVs was 2.7 × 10^-2 from all patients. The optimal number of clusters given by modified Dunn's and Silhouette indices was 2 or 3 leading to a very poor segmentation. WB and I indices suggested in median 5, [range 4-6] and 4, [range 3-6] clusters, respectively. For WB, I, modified Dunn's and Silhouette validity indices the suggested optimal number of clusters was not affected by the number of the voxels. The maximum coefficient of variation of WB, I, modified Dunn's, and Silhouette validity indices were 3 × 10^-2 , 1, 2 × 10^-1 and 3 × 10^-3 , respectively. WB-index showed a single global maximum, whereas the other indices showed also local extrema.

CONCLUSION

From the investigated cluster validity indices, the WB-index is best suited for automated determination of the optimal number of clusters for [¹⁸ F]FET-PET brain images for the investigated image reconstruction algorithm and the used scanner: it yields meaningful results allowing better differentiation of tissues with higher number of clusters, it is simple, reproducible and has an unique global minimum.

Identification of certain cancer-mediating genes using Gaussian fuzzy cluster validity index

In this article, we have used an index, called Gaussian fuzzy index (GFI), recently developed by the authors, based on the notion of fuzzy set theory, for validating the clusters obtained by a clustering algorithm applied on cancer gene expression data. GFI is then used for the identification of genes that have altered quite significantly from normal state to carcinogenic state with respect to their mRNA expression patterns. The effectiveness of the methodology has been demonstrated on three gene expression cancer datasets dealing with human lung, colon and leukemia. The performance of GFI is compared with 19 exiting cluster validity indices. The results are appropriately validated biologically and statistically. In this context, we have used biochemical pathways, p-value statistics of GO attributes, t-test and zscore for the validation of the results. It has been reported that GFI is capable of identifying high-quality enriched clusters of genes, and thereby is able to select more cancer-mediating genes.

A formal algorithm for verifying the validity of clustering results based on model checking

The limitations in general methods to evaluate clustering will remain difficult to overcome if verifying the clustering validity continues to be based on clustering results and evaluation index values. This study focuses on a clustering process to analyze crisp clustering validity. First, we define the properties that must be satisfied by valid clustering processes and model clustering processes based on program graphs and transition systems. We then recast the analysis of clustering validity as the problem of verifying whether the model of clustering processes satisfies the specified properties with model checking. That is, we try to build a bridge between clustering and model checking. Experiments on several datasets indicate the effectiveness and suitability of our algorithms. Compared with traditional evaluation indices, our formal method can not only indicate whether the clustering results are valid but, in the case the results are invalid, can also detect the objects that have led to the invalidity.

Canonical PSO Based K-Means Clustering Approach for Real Datasets

“Clustering” the significance and application of this technique is spread over various fields. Clustering is an unsupervised process in data mining, that is why the proper evaluation of the results and measuring the compactness and separability of the clusters are important issues. The procedure of evaluating the results of a clustering algorithm is known as cluster validity measure. Different types of indexes are used to solve different types of problems and indices selection depends on the kind of available data. This paper first proposes Canonical PSO based K-means clustering algorithm and also analyses some important clustering indices (intercluster, intracluster) and then evaluates the effects of those indices on real-time air pollution database, wholesale customer, wine, and vehicle datasets using typical K-means, Canonical PSO based K-means, simple PSO based K-means, DBSCAN, and Hierarchical clustering algorithms. This paper also describes the nature of the clusters and finally compares the performances of these clustering algorithms according to the validity assessment. It also defines which algorithm will be more desirable among all these algorithms to make proper compact clusters on this particular real life datasets. It actually deals with the behaviour of these clustering algorithms with respect to validation indexes and represents their results of evaluation in terms of mathematical and graphical forms.