Combining hierarchical clustering approaches using the PCA method

Purpose:Radiogenomics aims to establish relationships between patient genotypes and imaging phenotypes. An open question remains on how best to integrate information from these distinct datasets. This work investigates if similarities in genetic features across patients correspond to similarities in PET‐imaging features, assessed with various clustering algorithms.Methods:[18F]FDG PET data was obtained for 26 NSCLC patients from a public database (TCIA). Tumors were contoured using an in‐house segmentation algorithm combining gradient and region‐growing techniques; resulting ROIs were used to extract 54 PET‐based features. Corresponding genetic microarray data containing 48,778 elements were also obtained for each tumor. Given mismatch in feature sizes, two dimension reduction techniques were also applied to the genetic data: principle component analysis (PCA) and selective filtering of 25 NSCLC‐associated genes‐ofinterest (GOI). Gene datasets (full, PCA, and GOI) and PET feature datasets were independently clustered using K‐means and hierarchical clustering using variable number of clusters (K). Jaccard Index (JI) was used to score similarity of cluster assignments across different datasets.Results:Patient clusters from imaging data showed poor similarity to clusters from gene datasets, regardless of clustering algorithms or number of clusters (JImean= 0.3429±0.1623). Notably, we found clustering algorithms had different sensitivities to data reduction techniques. Using hierarchical clustering, the PCA dataset showed perfect cluster agreement to the full‐gene set (JI =1) for all values of K, and the agreement between the GOI set and the full‐gene set decreased as number of clusters increased (JI=0.9231 and 0.5769 for K=2 and 5, respectively). K‐means clustering assignments were highly sensitive to data reduction and showed poor stability for different values of K (JIrange: 0.2301–1).Conclusion:Using commonly‐used clustering algorithms, we found poor agreement in patient characterization from genomic versus imaging data. Interpretation of radiogenomic associations was found to be dependent on clustering algorithms and sensitive to data reduction techniques.

Today, with the development of technology, the decision-making capabilities of machines have also increased. With their high analytical skills, computers can easily catch points and relationships that may escape the human eye. Thanks to these capabilities, machines are also widely used in the field of health. For example, many machine learning techniques developed on cancer prediction have been successfully applied. Early detection of cancer is crucial to survival. In the early diagnosis of cancer, the rates of drug treatment, chemotherapy or radiotherapy that the person will be exposed to are significantly reduced and the patient gets through this process with the least amount of wear and tear. Gene Expression Cancer RNA-Seq Dataset was used in this study. This data set includes gene expression values of 5 cancer types (BRCA, KIRC, LUAD, LUSC, UCEC). DNA sequences in the dataset were analyzed using k-means and hierarchical clustering algorithms, which are unsupervised machine learning methods. The aim of the study is to develop a usable machine learning model for early detection of cancer at the gene level. Adjusted Rand Index (ARI), Silhouette Score, and Accuracy metrics were used to evaluate the analysis results. The rand index calculates similarity between clusters by counting the binaries assigned to clusters. The adjusted Rand Index is a randomly adjusted version of the Rand Index. The silhouette score indicates how well a data point fits within its own set among separated datasets. The accuracy metric is obtained as a percentage of correctly clustered data points divided by all predictions. Different connection methods are used in the hierarchical clustering algorithm. These are 'complete', 'ward', 'average' and 'single'. As a result of the study, the accuracy in the k-means algorithm was 0.990, the Adjusted Rand Index was 0.79, and the Silhouette Score was 0.14. Looking at the hierarchical clustering, ward performed the best of the four linkage methods, with an ARI score of 0.76 and a silhouette score of 0.13. As a result of the study, the accuracy of in the hierarchical clustering algorithm was 0.999.

