scholarly journals A Unified Formulation of k-Means, Fuzzy c-Means and Gaussian Mixture Model by the Kolmogorov–Nagumo Average

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 518
Author(s):  
Osamu Komori ◽  
Shinto Eguchi
Keyword(s):  
Pareto Distribution ◽  
Statistical Data ◽  
Learning Algorithm ◽  
Survival Function ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Simulation Studies ◽  
Probabilistic Framework ◽  
Underlying Distribution ◽  
Fuzzy C Means

Clustering is a major unsupervised learning algorithm and is widely applied in data mining and statistical data analyses. Typical examples include k-means, fuzzy c-means, and Gaussian mixture models, which are categorized into hard, soft, and model-based clusterings, respectively. We propose a new clustering, called Pareto clustering, based on the Kolmogorov–Nagumo average, which is defined by a survival function of the Pareto distribution. The proposed algorithm incorporates all the aforementioned clusterings plus maximum-entropy clustering. We introduce a probabilistic framework for the proposed method, in which the underlying distribution to give consistency is discussed. We build the minorize-maximization algorithm to estimate the parameters in Pareto clustering. We compare the performance with existing methods in simulation studies and in benchmark dataset analyses to demonstrate its highly practical utilities.

scholarly journals MGMM: An R Package for fitting Gaussian Mixture Models on Incomplete Data

2019 ◽  
Author(s):  
Zachary R. McCaw ◽  
Hanna Julienne ◽  
Hugues Aschard
Keyword(s):  
Missing Data ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Model Fitting ◽  
Simulated Data ◽  
R Package ◽  
Gaussian Mixture ◽  
Parameter Estimates ◽  
Cluster Assignment ◽  
Underlying Distribution

AbstractAlthough missing data are prevalent in applications, existing implementations of Gaussian mixture models (GMMs) require complete data. Standard practice is to perform complete case analysis or imputation prior to model fitting. Both approaches have serious drawbacks, potentially resulting in biased and unstable parameter estimates. Here we present MGMM, an R package for fitting GMMs in the presence of missing data. Using three case studies on real and simulated data sets, we demonstrate that, when the underlying distribution is near-to a GMM, MGMM is more effective at recovering the true cluster assignments than state of the art imputation followed by standard GMM. Moreover, MGMM provides an accurate assessment of cluster assignment uncertainty even when the generative distribution is not a GMM. This assessment may be used to identify unassignable observations. MGMM is available as an R package on CRAN: https://CRAN.R-project.org/package=MGMM.

scholarly journals Regression on imperfect class labels derived by unsupervised clustering

2020 ◽  
Author(s):  
Rasmus Froberg Brøndum ◽  
Thomas Yssing Michaelsen ◽  
Martin Bøgsted
Keyword(s):  
Gene Expression ◽  
Multiple Myeloma ◽  
Learning Algorithm ◽  
Gaussian Mixture Models ◽  
Simulated Data ◽  
Gaussian Mixture ◽  
Unsupervised Clustering ◽  
Expression Data ◽  
Method Performance ◽  
Class Labels

Abstract Outcome regressed on class labels identified by unsupervised clustering is custom in many applications. However, it is common to ignore the misclassification of class labels caused by the learning algorithm, which potentially leads to serious bias of the estimated effect parameters. Due to their generality we suggest to address the problem by use of regression calibration or the misclassification simulation and extrapolation method. Performance is illustrated by simulated data from Gaussian mixture models, documenting a reduced bias and improved coverage of confidence intervals when adjusting for misclassification with either method. Finally, we apply our method to data from a previous study, which regressed overall survival on class labels derived from unsupervised clustering of gene expression data from bone marrow samples of multiple myeloma patients.

scholarly journals Quantifying News Narratives to Predict Movements in Market Risk

2021 ◽  
pp. 265-285
Author(s):  
Thomas Dierckx ◽  
Jesse Davis ◽  
Wim Schoutens
Keyword(s):  
Machine Learning ◽  
Mixture Models ◽  
Learning Algorithm ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Machine Learning Algorithm ◽  
Market Participants ◽  
Financial News ◽  
Volatility Index ◽  
Time Horizons

AbstractThe theory of Narrative Economics suggests that narratives present in media influence market participants and drive economic events. In this chapter, we investigate how financial news narratives relate to movements in the CBOE Volatility Index. To this end, we first introduce an uncharted dataset where news articles are described by a set of financial keywords. We then perform topic modeling to extract news themes, comparing the canonical latent Dirichlet analysis to a technique combining doc2vec and Gaussian mixture models. Finally, using the state-of-the-art XGBoost (Extreme Gradient Boosted Trees) machine learning algorithm, we show that the obtained news features outperform a simple baseline when predicting CBOE Volatility Index movements on different time horizons.

scholarly journals A nazomaláris szög és szimotikus húr alkalmazása metrikus alapú taxonómiai osztályozási feladatokban

2020 ◽  
Vol 61 ◽  
pp. 53-62
Author(s):  
Tamás Szeniczey
Keyword(s):  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
True Positive ◽  
Probabilistic Framework ◽  
Linear Discriminant ◽  
Quantitative Characters ◽  
Asian Ancestry ◽  
Ancestry Estimation ◽  
Unsupervised Algorithms ◽  
True Positive Prediction

Ancestry can be estimated in a probabilistic framework using facial morphological signatures of the different population histories. While the assessment of qualitative traits requires more experience, the measurement of the most distinctive quantitative characters usually demands anthropological tools seldom available. However, some of the facial measurements related to ancestry can be easily recorded with a caliper. The study aims to present the efficiency of simotic chord (SC) and nasomalar angle (M77) in ancestry estimation by applying supervised and unsupervised algorithms to classify skulls with European and Asian ancestry. Linear discriminant analysis and Gaussian Mixture models were applied to a subset of the Howells’ craniometric dataset comprised of individuals with European and Asian ancestry. Prediction of ancestry was carried out on a set of craniometric traits describing height, length and width parameters of the crania and then repeated on this set supplemented with M77 and SC measurements. An increased percentage of true positive prediction of ancestry was achieved by involving the M77 and SC measurements.

scholarly journals Measure of Similarity between GMMs by Embedding of the Parameter Space That Preserves KL Divergence

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 957
Author(s):  
Branislav Popović ◽  
Lenka Cepova ◽  
Robert Cep ◽  
Marko Janev ◽  
Lidija Krstanović
Keyword(s):  
Computational Complexity ◽  
Parameter Space ◽  
Recognition Accuracy ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Dimensional Manifold ◽  
Dimensional Parameter ◽  
Trade Off ◽  
Measure Of Similarity ◽  
Lower Dimensional

In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional manifold. By doing so, we obtain a transformation from the original high-dimensional parameter space, into a much lower-dimensional resulting parameter space. Therefore, resolving the distance between two GMMs is reduced to (taking the account of the corresponding weights) calculating the distance between sets of lower-dimensional Euclidean vectors. Much better trade-off between the recognition accuracy and the computational complexity is achieved in comparison to measures utilizing distances between Gaussian components evaluated in the original parameter space. The proposed measure is much more efficient in machine learning tasks that operate on large data sets, as in such tasks, the required number of overall Gaussian components is always large. Artificial, as well as real-world experiments are conducted, showing much better trade-off between recognition accuracy and computational complexity of the proposed measure, in comparison to all baseline measures of similarity between GMMs tested in this paper.

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