Evaluation of Hierarchical Structures for Time Series Data

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 one of the techniques used to obtain useful information from web log file for better understanding of customer behaviour. Two clustering techniques that commonly used are Greedy Hierarchical Item Set-Based Clustering (GHIC) algorithm and Hierarchical Clustering Algorithm (HCA). The algorithms, however, have its weaknesses in terms of processing times and time complexity. This paper proposes a new approach called Hierarchical Pattern-Based Clustering (HPBC) algorithm to improve the processing times based on the difference of mean support values of each cluster. The simulation revealed that the proposed algorithm outperformed the HCA and GHIC up to 100% and 50% respectively, with less time complexity.

This study applied various clustering algorithms to a multivariate dataset from a MOBA (Multiplayer On- line Battle Arena) game. The results revealed similarities between players, which were examined in detail using visual analysis techniques. Clustering algorithms are one of the most effective machine learning methods for discovering structural similarities between observations. In this study, K-means and Hierarchi- cal clustering algorithms, both unsupervised learning methods, were used to identify meaningful groups, and various analyses were performed. The results were compared, the effects on data segmentation were evaluated, and the findings were made clearer. The data analysis process began with converting categor- ical variables into numerical format using appropriate preprocessing techniques and scaling all variables using the StandardScaler method. Then, K-means and Hierarchical clustering algorithms were successfully applied to obtain different segmentations of the player data, and the characteristics of each segment were examined in depth. The resulting clusters were reduced to a two-dimensional plane using Principal Com- ponent Analysis (PCA), and the structural differences between the clusters formed by the algorithms were clearly visualized. The analysis results showed that while similar clusters were produced by both K-means and Hierarchical algorithms, different structural patterns were also identified. Visualizations made with PCA facilitated a better understanding of these separations. The suitability of the number of clusters and the performance of the algorithms were measured using the Silhouette score, and it was found that the K-means algorithm provided more consistent and effective results. The findings of this study demonstrate that clustering algorithms can capture meaningful patterns in dynamic and high-dimensional data, such as those from a MOBA game. Future studies could increase the generalizability of these findings by repeating similar clustering analyses on larger and more heterogeneous datasets. Additionally, comparisons with den- sity-based algorithms like DBSCAN would allow for a deeper evaluation of the algorithms’ performance in different data structures.

The proliferation of big data and the growth of e-commerce have intensified the challenges associated with extracting actionable data for personalised recommendations and decision-making. With data-driven marketing strategies, understanding and predicting customer behaviour has become paramount for maintaining competitive advantage. This study leverages business analytics tools, focusing on Recency, Frequency, and Monetary (RFM) Analysis, alongside K-Means and Hierarchical (Agglomerative) Clustering algorithms, to segment customer transactional data. Data normalisation, a critical step for accurate clustering, was performed using log transformation and the Power Transformer technique with the Yeo-Johnson parameter, the latter proving more effective for handling both positively and negatively skewed data, enhancing data normalisation and suitability for analysis. This study reveals that RFM Analysis with Hierarchical Clustering outperforms K-Means Clustering, achieving a Silhouette Score of 0.47 and a Calinski–Harabasz Index of 3787.1, indicating a more accurate identification of customer segments. RFM Analysis alone generated eight clusters, while integrating RFM Analysis with both Hierarchical Clustering and K-Means generated three similar-sized clusters with interchanged labels. These metrics highlight the proficiency of Hierarchical Clustering in identifying unique customer segments and customising marketing strategies. The findings indicate that the RFM-Hierarchical Clustering approach enhances segmentation precision and facilitates more refined and effective marketing strategies.

In this paper, new parallel algorithms for single and complete link hierarchical agglomerative clustering are presented. The parallel algorithms have been mapped on a SIMD machine model with a linear interconnection network. The model consists of a linear array of N PE's, where N is the number of patterns, interfaced with a global host machine and the interconnection network provides inter-PE and PE-to-host/host-to-PE communication. The proposed algorithms are faster than previously known algorithms for hierarchical clustering. For clustering a data set with N patterns, using N PE's, the computation time for the single link clustering algorithm is shown to be O(NlogN) and that for the complete link clustering algorithm is shown to be O(N/sup 2/). The parallel algorithms have been verified through simulations on the Intel's iPSC/2 concurrent supercomputer.

The accuracy of the traditional hedge ratio estimation is affected by the fat-tailed and leptokurtic properties observed in a financial time series. In this study, a novel method based on the self-organizing map (SOM) is proposed to modify the probability distribution of the time series and improve the optimal hedge ratio (OHR) estimation. The financial time series data are hierarchically clustered by SOM based on similar patterns described by the technical indicators. These hierarchical clusters, to which the current daypsilas data belong and share a similar pattern with the data, are used for the current OHR estimation. The OHR is estimated using the ordinary least squares (OLS) method based on the data, which are obtained via bootstrap resampling from the hierarchical clusters and a more approximate normal distribution. Taiwan weighted index, S&P 500 index, and FTSE 100 index are adopted in the empirical experiments to test the hedging effectiveness. Experiment results demonstrate that resampling on the hierarchical SOM clusters can increase the accuracy of the OHR estimation and has a better hedge effectiveness than that of the traditional OLS method.