Clustering is an effective unsupervised machine learning method that can be used as a stand-alone heuristic or as a part of a data mining process. The goal of clustering analysis is to partition data into groups with high intra-cluster association, and low inter-cluster association. Hierarchical clustering requires minimal parameters, has flexibility with similarity measure, and has strong visualization power, all of which makes it ideal for exploratory analysis. Hierarchical clustering is a particular branch of clustering algorithms where the results are not given as partitions, but rather a nested structure, which can represent the ordering among elements within a dataset. The study of the performance of hierarchical structure on time series data is limited. In this paper, we examine the hierarchical structure of time series datasets. The most popular hierarchical structured clustering heuristics include the Hierarchical Agglomerative Clustering, which is distance based; and Ordering Points To Identify the Clustering Structure, which is density based. Both share many similar characteristics and are suitable for time series data processing. We examine the performance of different hierarchical clustering algorithms with time series both internally as well as externally.

The purpose of data clustering algorithm is to form clusters (groups) of data points such that there is high intra-cluster and low inter-cluster similarity. There are different types of clustering methods such as hierarchical, partitioning, grid and density based. Hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. A hierarchical clustering method can be thought of as a set of ordinary (flat) clustering methods organized in a tree structure. These methods construct the clusters by recursively partitioning the objects in either a top-down or bottom-up fashion. In this paper we present a new hierarchical clustering algorithm using Euclidean distance. To validate this method we have performed some experiments with low dimensional artificial datasets and high dimensional fMRI dataset. Finally the result of our method is compared to some of existing clustering methods.

In Indonesia, Dengue Fever (DF) is a contagious disease that is a significant issue in public health. The Kediri Regency in East Java, as reported by the Ministry of Health in 2019, had the highest number of DF cases. If not addressed promptly, DF can lead to outbreaks, creating a health emergency. The lack of a thorough investigation into the diversity of risk within a spatial and temporal region exacerbates this issue. Therefore, spatial-temporal analysis is crucial in developing a warning system to prevent and control DF. This paper proposes a method that combines the Euclidean Distance calculation with the Hierarchical Clustering method. We collected data from the Kediri Regency health department and conducted pre-processing and classification processes, considering the number of DF victims, death rate, population, rainfall, and public facilities. The hierarchical clustering algorithm was used to categorize the 344 village analyses into low, medium, and high vulnerability categories. This method allows for a comparison of yearly single, average, complete, and centroid linkage in DF vulnerability levels. We also employed spatial-temporal visualization based on cellular applications to create a clear picture of areas vulnerable to DF. The experimental results in clustering showed a satisfactory level of matching, with variant values calculated using the hierarchical clustering method. The variants for single linkages were 0.113; for average linkages, they were 0.120; for complete linkages, they were 0.178; and for centroid linkages, they were 0.106. The grouping validation results indicated that the centroid linkage method produced the best variant level. We suggest further enhancing the methods with better process steps using other pre-processing methods to improve the validation quality.

