Figure 1.
Illustration of the MULTSEG problem.
(Upper panel) 14 time series over 25 time points; (Middle panel) Networks reconstructed from the shown series. The networks correspond to the 4 optimal time series segments, depicted with light grey rectangles in the upper panel. The color coding of nodes correspond to the colors of the time series; (Lower panel, the last two rows) Symmetric difference and union networks from the consecutive segments resulting in the optimal value of 2.40 for the objective , with relative density as a distance measure.
Figure 2.
Directed acyclic graph (DAG) used as input in Algorithm 1 (Fig. 3).
The DAG for
time points is depicted. It contains
nodes, including the special nodes
and
. The label
of each node corresponds to the time points
,
, and
.
Figure 3.
Algorithm 1 - Optimal number of segments.
It presents the algorithm for computing the optimal segmentation based on the longest path in a directed acyclic graph.
Figure 4.
Illustration of the segmentation for synthetic data with relative density as network property.
The resulting partitions are highlighted in light grey and the simulated segmentation points are marked with red bars.
Table 1.
Optimal segmentation for synthetic data.
Figure 5.
Segmentation for yeast’s metabolic cycle.
The partitions found by applying our method are highlighted in light grey. The phases of the yeast metabolic cycle are indicated with colored rectangles above each panel following Tu et al. [36]. R/C stands for reductive charging, OX oxidative metabolism, and R/B, reductive metabolism. (a) shows the segmentations caught by relative density as global property; (b) illustrates the segmentations based on degree; (c) and (d) demonstrate segmentations with local-global properties, betweenness and closeness, respectively. The segmentations in panel (a) performs particularly well due to the global changes in the form of global cycles in the data set from yeast.
Table 2.
Optimal segmentation for data from yeast.