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Berry phases offer a geometric perspective on wave propagation and are key to designing materials with topological wave transport. However, controlling Berry phases is challenging due to their dependence on global integrals over the Brillouin zone, making differentiation difficult. We present an adjoint-based method for efficiently computing the gradient of the Berry phase with respect to system parameters, involving only one forward and one adjoint calculation. This approach enables the use of advanced optimization techniques, such as topology optimization, to design new materials with tailored topological wave properties., Comment: 9 pages, 1 figure

Detecting arbitrarily shaped clusters in high-dimensional noisy data is challenging for current clustering methods. We introduce SHADE (Structure-preserving High-dimensional Analysis with Density-based Exploration), the first deep clustering algorithm that incorporates density-connectivity into its loss function. Similar to existing deep clustering algorithms, SHADE supports high-dimensional and large data sets with the expressive power of a deep autoencoder. In contrast to most existing deep clustering methods that rely on a centroid-based clustering objective, SHADE incorporates a novel loss function that captures density-connectivity. SHADE thereby learns a representation that enhances the separation of density-connected clusters. SHADE detects a stable clustering and noise points fully automatically without any user input. It outperforms existing methods in clustering quality, especially on data that contain non-Gaussian clusters, such as video data. Moreover, the embedded space of SHADE is suitable for visualization and interpretation of the clustering results as the individual shapes of the clusters are preserved., Comment: Short version accepted at ICDM 2024

Over the last decade, the Dip-test of unimodality has gained increasing interest in the data mining community as it is a parameter-free statistical test that reliably rates the modality in one-dimensional samples. It returns a so called Dip-value and a corresponding probability for the sample's unimodality (Dip-p-value). These two values share a sigmoidal relationship. However, the specific transformation is dependent on the sample size. Many Dip-based clustering algorithms use bootstrapped look-up tables translating Dip- to Dip-p-values for a certain limited amount of sample sizes. We propose a specifically designed sigmoid function as a substitute for these state-of-the-art look-up tables. This accelerates computation and provides an approximation of the Dip- to Dip-p-value transformation for every single sample size. Further, it is differentiable and can therefore easily be integrated in learning schemes using gradient descent. We showcase this by exploiting our function in a novel subspace clustering algorithm called Dip'n'Sub. We highlight in extensive experiments the various benefits of our proposal.

High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of approaches are able to identify such non-redundant clusterings. However, most of these methods require the user to specify the expected number of subspaces and clusters for each subspace. Stating these values is a non-trivial problem and usually requires detailed knowledge of the input dataset. In this paper, we propose a framework that utilizes the Minimum Description Length Principle (MDL) to detect the number of subspaces and clusters per subspace automatically. We describe an efficient procedure that greedily searches the parameter space by splitting and merging subspaces and clusters within subspaces. Additionally, an encoding strategy is introduced that allows us to detect outliers in each subspace. Extensive experiments show that our approach is highly competitive to state-of-the-art methods.

Anomaly detection in imbalanced datasets is a frequent and crucial problem, especially in the medical domain where retrieving and labeling irregularities is often expensive. By combining the generative stability of a $\beta$-variational autoencoder (VAE) with the discriminative strengths of generative adversarial networks (GANs), we propose a novel model, $\beta$-VAEGAN. We investigate methods for composing anomaly scores based on the discriminative and reconstructive capabilities of our model. Existing work focuses on linear combinations of these components to determine if data is anomalous. We advance existing work by training a kernelized support vector machine (SVM) on the respective error components to also consider nonlinear relationships. This improves anomaly detection performance, while allowing faster optimization. Lastly, we use the deviations from the Gaussian prior of $\beta$-VAEGAN to form a novel anomaly score component. In comparison to state-of-the-art work, we improve the $F_1$ score during anomaly detection from 0.85 to 0.92 on the widely used MITBIH Arrhythmia Database., Comment: accepted at AI4TS @ ICDMW 2023

