We discuss several natural metrics on spaces of unbounded self– adjoint operators and their relations, among them the Riesz and the graph metric. We show that the topologies of the spaces of Fredholm operators resp. invertible operators depend heavily on the metric. Nevertheless we prove that in all cases the spectral flow is up to a normalization the only integer invariant of paths which is pa...

Distance metric plays an important role in machine learning which is crucial to the performance of a range of algorithms. Metric learning, which refers to learning a proper distance metric for a particular task, has attracted much attention in machine learning. In particular, multi-task learning deals with the scenario where there are multiple related metric learning tasks. By jointly training ...

Quality assessment of Multi-objective Optimization algorithms has been a major concern in the scientific field during the last decades. The entropy metric is introduced and highlighted in computing the diversity of Multi-objective Optimization Algorithms. In this paper, the definition of the entropy metric and the approach of diversity measurement based on entropy are presented. This measuremen...

This paper reports the results of a side-by-side evaluation of nine candidate metrics for quantifying edge blend quality in multi channel display systems. The metrics tested include eight variations of contemporary luminance difference and slope-based metrics and a new approach based on a just-noticeabledifference area (JNDA) analysis. The performance of each candidate metric was evaluated by a...

In this paper a hierarchical multi-resolution approach allowing for high precision and distinctiveness is presented. The method combines topological and metric paradigm. The metric approach, based on the Kalman Filter, uses a new concept to avoid the problem of the drift in odometry. For the topological framework the fingerprint sequence approach is used. During the construction of the topologi...

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