Single Linkage Clustering Research Articles

Phylogenetic structure of Shiga toxin-producing Escherichia coli O157:H7 from sub-lineage to SNPs.

Sequence similarity of pathogen genomes can infer the relatedness between isolates as the fewer genetic differences identified between pairs of isolates, the less time since divergence from a common ancestor. Clustering based on hierarchical single linkage clustering of pairwise SNP distances has been employed to detect and investigate outbreaks. Here, we evaluated the evidence-base for the interpretation of phylogenetic clusters of Shiga toxin-producing Escherichia coli (STEC) O157:H7. Whole genome sequences of 1193 isolates of STEC O157:H7 submitted to Public Health England between July 2015 and December 2016 were mapped to the Sakai reference strain. Hierarchical single linkage clustering was performed on the pairwise SNP difference between all isolates at descending distance thresholds. Cases with known epidemiological links fell within 5-SNP single linkage clusters. Five-SNP single linkage community clusters where an epidemiological link was not identified were more likely to be temporally and/or geographically related than sporadic cases. Ten-SNP single linkage clusters occurred infrequently and were challenging to investigate as cases were few, and temporally and/or geographically dispersed. A single linkage cluster threshold of 5-SNPs has utility for the detection of outbreaks linked to both persistent and point sources. Deeper phylogenetic analysis revealed that the distinction between domestic UK and imported isolates could be inferred at the sub-lineage level. Cases associated with domestically acquired infection that fall within clusters that are predominantly travel associated are likely to be caused by contaminated imported food.

Multi‐country outbreak of Salmonella Enteritidis sequence type (ST)11 infections linked to poultry products in the EU/EEA and the United Kingdom

EFSA Supporting PublicationsVolume 18, Issue 3 6486E Joint ECDC-EFSA rapid outbreak assessmentOpen Access Multi-country outbreak of Salmonella Enteritidis sequence type (ST)11 infections linked to poultry products in the EU/EEA and the United Kingdom First published: 01 March 2021 https://doi.org/10.2903/sp.efsa.2021.EN-6486 Requestor: European Commission Question number: EFSA-Q-2020-00724 This article was originally published on the EFSA website www.efsa.europa.eu on 25 February 2021 as part of EFSA's urgent publication procedures AboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Between May 2018 and December 2020, 193 human cases of Salmonella Enteritidis sequence type (ST)11 were reported in Denmark (2), Finland (4), France (33), Germany (6), Ireland (12), the Netherlands (3), Poland (5), Sweden (6), and the United Kingdom (UK) (122). One in five cases was hospitalised. One death was reported. Fifty percent of the cases were children ≤ 18 years. The most recent case was reported by the UK in December 2020. Epidemiological studies in the UK have identified an increased risk of S. Enteritidis infection associated with the consumption of frozen breaded chicken products. Five batches of non-ready-to-eat poultry products (e.g. breaded products) tested positive for S. Enteritidis matching the outbreak strain. Three of these were manufactured by the Polish Processing Company B where S. Enteritidis was not detected. The five positive batches were traced back to different meat suppliers, slaughterhouses, and/or farms in Poland. Some of these farms had positive results for S. Enteritidis in 2020 (no whole genome sequencing typing). The scarce typing information available for the primary production did not enable the identification of a microbiological link between the positive Polish farms and the contaminated products. Control measures were implemented for the products involved (e.g. withdrawals, recalls). The whole genome sequencing analysis of human and food S. Enteritidis isolates confirmed a cluster with 0-3 allelic differences through single linkage clustering. This, in combination with epidemiological and traceability data, suggests common source(s) in the food chain. There remains a risk of infection in connection with the consumption of implicated poultry products purchased before the withdrawals, if these products are not properly cooked. Unknown source(s) of contamination and the identification of other Salmonella serotypes and S. Enteritidis strains indicate that these poultry products pose a recurrent risk for Salmonella infections in the EU/EEA and the UK. Volume18, Issue3March 20216486E ReferencesRelatedInformation

