A Probabilistic Distance Clustering Algorithm Using Gaussian and Student-t Multivariate Density Distributions

Tortora, Cristina; McNicholas, Paul D.; Palumbo, Francesco

doi:10.1007/s42979-020-0067-z

Cited by 8 publications

(3 citation statements)

References 31 publications

(37 reference statements)

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“…An alternative distancebased method is probabilistic distance (PD) clustering (Ben-Israel and Iyigun 2008), which assigns units to a cluster according to their probability of membership, under the constraint that the product of the probability and the distance of each point to any cluster center is a constant. Tortora, Gettler Summa, Marino, and Palumbo (2016a) propose a transformation of the method for high-dimensional data sets, Rainey, Tortora, and Palumbo (2019) and Tortora, McNicholas, and Palumbo (2020a) propose a new distance measure.…”

Section: Introductionmentioning

confidence: 99%

Model-Based Clustering, Classification, and Discriminant Analysis Using the Generalized Hyperbolic Distribution: MixGHD R package

Tortora¹,

Browne²,

ElSherbiny³

et al. 2021

J. Stat. Soft.

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The MixGHD package for R performs model-based clustering, classification, and discriminant analysis using the generalized hyperbolic distribution (GHD). This approach is suitable for data that can be considered a realization of a (multivariate) continuous random variable. The GHD has the advantage of being flexible due to skewness, concentration, and index parameters; as such, clustering methods that use this distribution are capable of estimating clusters characterized by different shapes. The package provides five different models all based on the GHD, an efficient routine for discriminant analysis, and a function to measure cluster agreement. This paper is split into three parts: the first is devoted to the formulation of each method, extending them for classification and discriminant analysis applications, the second focuses on the algorithms, and the third shows the use of the package on real datasets.

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Section: Introductionmentioning

confidence: 99%

Model-Based Clustering, Classification, and Discriminant Analysis Using the Generalized Hyperbolic Distribution: MixGHD R package

Tortora¹,

Browne²,

ElSherbiny³

et al. 2021

J. Stat. Soft.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recent studies on Artificial Intelligence and Machine Learning (AI/ML) perspectives on mobile edge computing [1] lack detail, but provide guidance on how data can be processed [2]- [9] in realtime, reducing edge-cloud delay [10] and inform on the topic of cognitive cyber security at the edge. This paper is focused on the topic of predicting cyber risk loss magnitude through dynamic analytics of cyber-attack threat event frequencies.…”

Section: Introductionmentioning

confidence: 99%

“…365×24×60×.5= 262,800÷5=52,560÷262,800=0.2÷10,0002 SonicWall report[91] captured real-world data from more than one million sensors in over 215 countries with over 140,000 malware samples collected daily.…”

mentioning

confidence: 99%

Design of a Dynamic and Self-Adapting System, Supported with Artificial Intelligence, Machine Learning and Real-Time Intelligence for Predictive Cyber Risk Analytics in Extreme Environments – Cyber Risk in the Colonisation of Mars

Radanliev¹

2021

SSRN Journal

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Multiple governmental agencies and private organisations have made commitments for the colonisation of Mars. Such colonisation requires complex systems and infrastructure that could be very costly to repair or replace in cases of cyber-attacks. This paper surveys deep learning algorithms, IoT cyber security and risk models, and established mathematical formulas to identify the best approach for developing a dynamic and self-adapting system for predictive cyber risk analytics supported with Artificial Intelligence and Machine Learning and real-time intelligence in edge computing. The paper presents a new mathematical approach for integrating concepts for cognition engine design, edge computing and Artificial Intelligence and Machine Learning to automate anomaly detection. This engine instigates a step change by applying Artificial Intelligence and Machine Learning embedded at the edge of IoT networks, to deliver safe and functional real-time intelligence for predictive cyber risk analytics. This will enhance capacities for risk analytics and assists in the creation of a comprehensive and systematic understanding of the opportunities and threats that arise when edge computing nodes are deployed, and when Artificial Intelligence and Machine Learning technologies are migrated to the periphery of the internet and into local IoT networks. Keywords Dynamic and self-adapting systems. Artificial intelligence. Machine learning. Real-time intelligence. Predictive cyber risk analytics. Colonisation of Mars. Cyber-risk analytics in extreme environments. Cyber-risk in outer space * Petar Radanliev

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FPDclustering: a comprehensive R package for probabilistic distance clustering based methods

Tortora,

Palumbo

2024

Comput Stat

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Data clustering has a long history and refers to a vast range of models and methods that exploit the ever-more-performing numerical optimization algorithms and are designed to find homogeneous groups of observations in data. In this framework, the probability distance clustering (PDC) family methods offer a numerically effective alternative to model-based clustering methods and a more flexible opportunity in the framework of geometric data clustering. Given nJ-dimensional data vectors arranged in a data matrix and the number K of clusters, PDC maximizes the joint density function that is defined as the sum of the products between the distance and the probability, both of which are measured for each data vector from each center. This article shows the capabilities of the PDC family, illustrating the package .

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A Probabilistic Distance Clustering Algorithm Using Gaussian and Student-t Multivariate Density Distributions

Cited by 8 publications

References 31 publications

Model-Based Clustering, Classification, and Discriminant Analysis Using the Generalized Hyperbolic Distribution: MixGHD R package

Model-Based Clustering, Classification, and Discriminant Analysis Using the Generalized Hyperbolic Distribution: MixGHD R package

Design of a Dynamic and Self-Adapting System, Supported with Artificial Intelligence, Machine Learning and Real-Time Intelligence for Predictive Cyber Risk Analytics in Extreme Environments – Cyber Risk in the Colonisation of Mars

FPDclustering: a comprehensive R package for probabilistic distance clustering based methods

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