Clustering analysis of sequence data continues to address many applications in engineering design, aided with the rapid growth of machine learning in applied science. This paper presents an unsupervised machine learning algorithm to extract defining characteristics of earthquake ground-motion spectra, also called latent features, to aid in ground-motion selection (GMS). In this context, a latent feature is a low-dimensional machine-discovered spectral characteristic learned through nonlinear relationships of a neural network autoencoder. Machine discovered latent features can be combined with traditionally defined intensity measures and clustering can be performed to select a representative subgroup from a large ground-motion suite. The objective of efficient GMS is to choose characteristic records representative of what the structure will probabilistically experience in its lifetime. Three examples are presented to validate this approach, including the use of synthetic and field recorded ground-motion datasets. The presented deep embedding clustering of ground-motion spectra has three main advantages: 1. defining characteristics the represent the sparse spectral content of ground-motions are discovered efficiently through training of the autoencoder, 2. domain knowledge is incorporated into the machine learning framework with conditional variables in the deep embedding scheme, and 3. method exhibits excellent performance when compared to a benchmark seismic hazard analysis.

In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited capacity in representing graphs of varying structures. A promising candidate for the faithful embedding of data with varying structure is product manifolds of component spaces of different geometries (spherical, hyperbolic, or euclidean). In this paper, we take a closer look at the structure of product manifold embedding spaces and argue that each component space in a product contributes differently to expressing structures in the input graph, hence should be weighted accordingly. This is different from previous works which consider the roles of different components equally. We then propose WEIGHTED-PM, a data-driven method for learning embedding of heterogeneous graphs in weighted product manifolds. Our method utilizes the topological information of the input graph to automatically determine the weight of each component in product spaces. Extensive experiments on synthetic and real-world graph datasets demonstrate that WEIGHTED-PM is capable of learning better graph representations with lower geometric distortion from input data, and performs better on multiple downstream tasks, such as word similarity learning, top-$k$ recommendation, and knowledge graph embedding.

A real-world graph has a complex topology structure, which is often formed by the interaction of different latent factors. Disentanglement of these latent factors can effectively improve the robustness and interpretability of node representation of the graph. However, most existing methods lack consideration of the intrinsic differences in links caused by factor entanglement. In this paper, we propose an Adversarial Disentangled Graph Convolutional Network (ADGCN) for disentangled graph representation learning. Specifically, a dynamic multi-component convolution layer is designed to achieve micro-disentanglement by inferring latent components that caused links between nodes. On the basis of micro-disentanglement, we further propose a macro-disentanglement adversarial regularizer that improves the separability between component distributions, thus restricting interdependence among components. Additionally, to learn collaboratively a better disentangled representation and topological structure, a diversity preserving node sampling-based progressive refinement of graph structure is proposed. The experimental results on various real-world graph data verify that our ADGCN obtains remarkably more favorable performance over currently available alternatives.