Comparative Analysis of Hierarchical Clustering with Improve Feature for Herbs Leaves

Plants have different leaf morphological characteristics starting from the leaf surface, leaf bone, leaf tips, leaf edges, leaf base, and even leaf color. The study of plants has been progressing rapidly. One of them is the branch of science in plant morphology. Morphological characteristics of leaves are one of the properties possessed by leaves and can be seen clearly. This morphological study learns about the structure of the plant body, especially about the edge leaf shape. This study will be done based on leaf shape. Leaf shape can be used as a reference in the classification process. The classification process requires a good data extraction feature, so it is necessary to improve the feature process at the pre-processing level. Combining the median filter and image erosion is used to improve the feature process. As for feature extraction, the seven moment invariant method is used. The classification method used for grouping is the Hierarchical Clustering. This method consists of four kinds. There are complete link clustering, single link clustering, average link clustering, and centroid linked clustering. Based on the results of experiments conducted, the use of Average Linkage Clustering method obtained clustering accuracy of 87%. It proves that the average method successfully optimizes the result by calculating any distance between points of the cluster. While the smallest accuracy results using complete linkage clustering of 81%.

Hierarchical Density-Based Clustering Using MapReduce

Hierarchical density-based clustering is a powerful tool for exploratory data analysis, which can play an important role in the understanding and organization of datasets. However, its applicability to large datasets is limited because the computational complexity of hierarchical clustering methods has a quadratic lower bound in the number of objects to be clustered. MapReduce is a popular programming model to speed up data mining and machine learning algorithms operating on large, possibly distributed datasets. In the literature, there have been attempts to parallelize algorithms such as Single-Linkage, which in principle can also be extended to the broader scope of hierarchical density-based clustering, but hierarchical clustering algorithms are inherently difficult to parallelize with MapReduce. In this paper, we discuss why adapting previous approaches to parallelize Single-Linkage clustering using MapReduce leads to very inefficient solutions when one wants to compute density-based clustering hierarchies. Preliminarily, we discuss one such solution, which is based on an exact, yet very computationally demanding, random blocks parallelization scheme. To be able to efficiently apply hierarchical density-based clustering to large datasets using MapReduce, we then propose a different parallelization scheme that computes an approximate clustering hierarchy based on a much faster, recursive sampling approach. This approach is based on HDBSCAN*, the state-of-the-art hierarchical density-based clustering algorithm, combined with a data summarization technique called data bubbles. The proposed method is evaluated in terms of both runtime and quality of the approximation on a number of datasets, showing its effectiveness and scalability.

Assessment of lake water quality using multivariate statistical techniques and chlorophyll-nutrient relationships: a case study of the Göksu Lake

This study aimed to evaluate the water quality of the Goksu Lake, which is located in Ankara, Turkey. For this purpose, multivariate statistical analyses, namely, principal component analysis/factor analysis, regression analysis and cluster analysis, and linear regression analysis, were used to determine the relationship between the nutrients. In order to evaluate the status of the lake water quality, the limiting nutrient element was determined using the total nitrogen to total phosphorus ratio (TN/TP). The water quality parameters were selected as pH, turbidity, chemical oxygen demand (COD), suspended solids (SS), dissolved oxygen (DO), biochemical oxygen demand (BOD), total nitrogen (TN), chlorophyll-a (Chl-a), total phosphorus (TP), color, fecal coliform (FC), and total coliform (TC) count. For the cluster analysis, the single-link clustering method using Euclidean distance criteria was preferred. Cluster I consisted of sites 1, 2, 3, and 4, while cluster II consisted of site 5. Two factors were obtained as a result of the factor analysis. These two factors explained 88.2% of the total variance. The first factor clarifies the 45.62% of total variance has pH, COD, DO, TN, TP, color, BOD, and TC strong positive load value. This factor was thought to represent domestic wastewater. The second factor that affects water quality clarifies the 42.54% of total variance has turbidity, SS, Chl-a, and FC strong positive load value. This factor was thought to represent the microbiological activities that occurred as a result of the mixing of wastewaters and also pollution accumulating in the bottom sediment. The nutrient-limiting elements in the water lake quality are determined with TN/TP ratio. Accordingly, the lake water quality was determined as N-limited at two points and co-limited at three points. The relationship between the nutrients was evaluated using regression analysis.

