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Abstract. In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art techniques for classification, denoising, and the study of nonlinear dynamics. The main contribution of this work is to provide a theoretical explanation for the above experimental observations. Our approach relies on a detailed analysis of the commute time metric on prototypical graph models that epitomize the geometry observed in general patch graphs. We prove that a parametrization of the graph based on commute times shrinks the mutual distances between patches that correspond to rapid local changes in the signal, while the distances between patches that correspond to slow local changes expand. In effect, our results explain why the parametrization of the set of patches based on the eigenfunctions of the Laplacian can concentrate patches that correspond to rapid local changes, which would otherwise be shattered in the space of patches. While our results are based on a large sample analysis, numerical experimentations on synthetic and real data indicate that the results hold for datasets that are very small in practice.

S U M M A R YWe propose a new method to analyse seismic time-series and estimate the arrival times of seismic waves. Our approach combines two ingredients: the time-series are first lifted into a highdimensional space using time-delay embedding; the resulting phase space is then parametrized using a non-linear method based on the eigenvectors of the graph Laplacian. We validate our approach using a data set of seismic events that occurred in Idaho, Montana, Wyoming and Utah between 2005 and 2006. Our approach outperforms methods based on singular-spectrum analysis, wavelet analysis and short-term average/long-term average (STA/LTA).

This paper presents the Cogito submission to the Interspeech Computational Paralinguistics Challenge (ComParE), for the second sub-challenge. The aim of this second sub-challenge is to recognize self-assessed affect from short clips of speechcontaining audio data. We adopt a sequence classification-based approach where we use a long-short term memory (LSTM) network for modeling the evolution of low-level spectral coefficients, with added attention mechanism to emphasize salient regions of the audio clip. Additionally to deal with the underrepresentation of the negative valence class we use a combination of mitigation strategies including oversampling and loss function weighting. Our experiments demonstrate improvements in detection accuracy when including the attention mechanism and class balancing strategies in combination, with the best models outperforming the best single challenge baseline model.

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