8,784 research outputs found
An Efficient k-modes Algorithm for Clustering Categorical Datasets
No full textMining clusters from datasets is an important endeavor in many applications. The k-means algorithm is a popular and efficient distribution-free approach for clustering numerical-valued data but can not be applied to categorical-valued observations. The k-modes algorithm addresses this lacuna by taking the k-means objective function, replacing the dissimilarity measure and using modes instead of means in the modified objective function. Unlike many other clustering algorithms, both k-modes and k-means are scalable, because they do not require calculation of all pairwise dissimilarities. We provide a fast and computationally efficient implementation of k-modes, OTQT, and prove that it can find superior clusterings to existing algorithms. We also examine five initialization methods and three types of K-selection methods, many of them novel, and all appropriate for k-modes. By examining the performance on real and simulated datasets, we show that simple random initialization is the best intializer, a novel K-selection method is more accurate than two methods adapted from k-means, and that the new OTQT algorithm is more accurate and almost always faster than existing algorithms.This is a pre-print of the article Dorman, Karin S., and Ranjan Maitra. "An Efficient k-modes Algorithm for Clustering Categorical Datasets." arXiv preprint arXiv:2006.03936 (2020). Posted with permission.</p
An efficient k-modes algorithm for clustering categorical datasets
No full textMining clusters from data is an important endeavor in many applications. The k-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued observations. The k-modes method addresses this lacuna by replacing the Euclidean with the Hamming distance and the means with the modes in the k-means objective function. We provide a novel, computationally efficient implementation of k-modes, called Optimal Transfer Quick Transfer (OTQT). We prove that OTQT finds updates to improve the objective function that are undetectable to existing k-modes algorithms. Although slightly slower per iteration due to algorithmic complexity, OTQT is always more accurate and almost always faster (and only barely slower on some datasets) to the final optimum. Thus, we recommend OTQT as the preferred, default algorithm for k-modes optimization.This article is published as Dorman, Karin S., and Ranjan Maitra. "An efficient k‐modes algorithm for clustering categorical datasets." Statistical Analysis and Data Mining: The ASA Data Science Journal 15, no. 1 (2022): 83-97. doi:10.1002/sam.11546
The Weighted k-Center Problem in Trees for Fixed k
No full textWe present a linear time algorithm for the weighted k-center problem on trees for fixed k. This partially settles the long-standing question about the lower bound on the time complexity of the problem. The current time complexity of the best-known algorithm for the problem with k as part of the input is O(n log n) by Wang et al. [Haitao Wang and Jingru Zhang, 2018]. Whether an O(n) time algorithm exists for arbitrary k is still open
Investment protection a must in India-UK FTA
No full textThe India-UK investment relationship is no more a one-way street. In 2020, the stock of foreign direct investment from India in the UK was £10.6 billion as against £14.9 billion from the UK in India
Appendix – Supplemental material for Three-dimensional adhesion failure analysis of the single lap joint having pre-embedded circular defects
No full textSupplemental material, Appendix for Three-dimensional adhesion failure analysis of the single lap joint having pre-embedded circular defects by Ranjan K Behera, SK Parida and RR Das in The Journal of Strain Analysis for Engineering Design</p
Securing Federated Learning against Overwhelming Collusive Attackers
No full textIn the era of a data-driven society with the ubiquity of Internet of Things (IoT) devices storing large amounts of data localized at different places, distributed learning has gained a lot of traction, however, assuming independent and identically distributed data (iid) across the devices. While relaxing this assumption that anyway does not hold in reality due to the heterogeneous nature of devices, federated learning (FL) has emerged as a privacy-preserving solution to train a collaborative model over non-iid data distributed across a massive number of devices. However, the appearance of malicious devices (attackers), who intend to corrupt the FL model, is inevitable due to unrestricted participation. In this work, we aim to identify such attackers and mitigate their impact on the model, essentially under a setting of bidirectional label flipping attacks with collusion. We propose two graph theoretic algorithms, based on Minimum Spanning Tree and k-Densest graph, by leveraging correlations between local models. Our FL model can nullify the influence of attackers even when they are up to 70% of all the clients whereas prior works could not afford more than 50% of clients as attackers. The effectiveness of our algorithms is ascertained through experiments on two benchmark datasets, namely MNIST and Fashion-MNIST, with overwhelming attackers. We establish the superiority of our algorithms over the existing ones using accuracy, attack success rate, and early detection round
TiK‐means: Transformation‐infused K ‐means clustering for skewed groups
No full textThe K ‐means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK‐means and contributes a K ‐means‐type algorithm that assigns observations to groups while estimating their skewness‐transformation parameters. The resulting groups and transformation reveal general‐structured clusters that can be explained by inverting the estimated transformation. Further, a modification of the jump statistic chooses the number of groups. Our algorithm is evaluated on simulated and real‐life data sets and then applied to a long‐standing astronomical dispute regarding the distinct kinds of gamma ray bursts.This is the peer-reviewed version of the following article: Berry, Nicholas S., and Ranjan Maitra. "TiK‐means: Transformation‐infused K‐means clustering for skewed groups." Statistical Analysis and Data Mining: The ASA Data Science Journal 12, no. 3 (2019): 223-233, which has been published in final form at DOI: 10.1002/sam.11416. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Posted with permission.</p
A priori and a posteriori analysis of the hybrid two-level large-eddy simulation method for high Reynolds number complex flows
No full textWe present a priori and a posteriori analysis of the assumptions and predictions of the hybrid two-level large-eddy simulation (TLS-LES) method for high Reynolds number complex flows. The TLS-LES methodology is a multi-scale framework for simulation of turbulent flows in complex configurations at practically relevant Reynolds number. It additively combines the two-level simulation (TLS) model with a conventional large-eddy simulation (LES) approach by employing a static or dynamic blending function. In the present study, first we analyze the model assumptions employed by the TLS model to obtain the small-scale solution necessary for closure of the large-scale equations. Afterward, we analyze the large-scale and small-scale solutions to assess the predictive ability of the multi-scale framework for specific turbulence physics such as role of forward and backscatter of energy and presence of co- and counter-gradient diffusion. To perform these investigations, we consider cases with increasing degree of geometrical complexity, namely, flow in a periodic channel, flow past a bump placed on the lower surface of the channel and flow past a finite-span NACA0015 airfoil
An efficient k-means-type algorithm for clustering datasets with incomplete records
No full textThe k‐means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed missing‐completely‐at‐random mechanism or to ignore the incomplete records, and apply the algorithm on the resulting dataset. We develop an efficient version of the k‐means algorithm that allows for clustering in the presence of incomplete records. Our extension is called km‐means and reduces to the k‐means algorithm when all records are complete. We also provide initialization strategies for our algorithm and methods to estimate the number of groups in the dataset. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the analysis of activation images obtained from a functional magnetic resonance imaging experiment.This is the peer-reviewed version of the following article: Lithio, Andrew, and Ranjan Maitra. "An efficient k‐means‐type algorithm for clustering datasets with incomplete records." Statistical Analysis and Data Mining: The ASA Data Science Journal 11, no. 6 (2018): 296-311, which has been published in final form at DOI: 10.1002/sam.11392. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Posted with permission.</p
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