Listeria monocytogenes in Cooked Chicken: Detection of an Outbreak in the United Kingdom (2016 to 2017) and Analysis of L. monocytogenes from Unrelated Monitoring of Foods (2013 to 2017)

In England and Wales, Public Health England applies whole genome sequencing to cultures of Listeria monocytogenes recovered from human cases of listeriosis, foods, and food production environments. Following the routine inspection of a small retailer in February and March 2016, two unopened packs of cooked chicken produced by the same manufacturer were found to be contaminated with L. monocytogenes at levels of 340 and 20 CFU/g. A public recall of this product was issued in March 2016. Early in 2017, a less than five single-nucleotide polymorphism single-linkage cluster was detected between the L. monocytogenes isolates from the two cooked chicken products and cultures from five cases of human listeriosis in England and Scotland with onsets of illness between March 2016 and February 2017. Epidemiological data provided further supportive evidence that this cluster was an outbreak linked to a manufacturer of cooked chicken whose products were supplied to the small retailer that initiated the outbreak investigation. Unrelated to this outbreak, 34 L. monocytogenes isolates recovered from routine food monitoring of 2,007 samples of cooked chicken during 2013 to 2017 were analyzed by whole genome sequencing. Previously undetected fewer than five single-nucleotide polymorphism single-linkage clusters were identified between cultures from cooked chicken and with those from two clusters and two sporadic cases of human listeriosis that were consistent with foodborne transmission. This analysis identified linkage of L. monocytogenes clusters within specific food chains more readily than traditional manual tracing. Linking of data associated with L. monocytogenes cultures from cases of listeriosis with those from unrelated food testing is a unique source of information for communicable disease risk assessment, epidemiological studies, and disease prevention and control. This report provides further evidence that should act as a reminder of the association between cooked chicken consumption and human listeriosis.

Quantifying discrete seismic responses to mining

Applying analysis techniques developed for naturally occurring earthquakes to mine seismicity is common practice; however, these methodologies rarely consider the influence of blasting on the dynamic rock mass failure processes observed in mines. Due to the complex nature of bulk orebody extraction at depth, quantifying discrete seismic responses to mining can be challenging. This paper identifies seismic responses to mining by pairing single-link clustering with finite temporal windows bound by mine blasting practices. A methodology is presented to quantify the space−time characteristics of these responses using four seismic response parameters (SRPs): distance to blast, distance to centroid, time after blast, and time between events. Using SRPs, seismic responses to mining can be quantitatively classified as induced, complex, or triggered (with respect to discrete mine blasting). Because these response parameters do not require an extensive and (or) triaxial dense sensor array, they are applicable to a variety of underground mining operations. In this work, SRPs are applied to 189 discrete seismic responses occurring over 2 months of active mining, and a 2 week shutdown period, at Agnico Eagle’s LaRonde Mine.

Correction: Genus-wide Leptospira core genome multilocus sequence typing for strain taxonomy and global surveillance.

[This corrects the article DOI: 10.1371/journal.pntd.0007374.].

A publicly accessible database for Clostridioides difficile genome sequences supports tracing of transmission chains and epidemics.