Hierarchical clustering algorithm is a very important method in data mining. The disadvantage of hierarchical clustering lies in the time complexity of the algorithm and the one-way irreversibility of the algorithm. The inaccuracy of the conditions for cluster termination is another major disadvantage of hierarchical clustering. Hierarchical clustering requires the final cluster number. But for most datasets, the number of clusters cannot be known in advance. Therefore, a method is proposed to combine the split-based and agglomeration-based hierarchical clustering algorithms to first quickly and uniformly partition the original dataset, and then make similar partitions adaptively merge based on the partition density and partition distance on the basis of these partitions. In this paper, aiming at these defects of hierarchical clustering, a hierarchical clustering algorithm based on fast and uniform segmentation is proposed.

This work presents a study about dissimilarity measures for seismic signals, and their relation to clustering in the particular problem of the identification of earthquake focal mechanisms, i.e. the physical phenomena which have generated an earthquake. Starting from the assumption that waveform similarity implies similarity in the focal parameters, important details about them can be determined by studying waveforms related to the wave field produced by earthquakes and recorded by a seismic network. Focal mechanisms identification is currently investigated by clustering of seismic events, using mainly cross-correlation dissimilarity in conjunction with hierarchical clustering algorithm. By the way, it results that such adoptions have not been sufficiently validated. To shed light on this we have studied the cross correlation dissimilarity on simulated seismic signals in conjunction with hierarchical and partitional clustering algorithms, and compared its performance with a newly one recently introduced for the purpose called cumulative shape. In particular, we have properly created synthetic waveforms related to two types of focal mechanisms, showing that the cumulative shape perform better than cross-correlation in the identification of the expected clustering solution.

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.

Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a specific objective, [19] framed similarity-based hierarchical clustering as a combinatorial optimization problem, where a 'good' hierarchical clustering is one that minimizes some cost function. He showed that this cost function has certain desirable properties, such as in order to achieve optimal cost, disconnected components must be separated first and that in 'structureless' graphs, i.e., cliques, all clusterings achieve the same cost. We take an axiomatic approach to defining 'good' objective functions for both similarity and dissimilarity-based hierarchical clustering. We characterize a set of admissible objective functions (that includes the one introduced by Dasgupta) that have the property that when the input admits a 'natural' ground-truth hierarchical clustering, the ground-truth clustering has an optimal value. Equipped with a suitable objective function, we analyze the performance of practical algorithms, as well as develop better and faster algorithms for hierarchical clustering. For similarity-based hierarchical clustering, [19] showed that a simple recursive sparsest-cut based approach achieves an O(log3/2 n)-approximation on worst-case inputs. We give a more refined analysis of the algorithm and show that it in fact achieves an [Equation]-approximation1. This improves upon the LP-based O(log n)-approximation of [33]. For dissimilarity-based hierarchical clustering, we show that the classic average-linkage algorithm gives a factor 2 approximation, and provide a simple and better algorithm that gives a factor 3/2 approximation. This aims at explaining the success of these heuristics in practice. Finally, we consider a 'beyond-worst-case' scenario through a generalisation of the stochastic block model for hierarchical clustering. We show that Dasgupta's cost function also has desirable properties for these inputs and we provide a simple algorithm that for graphs generated according to this model yields a 1 + o(1) factor approximation.

This paper discusses the clustering quality and complexities of the hierarchical data clustering algorithm based on gravity theory. The gravitybased clustering algorithm simulates how the given N nodes in a K-dimensional continuous vector space will cluster due to the gravity force, provided that each node is associated with a mass. One of the main issues studied in this paper is how the order of the distance term in the denominator of the gravity force formula impacts clustering quality. The study reveals that, among the hierarchical clustering algorithms invoked for comparison, only the gravity-based algorithm with a high order of the distance term neither has a bias towards spherical clusters nor suffers the well-known chaining effect. Since bias towards spherical clusters and the chaining effect are two major problems with respect to clustering quality, eliminating both implies that high clustering quality is achieved. As far as time complexity and space complexity are concerned, the gravitybased algorithm enjoys either lower time complexity or lower space complexity, when compared with the most well-known hierarchical data clustering algorithms except single-link.Keywords:data clusteringagglomerative hierarchical clusteringgravity force

