Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

Change in suicide rates in Switzerland before and after firearm restriction resulting from the 2003 “Army XXI” reform

Objective: Firearms are the most common method of suicide among young men in Switzerland. From March 2003 through February 2004, the number of Swiss soldiers was halved as a result of an army reform (Army XXI), leading to a decrease in the availability of guns nationwide. The authors investigated the patterns of the overall suicide rate and the firearm suicide rate before and after the reform. Method: Using a naturalistic study design, the authors compared suicide rates before (1995–2003) and after the intervention (2004–2008) in the affected population (men ages 18–43) and in two comparison groups (women ages 18–44 and men ages 44–53). Data were received from the Swiss Federal Statistical Office. Interrupted time series analysis was used to control for preexisting temporal trends. Alternative methods (Poisson regression, autocorrelation analysis, and surrogate data tests) were used to check validity. Results: The authors found a reduction in both the overall suicide rate and the firearm suicide rate after the Army XXI reform. No significant increases were found for other suicide methods overall. An increase in railway suicides was observed. It was estimated that 22% of the reduction in firearm suicides was substituted by other suicide methods. The attenuation of the suicide rate was not compensated for during the follow-up years. Neither of the comparison groups showed statistically significant changes in firearm suicide rate and overall suicide rate. Conclusions: The restriction of firearm availability in Switzerland resulting from the Army XXI reform was followed by an enduring decrease in the general suicide rate.

Genuine cross-correlations: Which surrogate based measure reproduces analytical results best?

The analysis of short segments of noise-contaminated, multivariate real world data constitutes a challenge. In this paper we compare several techniques of analysis, which are supposed to correctly extract the amount of genuine cross-correlations from a multivariate data set. In order to test for the quality of their performance we derive time series from a linear test model, which allows the analytical derivation of genuine correlations. We compare the numerical estimates of the four measures with the analytical results for different correlation pattern. In the bivariate case all but one measure performs similarly well. However, in the multivariate case measures based on the eigenvalues of the equal-time cross-correlation matrix do not extract exclusively information about the amount of genuine correlations, but they rather reflect the spatial organization of the correlation pattern. This may lead to failures when interpreting the numerical results as illustrated by an application to three electroencephalographic recordings of three patients suffering from pharmacoresistent epilepsy.