Clostridioides difficile is the primary infectious cause of antibiotic-associated diarrhea. Local transmissions and international outbreaks of this pathogen have been previously elucidated by bacterial whole-genome sequencing, but comparative genomic analyses at the global scale were hampered by the lack of specific bioinformatic tools. Here we introduce a publicly accessible database within EnteroBase (http://enterobase.warwick.ac.uk) that automatically retrieves and assembles C. difficile short-reads from the public domain, and calls alleles for core-genome multilocus sequence typing (cgMLST). We demonstrate that comparable levels of resolution and precision are attained by EnteroBase cgMLST and single-nucleotide polymorphism analysis. EnteroBase currently contains 18 254 quality-controlled C. difficile genomes, which have been assigned to hierarchical sets of single-linkage clusters by cgMLST distances. This hierarchical clustering is used to identify and name populations of C. difficile at all epidemiological levels, from recent transmission chains through to epidemic and endemic strains. Moreover, it puts newly collected isolates into phylogenetic and epidemiological context by identifying related strains among all previously published genome data. For example, HC2 clusters (i.e. chains of genomes with pairwise distances of up to two cgMLST alleles) were statistically associated with specific hospitals (P<10−4) or single wards (P=0.01) within hospitals, indicating they represented local transmission clusters. We also detected several HC2 clusters spanning more than one hospital that by retrospective epidemiological analysis were confirmed to be associated with inter-hospital patient transfers. In contrast, clustering at level HC150 correlated with k-mer-based classification and was largely compatible with PCR ribotyping, thus enabling comparisons to earlier surveillance data. EnteroBase enables contextual interpretation of a growing collection of assembled, quality-controlled C. difficile genome sequences and their associated metadata. Hierarchical clustering rapidly identifies database entries that are related at multiple levels of genetic distance, facilitating communication among researchers, clinicians and public-health officials who are combatting disease caused by C. difficile .

Improving Density Peak Clustering by Automatic Peak Selection and Single Linkage Clustering

Density peak clustering (DPC) is a density-based clustering method that has attracted much attention in the academic community. DPC works by first searching density peaks in the dataset, and then assigning each data point to the same cluster as its nearest higher-density point. One problem with DPC is the determination of the density peaks, where poor selection of the density peaks could yield poor clustering results. Another problem with DPC is its cluster assignment strategy, which often makes incorrect cluster assignments for data points that are far from their nearest higher-density points. This study modifies DPC and proposes a new clustering algorithm to resolve the above problems. The proposed algorithm uses the radius of the neighborhood to automatically select a set of the likely density peaks, which are far from their nearest higher-density points. Using the potential density peaks as the density peaks, it then applies DPC to yield the preliminary clustering results. Finally, it uses single-linkage clustering on the preliminary clustering results to reduce the number of clusters, if necessary. The proposed algorithm avoids the cluster assignment problem in DPC because the cluster assignments for the potential density peaks are based on single-linkage clustering, not based on DPC. Our performance study shows that the proposed algorithm outperforms DPC for datasets with irregularly shaped clusters.

Deteksi Plagiarisme Skripsi Mahasiswa dengan Metode Single-link Clustering dan Jaro-Winkler Distance

Abstract— The rise of plagiarism is one of the negative impacts of the development of information and communication technology. Plagiarism can occur anywhere. One of the examples is a university with the object of plagiarism as a student's final project. So we need a system to detect plagiarism so that it can suppress plagiarism in the college environment. In detecting the similarity of a writing will be faster if the writing has been grouped before compared to each other. Single-link clustering was chosen because it has a simple algorithm and can be implemented without the initial cluster. In plagiarism plagiarism usually changes the sentence structure so that it looks different Jaro-Winkler distance is chosen because it can detect similarities in paragraphs that have been changed in sentence structure because Jaro-Winkler distance has a flexible indexing with theoretical distance so that a word or character is considered the same. The stages in this study include data collection, preprocessing, grouping writing with Single-link clustering, comparing writing with jaro-winkler distance, and testing with precision and recall. After testing, the average value of precision was 84.37% and recall was 84.37% with a level of plagiarism of 99.1%. Keywords—: jaro-winkler distance; plagiarisme; single-link clustering.

