Horocycle Decision Boundaries for Large Margin Classification in Hyperbolic Space

Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries in a large margin classifiers setting leading to a non-convex optimization problem. In this paper, we propose a novel large margin classifier based on horocycle (horosphere) decision boundaries that leads to a geodesically convex optimization problem that can be optimized using any Riemannian gradient descent technique guaranteeing a globally optimal solution. We present several experiments depicting the performance of our classifier

A rest time-based prognostic framework for state of health estimation of lithium-ion batteries with regeneration phenomena

State of health (SOH) prognostics is significant for safe and reliable usage of lithium-ion batteries. To accurately predict regeneration phenomena and improve long-term prediction performance of battery SOH, this paper proposes a rest time-based prognostic framework (RTPF) in which the beginning time interval of two adjacent cycles is adopted to reflect the rest time. In this framework, SOH values of regeneration cycles, the number of cycles in regeneration regions and global degradation trends are extracted from raw SOH time series and predicted respectively, and then the three sets of prediction results are integrated to calculate the final overall SOH prediction values. Regeneration phenomena can be found by support vector machine and hyperplane shift (SVM-HS) model by detecting long beginning time intervals. Gaussian process (GP) model is utilized to predict the global degradation trend, and nonlinear models are utilized to predict the regeneration amplitude and the cycle number of each regeneration region. The proposed framework is validated through experimental data from the degradation tests of lithium-ion batteries. The results demonstrate that both the global degradation trend and the regeneration phenomena of the testing batteries can be well predicted. Moreover, compared with the published methods, more accurate SOH prediction results can be obtained under this framewor