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By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

This work is dedicated to the topological analysis of complex transitional networks for dynamic state detection. Transitional networks are formed from time series data and they leverage graph theory tools to reveal information about the…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Modern deep neural networks are powerful predictive tools yet often lack valid inference for causal parameters, such as treatment effects or entire survival curves. While frameworks like Double Machine Learning (DML) and Targeted Maximum…

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…

Deep learning is widely applied in computer-aided pathological diagnosis, which alleviates the pathologist workload and provide timely clinical analysis. However, most models generally require large-scale annotated data for training, which…

Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric…

Latent Dirichlet Allocation (LDA) is a three-level hierarchical Bayesian model for topic inference. In spite of its great success, inferring the latent topic distribution with LDA is time-consuming. Motivated by the transfer learning…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Feature space is an environment where data points are vectorized to represent the original dataset. Reconstructing a good feature space is essential to augment the AI power of data, improve model generalization, and increase the…

The structural characterization of hetero-aggregates in 3D is of great interest, e.g., for deriving process-structure or structure-property relationships. However, since 3D imaging techniques are often difficult to perform as well as time…

Recent work has shown the ability to learn generative models for 3D shapes from only unstructured 2D images. However, training such models requires differentiating through the rasterization step of the rendering process, therefore past work…

Deep learning has gained broad interest in remote sensing image scene classification thanks to the effectiveness of deep neural networks in extracting the semantics from complex data. However, deep networks require large amounts of training…

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

In this paper, we present a novel approach to perform deep neural networks layer-wise weight initialization using Linear Discriminant Analysis (LDA). Typically, the weights of a deep neural network are initialized with: random values,…

The performance of neural network models is often limited by the availability of big data sets. To treat this problem, we survey and develop novel synthetic data generation and augmentation techniques for enhancing low/zero-sample learning…

Training Deep neural networks (DNNs) on noisy labeled datasets is a challenging problem, because learning on mislabeled examples deteriorates the performance of the network. As the ground truth availability is limited with real-world noisy…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…