Specific category region proposal network for text detection in natural scene

Natural scene text usually carries considerable abstract semantic information, which is closely related to the surrounding environment. Thus, natural scene text detection plays a vital role in image content retrieval and understanding. In this study, the authors propose a novel specific category region proposal network (SCRPN) based on maximally stable extremal regions (MSER) and fully convolutional network (FCN) for natural scene text detection. First, FCN for pixel-level recognition is utilised to obtain the text saliency map and MSER is used to obtain oversegmented regions. Then, the multiple features of oversegmented regions and text saliency map are used for region aggregation. Next, single-linkage clustering method is adopted to cluster the segmentation regions to obtain a hierarchical structure of text region proposals. Finally, for the top-ranking region proposals, SCRPN built an end-to-end pipeline for scene text detection directly. Experiments on street view text and international conference on document analysis and recognition (ICDAR) 2013 have demonstrated the effectiveness of SCRPN for generating the text proposals. SCRPN could work with various two-stage text detection networks; thus, faster region convolutional neural network was used as the text detection framework to evaluate the performance of SCRPN in the ICDAR 2015 and MSRA-TD500 benchmarks. The experimental results confirmed that SCRPN makes text detection more robust in complex scenarios.

Classification Program and Story Boundaries Segmentation in TV News Broadcast Videos via Deep Convolutional Neural Network

Given the amount of video information on the net, the user has had difficulty finding the information in a reasonable amount of time. Thus, all video content must be segmented and annotated so that he/she can access the information directly. The goal of the proposed approach is to allow a better exploitation of video by multimedia services (TV-On- Demand, catch-up TV), social community and video-sharing platforms (Youtube, Facebook…). In this work, an approach to classify TV programs and story boundaries segmentation in TV news broadcast video using Deep Convolutional Neural Network (DCNN) is presented. The first step is to extract features from video. This characteristics will modeled as video corpus governings the organization of TV stream content. This organization is carried out on two levels. The first consists in the identification of anchorperson by Single-Linkage Clustering through CNN faces and the second level aims to identify the story of news program due to the large audience because of the pertinent information they contain. In addition, we implement a 360-h broadcast video dataset obtained from five French news channels with ground-truth marked semantic shot categories, program genres and story boundaries. Experiments on this dataset prove the relevance of our approach for news broadcast video segmentation.

Silhouette width using generalized mean-A flexible method for assessing clustering efficiency.

Cluster analysis plays vital role in pattern recognition in several fields of science. Silhouette width is a widely used index for assessing the fit of individual objects in the classification, as well as the quality of clusters and the entire classification. Silhouette combines two clustering criteria, compactness and separation, which imply that spherical cluster shapes are preferred over others—a property that can be seen as a disadvantage in the presence of complex, nonspherical clusters, which is common in real situations. We suggest a generalization of the silhouette width using the generalized mean. By changing the p parameter of the generalized mean between −∞ and +∞, several specific summary statistics, including the minimum, maximum, the arithmetic, harmonic, and geometric means, can be reproduced. Implementing the generalized mean in the calculation of silhouette width allows for changing the sensitivity of the index to compactness versus connectedness. With higher sensitivity to connectedness, the preference of silhouette width toward spherical clusters should reduce. We test the performance of the generalized silhouette width on artificial data sets and on the Iris data set. We examine how classifications with different numbers of clusters prepared by different algorithms are evaluated, if p is set to different values. When p was negative, well‐separated clusters achieved high silhouette widths despite their elongated or circular shapes. Positive values of p increased the importance of compactness; hence, the preference toward spherical clusters became even more detectable. With low p, single linkage clustering was deemed the most efficient clustering method, while with higher parameter values the performance of group average, complete linkage, and beta flexible with beta = −0.25 seemed better. The generalized silhouette allows for adjusting the contribution of compactness and connectedness criteria, thus avoiding underestimation of clustering efficiency in the presence of clusters with high internal heterogeneity.

