The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce port-Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.

Heterogeneous data is common in many real-world machine learning applications, such as healthcare, market analysis, environmental sciences, and social media analysis. In these domains, data is often represented in different modalities and, most of the time, in non-vectorial formats, like text, images, and video. Traditional machine learning algorithms are often limited in their ability to effectively analyze and learn from such diverse data types. In this paper, we propose two approaches for such heterogeneous data analysis: static and adaptive subspace kernel fusion. The first approach is a kernel-based method extracting the essential parts of the subspace of each input modality and creating one single fused representation of the data. The second approach utilizes an adaptation step by integrating the weighting of spectral properties into the fusion process in order to improve the data’s representation with respect to a given classification task. Our proposed methods are evaluated on several multi-modal, heterogeneous data sets and demonstrate significant performance improvement compared to other methods in the field. Our results highlight the importance of fusing the underlying subspace information of heterogeneous data for achieving superior performance in machine learning tasks.

Data and information are nowadays frequently available in multiple modalities like different sensor signals, textual descriptions, graph structures, and other formats.The maximum information from these heterogeneous representations can be obtained by fusing the various modalities by specific embeddings or proximity measures.Current approaches are widely limited in the fusion model and the applied measures, especially when the given data is non-vectorial.We propose a model to learn the spectral properties of the different inner product representations in a joined optimization problem.The approach is evaluated on various multimodal data and compared to modern multiple-kernel learning and baseline techniques.* MM and MR are supported by the Bavarian HighTech agenda and the Würzburg Center for Artificial Intelligence and Robotics (CAIRO).Additionally, we thank Dr. Benjamin Paaßen for the invaluable discussions about this research topic during a fantastic boating trip.

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently pro-posed method MEKA [1] effectively employs two common assumptions in Hilbert spaces: the low-rank property of an inner product matrix obtained from a shift-invariant kernel function and a data compactness hypothesis by means of an inherent block-cluster structure. In this work, we extend MEKA to be applicable not only for shift-invariant kernels but also for non-stationary kernels like polynomial kernels and an extreme learning kernel. We also address in detail how to handle non-positive semi-definite kernel functions within MEKA, either caused by the approximation itself or by the intentional use of general kernel functions. We present a Lanczos-based estimation of a spectrum shift to develop a stable positive semi-definite MEKA approximation, also usable in classical convex optimization frameworks. Furthermore, we support our findings with theoretical considerations and a variety of experiments on synthetic and real-world data.

The interest in time series analysis is rapidly increasing, providing new challenges for machine learning.Over many decades, Dynamic Time Warping (DTW) is referred to as the de facto standard distance measure for time series and the tool of choice when analyzing such data.Nevertheless, DTW has two major drawbacks: (a) it is non-metric and therefore hard to handle by standard machine learning techniques, and (b) it is not well suited for multi-dimensional time series.For this purpose, we propose a multi-perspective embedding of the time series into a complex-valued vector space and the evaluation by a model that is able to handle complex-valued data.The approach is evaluated on various multi-dimensional time series data and with different classifier techniques.