Magnetic resonance spectroscopy (MRS) has been shown to have great clinical potential as a supplement to magnetic resonance imaging in the detection of prostate cancer (CaP). MRS provides functional information in the form of changes in the relative concentration of specific metabolites including choline, creatine, and citrate which can be used to identify potential areas of CaP. With a view to assisting radiologists in interpretation and analysis of MRS data, some researchers have begun to develop computer-aided detection (CAD) schemes for CaP identification from spectroscopy. Most of these schemes have been centered on identifying and integrating the area under metabolite peaks which is then used to compute relative metabolite ratios. However, manual identification of metabolite peaks on the MR spectra, and especially via CAD, is a challenging problem due to low signal-to-noise ratio, baseline irregularity, peak overlap, and peak distortion. In this article the authors present a novel CAD scheme that integrates nonlinear dimensionality reduction (NLDR) with an unsupervised hierarchical clustering algorithm to automatically identify suspicious regions on the prostate using MRS and hence avoids the need to explicitly identify metabolite peaks. The methodology comprises two stages. In stage 1, a hierarchical spectral clustering algorithm is used to distinguish between extracapsular and prostatic spectra in order to localize the region of interest (ROI) corresponding to the prostate. Once the prostate ROI is localized, in stage 2, a NLDR scheme, in conjunction with a replicated clustering algorithm, is used to automatically discriminate between three classes of spectra (normal appearing, suspicious appearing, and indeterminate). The methodology was quantitatively and qualitatively evaluated on a total of 18 1.5 T in vivo prostate T2-weighted (w) and MRS studies obtained from the multisite, multi-institutional American College of Radiology (ACRIN) trial. In the absence of the precise ground truth for CaP extent on the MR imaging for most of the ACRIN studies, probabilistic quantitative metrics were defined based on partial knowledge on the quadrant location and size of the tumor. The scheme, when evaluated against this partial ground truth, was found to have a CaP detection sensitivity of 89.33% and specificity of 79.79%. The results obtained from randomized threefold and fivefold cross validation suggest that the NLDR based clustering scheme has a higher CaP detection accuracy compared to such commonly used MRS analysis schemes as z score and PCA. In addition, the scheme was found to be robust to changes in system parameters. For 6 of the 18 studies an expert radiologist laboriously labeled each of the individual spectra according to a five point scale, with 1/2 representing spectra that the expert considered normal and 3/4/5 being spectra the expert deemed suspicious. When evaluated on these expert annotated datasets, the CAD system yielded an average sensitivity (cluster corresponding to suspicious spectra being identified as the CaP class) and specificity of 81.39% and 64.71%, respectively.

Clustering algorithms play a pivotal role in data mining, offering powerful tools for uncovering hidden patterns and structures within datasets. These algorithms aim to divide data points into coherent groups based on similarities or dissimilarities, making it easier to explore and understand complex data. Clustering algorithms typically rely on similarity measures to assess the likeness between data points. Consequently, selecting a suitable similarity measure is crucial for achieving satisfactory clustering outcomes. However, this decision can pose significant challenges, especially for non-experts, given the plethora of similarity measures available in the literature and their performance which is closely linked to the specific dataset, clustering algorithm, and cluster validity index employed. This difficulty is even more important when considering mixed data clustering. Mixed data refers to heterogeneous data characterized by both numerical and categorical attributes. In such a context, the same similarity measure cannot be used for both types of attributes due to their different nature. Commonly, two similarity measures are combined, one for numerical attributes and one for categorical attributes. This adds a layer of complexity to the problem since it requires the selection of two similarity measures instead of just one. This paper introduces SIMREC, a similarity measure recommendation system for mixed data clustering. The system uses meta-learning to mine the relationship between dataset characteristics and similarity measures performances for different mixed data clustering algorithms and cluster validity indices. Therefore, given a mixed dataset, a mixed data clustering algorithm, and a cluster validity index, the system can recommend suitable pairs of numerical and categorical similarity measures based on the characteristics of the dataset. We implemented the proposed system using 130 pairs of similarity measures (10 numerical and 13 categorical), 4 commonly used mixed data clustering algorithms (K-Prototypes, LSH-K-Prototypes, K-Medoids, and Hierarchical Clustering), and three cluster validity indices (Silhouette, Clustering Accuracy, and Adjusted Rand Index). Our experiments on 185 publicly available mixed datasets show that the pairs of similarity measures recommended by SIMREC outperform the baseline pairs, including classically used pairs of similarity measures in the literature.

Combining hierarchical clustering approaches using the PCA method

Conventional methods for speaker diarization involve windowing an audio file into short segments to extract speaker embeddings, followed by an unsupervised clustering of the embeddings. This multistep approach generates speaker assignments for each segment. In this paper, we propose a novel Supervised HierArchical gRaph Clustering algorithm (SHARC) for speaker diarization where we introduce a hierarchical structure using Graph Neural Network (GNN) to perform supervised clustering. The supervision allows the model to update the representations and directly improve the clustering performance, thus enabling a single-step approach for diarization. In the proposed work, the input segment embeddings are treated as nodes of a graph with the edge weights corresponding to the similarity scores between the nodes. We also propose an approach to jointly update the embedding extractor and the GNN model to perform end-to-end speaker diarization (E2E-SHARC). During inference, the hierarchical clustering is performed using node densities and edge existence probabilities to merge the segments until convergence. In the diarization experiments, we illustrate that the proposed E2E-SHARC approach achieves 53% and 44% relative improvements over the baseline systems on benchmark datasets like AMI and Voxconverse, respectively.