Variability Assessment of Different Maintainer Lines for Hybrid Rice Development Based on Qualitative Traits

The assessment of genetic diversity among nineteen maintainer lines was studied based on thirteen qualitative traits. The single linkage clustering, morphological dendogram were performed to assess the traits. Most of the traits showed variation in different maintainer lines except auricle colour. On the basis of flag leaf attitude, a maximum four groups were formed with erect, semi-erect, horizontal and descending type leaf angle. The maintainer line BRRI20B has awn tip, which is unique from the rest of the studied maintainer lines. Nineteen maintainer lines were grouped into four different clusters and a considerable level of variability was displayed for most of the traits examined. The clustering pattern revealed, cluster I was the largest and consisted seven maintainer lines. Among them maintainer lines BRRI52B and BRRI60B were the most closely associated. Cluster II represent diverse sources materials and its revealed non-correspondence of geographic diversity with genetic divergence. Thus the cluster analysis has revealed the genetic variation and the traits contributing for the variation. Hence, this maintainer lines can be utilized for trait improvement in breeding programmes for the traits contributing for major variation.&#x0D; Bangladesh Rice j. 2018, 22(2): 79-87

Use of whole-genome sequencing to identify clusters of Shigella flexneri associated with sexual transmission in men who have sex with men in England: a validation study using linked behavioural data.

Since the 1970s, shigellosis has been reported as a sexually transmissible infection, and in recent years, genomic data have revealed the breadth of Shigella spp. transmission among global networks of men who have sex with men (MSM). In 2015, Public Health England (PHE) introduced routine whole-genome sequencing (WGS) of Shigella spp. to identify transmission clusters. However, limited behavioural information for the cases hampers interpretation. We investigated whether WGS can distinguish between clusters representing sexual transmission in MSM and clusters representing community (non-sexual) transmission to inform infection control. WGS data for Shigella flexneri from August 2015 to July 2017 were aggregated into single linkage clusters based on SNP typing using a range of SNP distances (the standard for Shigella surveillance at PHE is 10 SNPs). Clusters were classified as ‘adult male’, ‘household’, ‘travel-associated’ or ‘community’ using routine demographic data submitted alongside laboratory cultures. From August 2015 to March 2017, PHE contacted those with shigellosis as part of routine public-health follow-up and collected exposure data on a structured questionnaire, which for the first time included questions about sexual identity and behaviour. The questionnaire data were used to determine whether clusters classified as ‘adult male’ represented likely sexual transmission between men, thereby validating the use of the SNP clustering tool for informing appropriate public-health responses. Overall, 1006 S . flexneri cases were reported, of which 563 clustered with at least one other case (10-SNP threshold). Linked questionnaire data were available for 106 clustered cases, of which 84.0 % belonged to an ‘adult male’ cluster. At the 10-SNP threshold, 95.1 % [95 % confidence interval (CI) 88.0–98.1%] of MSM belonged to an ‘adult male’ cluster, while 73.2 % (95 % CI 49.1–87.5%) of non-MSM belonged to a ‘community’ or ‘travel-associated’ cluster. At the 25-SNP threshold, all MSM (95 % CI 96.0–100%) belonged to an ‘adult male’ cluster and 77.8 % (95 % CI 59.2–89.4%) of non-MSM belonged to a ‘community’ or ‘travel-associated’ cluster. Within one phylogenetic clade of S. flexneri , 9 clusters were identified (7 ‘adult male’; 2 ‘community’) using a 10-SNP threshold, while a single ‘adult male’ cluster was identified using a 25-SNP threshold. Genotypic markers of azithromycin resistance were detected in 84.5 % (294/348) of ‘adult male’ cases and 20.9 % (9/43) of cases in other clusters (10-SNP threshold), the latter of which contained gay-identifying men who reported recent same-sex sexual contact. Our study suggests that SNP clustering can be used to identify Shigella clusters representing likely sexual transmission in MSM to inform infection control. Defining clusters requires a flexible approach in terms of genetic relatedness to ensure a clear understanding of underlying transmission networks.