The development of tissue-engineered cardiovascular implants can improve the lives of large segments of our society who suffer from cardiovascular diseases. Regenerative tissues are fabricated using a process called tissue maturation. Furthermore, it is highly challenging to produce cardiovascular regenerative implants with sufficient mechanical strength to withstand the loading conditions within the human body. Therefore, biohybrid implants for which the regenerative tissue is reinforced by standard reinforcement material (e.g. textile or 3d printed scaffold) can be an interesting solution. In silico models can significantly contribute to characterizing, designing, and optimizing biohybrid implants. The first step towards this goal is to develop a computational model for the maturation process of tissue-engineered implants. This paper focuses on the mechanical modeling of textile-reinforced tissue-engineered cardiovascular implants. First, we propose an energy-based approach to compute the collagen evolution during the maturation process. Then, we apply the concept of structural tensors to model the anisotropic behavior of the extracellular matrix and the textile scaffold. Next, the newly developed material model is embedded into a special solid-shell finite element formulation with reduced integration. Finally, we use our framework to compute two structural problems: a pressurized shell construct and a tubular-shaped heart valve. The results show the ability of the model to predict collagen growth in response to the boundary conditions applied during the maturation process. Consequently, we can predict the implant's mechanical response, such as the deformation and stresses of the implant., Comment: Preprint submitted to Elsevier

Although deep neural networks have shown well-performance in various tasks, the poor interpretability of the models is always criticized. In the paper, we propose a new interpretable neural network method, by embedding neurons into the semantic space to extract their intrinsic global semantics. In contrast to previous methods that probe latent knowledge inside the model, the proposed semantic vector externalizes the latent knowledge to static knowledge, which is easy to exploit. Specifically, we assume that neurons with similar activation are of similar semantic information. Afterwards, semantic vectors are optimized by continuously aligning activation similarity and semantic vector similarity during the training of the neural network. The visualization of semantic vectors allows for a qualitative explanation of the neural network. Moreover, we assess the static knowledge quantitatively by knowledge distillation tasks. Empirical experiments of visualization show that semantic vectors describe neuron activation semantics well. Without the sample-by-sample guidance from the teacher model, static knowledge distillation exhibit comparable or even superior performance with existing relation-based knowledge distillation methods.

The field of deep clustering combines deep learning and clustering to learn representations that improve both the learned representation and the performance of the considered clustering method. Most existing deep clustering methods are designed for a single clustering method, e.g., k-means, spectral clustering, or Gaussian mixture models, but it is well known that no clustering algorithm works best in all circumstances. Consensus clustering tries to alleviate the individual weaknesses of clustering algorithms by building a consensus between members of a clustering ensemble. Currently, there is no deep clustering method that can include multiple heterogeneous clustering algorithms in an ensemble to update representations and clusterings together. To close this gap, we introduce the idea of a consensus representation that maximizes the agreement between ensemble members. Further, we propose DECCS (Deep Embedded Clustering with Consensus representationS), a deep consensus clustering method that learns a consensus representation by enhancing the embedded space to such a degree that all ensemble members agree on a common clustering result. Our contributions are the following: (1) We introduce the idea of learning consensus representations for heterogeneous clusterings, a novel notion to approach consensus clustering. (2) We propose DECCS, the first deep clustering method that jointly improves the representation and clustering results of multiple heterogeneous clustering algorithms. (3) We show in experiments that learning a consensus representation with DECCS is outperforming several relevant baselines from deep clustering and consensus clustering. Our code can be found at https://gitlab.cs.univie.ac.at/lukas/deccs, Comment: Accepted by the IEEE International Conference on Data Mining (ICDM) 2022

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular-spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10\% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons., Comment: 18 pages, 7 figures

