Related papers: Distance Correlation: A New Tool for Detecting Ass…
The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of…
The use of Pearson's correlation coefficient in Author Cocitation Analysis was compared with Salton's cosine measure in a number of recent contributions. Unlike the Pearson correlation, the cosine is insensitive to the number of zeros.…
Knowing the distance of an astrophysical object is key to understanding it. However, at present, comparisons of theory and observations are hampered by precision (or lack thereof) in distance measurements or estimates. Putting the many…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
The most useful data mining primitives are distance measures. With an effective distance measure, it is possible to perform classification, clustering, anomaly detection, segmentation, etc. For single-event time series Euclidean Distance…
Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an…
Determining and measuring cause-effect relationships is fundamental to most scientific studies of natural phenomena. The notion of causation is distinctly different from correlation which only looks at association of trends or patterns in…
We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to…
We give a pedagogical introduction to quantum discord. We the discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy…
Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that…
Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…
The statistical properties of photons are fundamental to investigating quantum mechanical phenomena using light. In multi-photon, two-mode systems, correlations may exist between outcomes of measurements made on each mode which exhibit…
Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research…
In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
Correlations play a pivotal role in various fields of science, particularly in quantum mechanics, yet their proper quantification remains a subject of debate. In this work, we aim to discuss the challenge of defining a reliable measure of…