To the Editor: We read with great interest the article by Hadanny et al,1 published in Neurosurgery. In this study, the authors used an approach which augmented unsupervised and supervised machine learning methods to predict response to spinal cord stimulators. This paper is an excellent example of how both approaches can be used together to prognosticate on patient outcomes, and the methodological implications span beyond the impact on patients with spinal cord stimulators. Unsupervised machine learning (UML) operates on the premise that the ground truth is not known—for this reason, there are no training data involved in the model. The outcomes of UML algorithms are usually unique clusters identified in the data set. This varies from supervised machine learning (SML) algorithms, which construct a model based on known input and output data. In the literature, UML methods are commonly used to identify novel and emergent phenotypes, whereas SML has commonly been used to perform outcome prediction.2,3 When using UML methods, there are several important parameters to consider which may influence the outcomes seen. First parameter is the cluster number identification. In this paper, the authors used the K-nearest neighbor algorithm (KNN), preceded by an elbow-based cluster optimization step. The KNN algorithm itself is not a completely unsupervised algorithm and requires the inclusion of the number of preset clusters. It requires a cluster optimization step to identify this parameter. In their supplementary methods, they argue that, using the elbow method, a pseudoelbow was created at K = 3. As a result, the decision is made that two clusters exist in the data. We encourage the authors to consider the use of other approaches to validate this finding, including the silhouette method, which has been shown to be more robust and quantifiable in some cases and may be less prone to subjective examination of the analyst.4 The number of clusters is also not readily apparent in the reprojections to the principal component analysis domain space. We suggest the use of other dimensionality reduction approaches to visualize the clusters, namely t-distributed stochastic network embedding or uniform manifold approximation and projection. While the clustering should remain in the multidimensional space, dimensionality reduction approaches have been useful in visualizing multidimensional data otherwise difficult to appreciate. Second parameter is the algorithm itself. KNN is a very well-documented partitioning algorithm. However, it has several limitations. First, the algorithm requires the use of numerical data, which may distort the categorical data, such as patient biological sex, diagnosis, smoking status, and present inherent to the data set. In addition, the sample size required for use of the KNN method is also relatively large, with some studies suggesting the need for a sample size of 2^n, where n is the number of features (24 features in this study).5,6 Other clustering algorithms, such as hierarchical clustering, have been shown to be far more effective for smaller data sets, and we encourage the authors to explore the use of more robust algorithms that would better fit the constraints of the data. As more neurosurgical studies use machine learning, specifically UML, approaches for the analysis of data, it becomes very important for researchers to consider the aforementioned parameters to strengthen their observations and findings. We applaud Hadanny et al1 for an excellent presentation of how both UML and SML approaches can be augmented, and we look forward to additional novel contributions using both approaches in the future to better help understand complex disease processes and ultimately help patients.

Similarity and cluster analysis are important aspects for analyzing microarray data. Based on our perspective of viewing microarrays as time series data, both similarity analysis and cluster analysis are carried out through indexing on time series data using R*-Trees. We have developed algorithms for similarity and cluster analysis on microarray data, and conducted experimental studies and comparative studies. First, our study shows that principle components analysis (PCA) has superiority over several other methods (such as DFT and PAA) as far as distance conservation is concerned. A similarity analysis tool based on PCA has been developed, which is able to explore less R*-Tree nodes before finding its similar counterparts and returns less false positives than other methods. In addition, we also extend R*-Tree's application to cluster analysis. With the aid of R*-Tree indexing, two clustering algorithms. KMeans-R and Hierarchy-R, are proposed as an improved version of K-Means and hierarchical clustering, respectively. Experiments for similarity search and cluster analysis based on proposed algorithms have been carried out and have shown favorable results. Experiments related to yeast cell cycle dataset are reported in this paper.

This work aims to expand the knowledge of the area of data analysis through persistence homology and representations of directed graphs. To be specific, we looked for how we can analyze homology cluster groups using agglomerative Hierarchical Clustering algorithms and methods. Additionally, the Wine data, which is offered in R studio, was analyzed using various cluster algorithms such as Hierarchical Clustering, K-Means Clustering, and PAM Clustering. The goal of the analysis was to find out which cluster's method is proper for a given numerical dataset. We tried to find the agglomerative hierarchical clustering method by testing the data that will be the optimal clustering algorithm among these three; K-Means, PAM, and Random Forest methods. By comparing each model's accuracy value with cultivar coefficients, we concluded that K-Means methods are the most helpful when working with numerical variables. On the other hand, PAM clustering and Gower with Random Forest are the most beneficial approaches when using categorical variables. These tests can determine the optimal number of clustering groups, given the data set, and by doing the proper analysis. Using those the project, we can apply our method to several industrial areas such that clinical, business, and others. For example, people can make different groups based on each patient who has a common disease, required therapy, and other things in the clinical society. Additionally, people can expect to get several clustered groups based on the marginal profit, marginal cost, or other economic indicators for the business area.