Natural scene text localization using edge color signature

Localizing text regions in images taken from natural scenes is one of the challenging problems dueto variations in font, size, color and orientation of text. In this paper, we introduce a new concept socalled Edge Color Signature for localizing text regions in an image. This method is able to localizeboth Farsi and English texts. In the proposed method rst a pyramid using different scales of theinput image is created. Then for each level of the pyramid an edge map is extracted. Afterward,several geometric features are employed to lter out the non-text edges from the extracted edges.At this stage we describe an edge using colors of its neighboring pixels. We use the mean-Shiftalgorithm to obtain the color modes surrounding each edge pixel. Subsequently, the connectededge pixels with similar color signatures are clustered using Single-Linkage clustering algorithm toconstruct meaningful groups. Finally, each of the clusters is labeled as text or non-text using anMLP based cascade classi er. The proposed method has been evaluated on well-known ICDAR 2013and our Farsi dataset, the result is very promising.

Chain-detection Between Clusters

Chains connecting two or more different clusters are a well known problem of clustering algorithms like DBSCAN or Single Linkage Clustering. Since already a small number of points resulting from, e. g., noise can form such a chain and build a bridge between different clusters, it can happen that the results of the clustering algorithm are distorted: several disparate clusters get merged into one. This single-link effect is rather known but to the best of our knowledge there are no satisfying solutions which extract those chains, yet. We present a new algorithm detecting not only straight chains between clusters, but also bent and noisy ones. Users are able to choose between eliminating one dimensional and higher dimensional chains connecting clusters to receive the underlying cluster structure. Also, the desired straightness can be set by the user. As this paper is an extension of [8], we apply our technique not only in combination with DBSCAN but also with single link hierarchical clustering. On a real world dataset containing traffic accidents in Great Britain we were able to detect chains emerging from streets between cities and villages, which led to clusters composed of diverse villages. Additionally, we analyzed the robustness regarding the variance of chains in synthetic experiments.

Maximum likelihood estimation in Gaussian models under total positivity

We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_{2}$). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof that the maximum likelihood estimator (MLE) for such distributions exists based on $n\geq2$ observations, irrespective of the underlying dimension. Slawski and Hein [Linear Algebra Appl. 473 (2015) 145–179], who first proved this result, also provided empirical evidence showing that the $\mathrm{MTP}_{2}$ constraint serves as an implicit regularizer and leads to sparsity in the estimated inverse covariance matrix, determining what we name the ML graph. We show that we can find an upper bound for the ML graph by adding edges corresponding to correlations in excess of those explained by the maximum weight spanning forest of the correlation matrix. Moreover, we provide globally convergent coordinate descent algorithms for calculating the MLE under the $\mathrm{MTP}_{2}$ constraint which are structurally similar to iterative proportional scaling. We conclude the paper with a discussion of signed $\mathrm{MTP}_{2}$ distributions.

Estimating distance threshold for greedy subspace clustering

Many approaches have been proposed to recognize clusters in subspaces. However, their performance is highly sensitive to input parameter values. The purpose and expected ranges of these parameters may not available to a non-expert user. The parameter setting producing optimal results can only be known after repeated execution of the clustering process every time with a different set, which is very time consuming. Most of the existing algorithms show high runtimes due to excessive data scans. In this work, we propose a subspace clustering technique that estimates the distance threshold parameter automatically from the data for each attribute and works on the basis of single linkage clustering, in bottom up, greedy fashion. The experimental results show that, the algorithm produces optimal results without accepting any input from the user, achieves up to 10 times better runtime and improved accuracy in a single run without requiring any tuning of parameter values.