Information Theoretic Clustering Using Minimum Spanning Trees

Müller, Andreas; Nowozin, Sebastian; Lampert, Christoph H.

doi:10.1007/978-3-642-32717-9_21

Cited by 36 publications

(20 citation statements)

References 14 publications

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“…In fact I S = 0 if and only if the two studied random variable are strictly independent. Mutual information is then a natural measure which can be used to extend the similarity measure to make it sensitive to non-linear dependencies, and has been successfully used in some applications [45][46][47]. Recently we have used it in the creation of dependency networks on financial markets [20].…”

Section: Introductionmentioning

confidence: 99%

Information-theoretic approach to lead-lag effect on financial markets

Fiedor

2014

Eur. Phys. J. B

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Abstract.Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both types of analysis are concentrated mostly on Pearson's correlation coefficient and consequently intraday lead-lag relationships (where one of the variables in a pair is time-lagged) are also associated with them. Under the Efficient-Market Hypothesis such relationships are not possible as all information is embedded in the prices, but in real markets we find such dependencies. In this paper we analyse lead-lag relationships of financial instruments and extend known methodology by using mutual information instead of Pearson's correlation coefficient. Mutual information is not only a more general measure, sensitive to non-linear dependencies, but also can lead to a simpler procedure of statistical validation of links between financial instruments. We analyse lagged relationships using New York Stock Exchange 100 data not only on an intraday level, but also for daily stock returns, which have usually been ignored.

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Section: Introductionmentioning

confidence: 99%

Information-theoretic approach to lead-lag effect on financial markets

Fiedor

2014

Eur. Phys. J. B

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“…x − x , in which · can be any norm. 2 and ∞ are commonly used. c dx is the volume of corresponding unit norm ball.…”

Section: Kl Entropy Estimatormentioning

confidence: 99%

“…Information theoretic quantities, such as Shannon entropy and mutual information, have a broad range of applications in statistics and machine learning, such as clustering [2,3], feature selection [4,5], anomaly detection [6], test of normality [7], etc. These quantities are determined by the distributions of random variables, which are usually unknown in real applications.…”

Section: Introductionmentioning

confidence: 99%

Analysis of KNN Information Estimators for Smooth Distributions

Zhao

Lai

2018

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away from zero in its support. In practice, however, KSG estimator also performs well for a much broader class of distributions, including not only those with bounded support and densities bounded away from zero, but also those with bounded support but densities approaching zero, and those with unbounded support. In this paper, we analyze the convergence rate of the error of KSG estimator for smooth distributions, whose support of density can be both bounded and unbounded. As KSG mutual information estimator can be viewed as an adaptive recombination of KL entropy estimators, in our analysis, we also provide convergence analysis of KL entropy estimator for a broad class of distributions. Index TermsKSG mutual information estimator, KL entropy estimator, KNN

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“…To address this problem, we propose to calculate the global and local density of the point. Some MST-based algorithms are combined with other methods, such as information theory [16], k-means [17], and multivariate Gaussians [18].…”

Section: Related Workmentioning

confidence: 99%

CciMST: A Clustering Algorithm Based on Minimum Spanning Tree and Cluster Centers

et al. 2018

Mathematical Problems in Engineering

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The minimum spanning tree-(MST-) based clustering method can identify clusters of arbitrary shape by removing inconsistent edges. The definition of the inconsistent edges is a major issue that has to be addressed in all MST-based clustering algorithms. In this paper, we propose a novel MST-based clustering algorithm through the cluster center initialization algorithm, called cciMST. First, in order to capture the intrinsic structure of the data sets, we propose the cluster center initialization algorithm based on geodesic distance and dual densities of the points. Second, we propose and demonstrate that the inconsistent edge is located on the shortest path between the cluster centers, so we can find the inconsistent edge with the length of the edges as well as the densities of their endpoints on the shortest path. Correspondingly, we obtain two groups of clustering results. Third, we propose a novel intercluster separation by computing the distance between the points at the intersection of clusters. Furthermore, we propose a new internal clustering validation measure to select the best clustering result. The experimental results on the synthetic data sets, real data sets, and image data sets demonstrate the good performance of the proposed MST-based method.

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Information Theoretic Clustering Using Minimum Spanning Trees

Cited by 36 publications

References 14 publications

Information-theoretic approach to lead-lag effect on financial markets

Information-theoretic approach to lead-lag effect on financial markets

Analysis of KNN Information Estimators for Smooth Distributions

CciMST: A Clustering Algorithm Based on Minimum Spanning Tree and Cluster Centers

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