An alternative approach to ultrasound computed tomography (USCT) for medical imaging is proposed, with the intent to (i) shorten acquisition time for devices with a large number of emitters, (ii) eliminate the calibration step, and (iii) suppress instrument noise. Inspired by seismic ambient field interferometry, the method rests on the active excitation of diffuse ultrasonic wavefields and the extraction of deterministic travel time information by inter-station correlation. To reduce stochastic errors and accelerate convergence, ensemble interferograms are obtained by phase-weighted stacking of observed and computed correlograms, generated with identical realizations of random sources. Mimicking a breast imaging setup, the accuracy of the travel time measurements as a function of the number of emitters and random realizations can be assessed both analytically and with spectral-element simulations for realistic breast phantoms. The results warrant tomographic reconstructions with straight- or bent-ray approaches, where the effect of inherent stochastic fluctuations can be made significantly smaller than the effect of subjective choices on regularisation. This work constitutes a first conceptual study and a necessary prelude to future implementations., Comment: 18 pages, 9 Figures

Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the real-world networks can be reflected by dynamical transfer behaviors among nodes. This paper proposes a network embedding framework to capture the transfer behaviors on structured networks via deep prediction models. We first design a degree-weight biased random walk model to capture the transfer behaviors on the network. Then a deep network embedding method is introduced to preserve the transfer possibilities among the nodes. A network structure embedding layer is added into conventional deep prediction models, including Long Short-Term Memory Network and Recurrent Neural Network, to utilize the sequence prediction ability. To keep the local network neighborhood, we further perform a Laplacian supervised space optimization on the embedding feature representations. Experimental studies are conducted on various datasets including social networks, citation networks, biomedical network, collaboration network and language network. The results show that the learned representations can be effectively used as features in a variety of tasks, such as clustering, visualization, classification, reconstruction and link prediction, and achieve promising performance compared with state-of-the-arts.

To fully exploit the performance potential of modern multi-core processors, machine learning and data mining algorithms for big data must be parallelized in multiple ways. Today's CPUs consist of multiple cores, each following an independent thread of control, and each equipped with multiple arithmetic units which can perform the same operation on a vector of multiple data objects. Graph embedding, i.e. converting the vertices of a graph into numerical vectors is a data mining task of high importance and is useful for graph drawing (low-dimensional vectors) and graph representation learning (high-dimensional vectors). In this paper, we propose MulticoreGEMPE (Graph Embedding by Minimizing the Predictive Entropy), an information-theoretic method which can generate low and high-dimensional vectors. MulticoreGEMPE applies MIMD (Multiple Instructions Multiple Data, using OpenMP) and SIMD (Single Instructions Multiple Data, using AVX-512) parallelism. We propose general ideas applicable in other graph-based algorithms like \emph{vectorized hashing} and \emph{vectorized reduction}. Our experimental evaluation demonstrates the superiority of our approach.

Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures, computer graphics, numerical simulation, cryptographics and can be used to make various algorithms cache-oblivious. In this paper, we describe some details of the Hilbert-curve. We define the Hilbert-curve in terms of a finite automaton of Mealy-type which determines from the two-dimensional coordinate space the Hilbert order value and vice versa in a logarithmic number of steps. And we define a context-free grammar to generate the whole curve in a time which is linear in the number of generated coordinate/order value pairs, i.e. a constant time per coordinate pair or order value. We also review two different strategies which enable the generation of curves without the usual restriction to square-like grids where the side-length is a power of two. Finally, we elaborate on a few applications, namely matrix multiplication, Cholesky decomposition, the Floyd-Warshall algorithm, k-Means clustering, and the similarity join.

Large-scale PDE simulations using high-order finite-element methods on unstructured meshes are an indispensable tool in science and engineering. The widely used open-source PETSc library offers an efficient representation of generic unstructured meshes within its DMPlex module. This paper details our recent implementation of parallel mesh reading and topological interpolation (computation of edges and faces from a cell-vertex mesh) into DMPlex. We apply these developments to seismic wave propagation scenarios on Mars as an example application. The principal motivation is to overcome single-node memory limits and reach mesh sizes which were impossible before. Moreover, we demonstrate that scalability of I/O and topological interpolation goes beyond 12'000 cores, and memory-imposed limits on mesh size vanish., Comment: 23 pages, 11 figures

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination as Compactness. Further, we propose LOCLU to optimize the Compactness score. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.