This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the L2 norm) and (ii) an established topological distance between persistence diagrams (the L2-Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.

We explore techniques for eye gaze estimation using machine learning. Eye gaze estimation is a common problem for various behavior analysis and human-computer interfaces. The purpose of this work is to discuss various model types for eye gaze estimation and present the results from predicting gaze direction using eye landmarks in unconstrained settings. In unconstrained real-world settings, feature-based and model-based methods are outperformed by recent appearance-based methods due to factors like illumination changes and other visual artifacts. We discuss a learning-based method for eye region landmark localization trained exclusively on synthetic data. We discuss how to use detected landmarks as input to iterative model-fitting and lightweight learning-based gaze estimation methods and how to use the model for person-independent and personalized gaze estimations.

Motivation: Cancer is heterogeneous, affecting the precise approach to personalized treatment. Accurate subtyping can lead to better survival rates for cancer patients. High-throughput technologies provide multiple omics data for cancer subtyping. However, precise cancer subtyping remains challenging due to the large amount and high dimensionality of omics data. Results: This study proposed Subtype-Former, a deep learning method based on MLP and Transformer Block, to extract the low-dimensional representation of the multi-omics data. K-means and Consensus Clustering are also used to achieve accurate subtyping results. We compared Subtype-Former with the other state-of-the-art subtyping methods across the TCGA 10 cancer types. We found that Subtype-Former can perform better on the benchmark datasets of more than 5000 tumors based on the survival analysis. In addition, Subtype-Former also achieved outstanding results in pan-cancer subtyping, which can help analyze the commonalities and differences across various cancer types at the molecular level. Finally, we applied Subtype-Former to the TCGA 10 types of cancers. We identified 50 essential biomarkers, which can be used to study targeted cancer drugs and promote the development of cancer treatments in the era of precision medicine.

In this paper, we study private optimization problems for non-smooth convex functions $F(x)=\mathbb{E}_i f_i(x)$ on $\mathbb{R}^d$. We show that modifying the exponential mechanism by adding an $\ell_2^2$ regularizer to $F(x)$ and sampling from $\pi(x)\propto \exp(-k(F(x)+\mu\|x\|_2^2/2))$ recovers both the known optimal empirical risk and population loss under $(\epsilon,\delta)$-DP. Furthermore, we show how to implement this mechanism using $\widetilde{O}(n \min(d, n))$ queries to $f_i(x)$ for the DP-SCO where $n$ is the number of samples/users and $d$ is the ambient dimension. We also give a (nearly) matching lower bound $\widetilde{\Omega}(n \min(d, n))$ on the number of evaluation queries. Our results utilize the following tools that are of independent interest: (1) We prove Gaussian Differential Privacy (GDP) of the exponential mechanism if the loss function is strongly convex and the perturbation is Lipschitz. Our privacy bound is \emph{optimal} as it includes the privacy of Gaussian mechanism as a special case and is proved using the isoperimetric inequality for strongly log-concave measures. (2) We show how to sample from $\exp(-F(x)-\mu \|x\|^2_2/2)$ for $G$-Lipschitz $F$ with $\eta$ error in total variation (TV) distance using $\widetilde{O}((G^2/\mu) \log^2(d/\eta))$ unbiased queries to $F(x)$. This is the first sampler whose query complexity has \emph{polylogarithmic dependence} on both dimension $d$ and accuracy $\eta$.

Background In hierarchical clustering, one seeks a recursive partitioning of the data that captures clustering information at different levels of granularity. Classical work on the subject mostly takes an algorithmic perspective. In particular, various iterative clustering methods have been developed, including the well-known bottom-up dissimilarity-based approaches single linkage, average linkage, etc. (see, e.g., [Mur12, Chapter 25]). Recent work on dissimilarity-based hierarchical clustering has emphasized a different, optimization-based, perspective. This has led to the introduction of global objective functions for this classical problem [Das16].