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

A novel similarity measure based on spatial overlapping relation is proposed in this paper, which calculates the similarity between a pair of data points by using the mutual overlapping relation between them in a multi-dimensional space. A spatial overlapping based hierarchical clustering method SOHC was also developed and implemented aimed to justify the effectiveness of the proposed similarity measure. SOHC works well both in low-dimensional and high-dimensional datasets, and is able to cluster arbitrary shape of clusters. Moreover, it can work for both numerical and categorical attributes in a uniform way. Experimental results carried out on some public datasets collected from the UCI machine learning repository and predictive toxicology domain show that SOHC is a promising clustering method in data mining.

Today, learner grouping has an important role in sagacity of E-learning systems. In recent researches in this field, researchers have tried to improve basic grouping methods by combining them with optimization approaches. This complicates learner grouping methods and one dimensionality looking toward clustering, causes the quality of produced groups decreases. This paper proposes a new method based on feedback from basic clustering method such as Fuzzy C-means and K-means which it is called Hybrid Clustering Method (HCM). To judge of the best cluster, in HCM, based on cluster's center proximity, a correspondence is made between similar clusters and then the best cluster is selected among similar clusters based on an index relating to cluster's density concept. In the next stage, repetitive and eliminated elements are modified. This method looks at clustering problem as perspective of several different methods while maintaining the simplicity of basic cluster algorithms. The proposed method is evaluated and compared with other methods by using Purity and Gathering (P&G) index. The experimental results show that the proposed method has the best results comparing to the other methods such as Fuzzy C-means, K-means and Evolutionary Fuzzy C-means (EFC) in perceptual dimension of learners grouping.

Hierarchical clustering, a traditional clustering method, has been getting attention again. Among several reasons, a credit goes to a recent paper by Dasgupta in 2016 that proposed a cost function that quantitatively evaluates hierarchical clustering trees. An important question is how to combine this recent advance with existing successful clustering methods. In this paper, we propose a hierarchical clustering method to minimize the cost function of clustering tree by incorporating existing clustering techniques. First, we developed an ensemble tree-search method that finds an integrated tree with reduced cost by integrating multiple existing hierarchical clustering methods. Second, to operate on large and arbitrary shape data, we designed an efficient hierarchical clustering framework, called integrating divisive and ensemble-agglomerate (IDEA) by combining it with advanced clustering techniques such as nearest neighbor graph construction, divisive-agglomerate hybridization, and dynamic cut tree. The IDEA clustering method showed better performance in minimizing Dasgupta's cost and improving accuracy (adjusted rand index) over existing cost-minimization-based, and density-based hierarchical clustering methods in experiments using arbitrary shape datasets and complex biology-domain datasets.

In view of the advantages of deep learning model in the extraction of abstract concept, a new text clustering algorithm is designed based on Deep Boltzmann Machines. Based on Replicate Softmax Model and new Deep Boltzmann Machine, energy function of this model is proposed and the detail learning algorithm is introduced.

Clustering algorithm is an unsupervised machine learning method, which has important applications in the fields of intrusion detection and pattern recognition. Based on the two new proposed verdict criterions, a new possibility fuzzy clustering algorithm was presented based on the uncertainty membership, to realize self-learning and detection based on intrusion dataset. The experimental results based on the datum of KDDCUP99 demonstrate that the algorithm possesses higher detection rate and lower misuse detection rate.

The two most widely studied clustering algorithms are partitional and hierarchical clustering. These algorithms have been heavily used in a wide range of applications primarily due to their simplicity and ease of implementation relative to other clustering algorithms. Partitional methods need to be provided with a set of initial seeds which are then improved iteratively. Hierarchical clustering can be achieved in two different ways, namely, bottom-up and top-down clustering. Hierarchical methods can start off with the individual data points in single clusters and build the clustering. Hierarchical clustering algorithms approach the problem of clustering by developing a binary tree-based data structure called the dendrogram. Once the dendrogram is constructed, one can automatically choose the right number of clusters by splitting the tree at different levels to obtain different clustering solutions for the same dataset without rerunning the clustering algorithm again.