The definition of adequate metrics between objects to be compared is at the core of many machine learning methods (e.g., nearest neighbors, kernel machines, etc.). When complex objects are involved, such metrics have to be carefully designed in order to leverage on desired notions of similarity.

This section covers my works related to the definition of new metrics for structured data such as time series or graphs. Three tracks are investigated. First, in Sec. 1.1, time series are seen as discrete distributions over the feature-time product space and a kernel that efficiently compares such representations is defined. Second, in Sec. 1.2, time series are seen as sequences, which means that only ordering is of importance (time delay between observations is ignored) and variants of the Dynamic Time Warping algorithm are used. Finally, in Sec. 1.3, undirected labeled graphs are seen as discrete distributions over the feature-structure product space and optimal transport distances are used.