Exemplar-free Class-incremental Learning (CIL) is a challenging problem because rehearsing data from previous phases is strictly prohibited, causing catastrophic forgetting of Deep Neural Networks (DNNs). In this paper, we present iVoro, a holistic framework for CIL, derived from computational geometry. We found Voronoi Diagram (VD), a classical model for space subdivision, is especially powerful for solving the CIL problem, because VD itself can be constructed favorably in an incremental manner -- the newly added sites (classes) will only affect the proximate classes, making the non-contiguous classes hardly forgettable. Further, in order to find a better set of centers for VD construction, we colligate DNN with VD using Power Diagram and show that the VD structure can be optimized by integrating local DNN models using a divide-and-conquer algorithm. Moreover, our VD construction is not restricted to the deep feature space, but is also applicable to multiple intermediate feature spaces, promoting VD to be multi-centered VD (CIVD) that efficiently captures multi-grained features from DNN. Importantly, iVoro is also capable of handling uncertainty-aware test-time Voronoi cell assignment and has exhibited high correlations between geometric uncertainty and predictive accuracy (up to ~0.9). Putting everything together, iVoro achieves up to 25.26%, 37.09%, and 33.21% improvements on CIFAR-100, TinyImageNet, and ImageNet-Subset, respectively, compared to the state-of-the-art non-exemplar CIL approaches. In conclusion, iVoro enables highly accurate, privacy-preserving, and geometrically interpretable CIL that is particularly useful when cross-phase data sharing is forbidden, e.g. in medical applications. Our code is available at https://machunwei.github.io/ivoro.

Training machine learning models on massive datasets incurs substantial computational costs. To alleviate such costs, there has been a sustained effort to develop data-efficient training methods that can carefully select subsets of the training examples that generalize on par with the full training data. However, existing methods are limited in providing theoretical guarantees for the quality of the models trained on the extracted subsets, and may perform poorly in practice. We propose AdaCore, a method that leverages the geometry of the data to extract subsets of the training examples for efficient machine learning. The key idea behind our method is to dynamically approximate the curvature of the loss function via an exponentially-averaged estimate of the Hessian to select weighted subsets (coresets) that provide a close approximation of the full gradient preconditioned with the Hessian. We prove rigorous guarantees for the convergence of various first and second-order methods applied to the subsets chosen by AdaCore. Our extensive experiments show that AdaCore extracts coresets with higher quality compared to baselines and speeds up training of convex and non-convex machine learning models, such as logistic regression and neural networks, by over 2.9x over the full data and 4.5x over random subsets.

The acquisition and evaluation of pavement surface data play an essential role in pavement condition evaluation. In this paper, an efficient and effective end-to-end network for automatic pavement crack segmentation, called RHA-Net, is proposed to improve the pavement crack segmentation accuracy. The RHA-Net is built by integrating residual blocks (ResBlocks) and hybrid attention blocks into the encoder-decoder architecture. The ResBlocks are used to improve the ability of RHA-Net to extract high-level abstract features. The hybrid attention blocks are designed to fuse both low-level features and high-level features to help the model focus on correct channels and areas of cracks, thereby improving the feature presentation ability of RHA-Net. An image data set containing 789 pavement crack images collected by a self-designed mobile robot is constructed and used for training and evaluating the proposed model. Compared with other state-of-the-art networks, the proposed model achieves better performance and the functionalities of adding residual blocks and hybrid attention mechanisms are validated in a comprehensive ablation study. Additionally, a light-weighted version of the model generated by introducing depthwise separable convolution achieves better a performance and a much faster processing speed with 1/30 of the number of U-Net parameters. The developed system can segment pavement crack in real-time on an embedded device Jetson TX2 (25 FPS). The video taken in real-time experiments is released at https://youtu.be/3XIogk0fiG4.

This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with possibly non-white and low-rank excitation. While the mixture model is motivated from practical scenarios, it presents significant challenges to prior graph learning methods. As a remedy, we consider an inference problem focusing on the node centrality of graphs. We design an expectation-maximization (EM) algorithm with a unique low-rank plus sparse prior derived from low pass signal property. We propose a novel online EM algorithm for inference from streaming data. As an example, we extend the online algorithm to detect if the signals are generated from an abnormal graph. We show that the proposed algorithms converge to a stationary point of the maximum-a-posterior (MAP) problem. Numerical experiments support our analysis.

Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removes many algorithm metaparameters and identifies a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multiple co-existing dynamical states (attractors). We compare the next-generation and traditional reservoir computer using metrics quantifying the geometry of the ground-truth and forecasted attractors. For the studied four-dimensional system, the next-generation reservoir computing approach uses $\sim 1.7 \times$ less training data, requires $10^3 \times$ shorter `warm up' time, has fewer metaparameters, and has an $\sim 100\times$ higher accuracy in predicting the co-existing attractor characteristics in comparison to a traditional reservoir computer. Furthermore, we demonstrate that it predicts the basin of attraction with high accuracy. This work lends further support to the superior learning ability of this new machine learning algorithm for dynamical systems.