Fig. 1. First example of cortical cell recordings. In the middle traces the two recorded time series are shown. The detected spikes are marked in blue (input) and red (output), respectively. On top the ISI-values according to Eq. 2 are depicted, at the bottom the corresponding renormalized ISI-distance (cf. Eq. 4). Here colors mark the times where the respective spike train is slower. For this pair of spike trains an ISI-distance D_I=0.06 is obtained. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 2. Second example of cortical cell recording shown in the same way as in Fig. 1. In this case the ISI-distance attains the value D_I=0.11.

Fig. 3. Third example of cortical cell recording shown in the same way as in Fig. 1. The ISI-distance for this example is D_I=0.34.

Fig. 4. Example of a hierarchical cluster tree obtained from 29 Hindemarsh–Rose time series employing the event distance D_Q. The three principal clusters C₁, C₂ and C_S are distinguished by different colors. The merging of the first two time series S_i and S_j to cluster C_α is highlighted by very thick blue lines, the consecutive merging of this cluster with S_k by thick blue lines. Finally, black lines mark the separation of the three principal clusters used for the definition of the cluster-separation F. The clustering performance values for this example are H=1 and F=0.57. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 5. Two time series from two neurons coding both for the same pattern B (middle). The detected spikes are marked in blue and red, respectively. On top the ISIs, at the bottom the corresponding renormalized ISI-distance. Here colors mark the times where the respective spike train is slower. For this combination an ISI-distance D_I=0.019 is obtained. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 6. Same as Fig. 5 but this time for two time series from two neurons coding for different patterns. In this case the ISI-distance D_I=0.032 is much higher. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 7. Distance matrix for 29 time series from the Hindemarsh–Rose model. Results are obtained by using the ISI-distance D_I. Neurons are labelled by ‘1’, ‘2’ and ‘S’, respectively, depending on their affiliation to pattern 1, 2 or both (‘shared’).

Fig. 8. Clustering of 29 time series from the Hindemarsh–Rose model using the ISI-distance. The existence of three clearly separated clusters is evident. The cluster performance values are H=1 and F=0.66.

Fig. 9. Dependence of the Victor-Purpura spike train distance D_V on the cost parameter c_V. For each combination of cluster affiliations a different color is used. The dotted line marks the cost value for which the best clustering separation is obtained. On the right hand side of the dashed line the values obtained for the ISI-distance without any optimization are depicted. Note that due to different normalizations and scalings, the measures appear on different y-axes.

Fig. 10. For the Victor-Purpura spike train distance the clustering entropy H (solid line) and the cluster separation F (dashed line) in dependence of the parameter c_V that sets the time scale. Remember that F is only calculated for those cases where a correct clustering (as reflected by H=1) is obtained. The optimum performance F=0.67 is marked by a large asterisk at c_V=0.01. On the right hand side of the dashed line the respective values for the ISI-distance (H=1 and F=0.66), which required no parameter optimization, are depicted.

Fig. 11. Comparison of measures: separation of clusters.

Fig. 12. Correlation coefficients between the six measures of spike train dissimilarity.

Fig. 13. Clustering for the six measures of spike train dissimilarity.