Hao Ji

Hao Ji, Wenjian Yu, Yaohang Li

In this paper, we present a Rank Revealing Randomized Singular Value Decomposition (R3SVD) algorithm to incrementally construct a low-rank approximation of a potentially large matrix while adaptively estimating the appropriate rank that can capture most of the actions of the matrix. Starting from a low-rank approximation with an initial guessed rank, R3SVD adopts an orthogonal Gaussian sampling approach to obtain the dominant subspace within the leftover space, which is used to add up to the existing low-rank approximation. Orthogonal Gaussian sampling is repeated until an appropriate low-rank approximation with satisfactory accuracy, measured by the overall energy percentage of the original matrix, is obtained. While being a fast algorithm, R3SVD is also a memory-aware algorithm where the computational process can be decomposed into a series of sampling tasks that use constant amount of memory. Numerical examples in image compression and matrix completion are used to demonstrate the effectiveness of R3SVD in low-rank approximation.

Hao Ji, Seth H. Weinberg, Yaohang Li

In this paper, we revisit the generalized block power methods for approximating the eigenvector associated with $λ_1 = 1$ of a Markov chain transition matrix. Our analysis of the block power method shows that when $s$ linearly independent probability vectors are used as the initial block, the convergence of the block power method to the stationary distribution depends on the magnitude of the $(s+1)$th dominant eigenvalue $λ_{s+1}$ of $P$ instead of that of $λ_2$ in the power method. Therefore, the block power method with block size $s$ is particularly effective for transition matrices where $|λ_{s+1}|$ is well separated from $λ_1 = 1$ but $|λ_2|$ is not. This approach is particularly useful when visiting the elements of a large transition matrix is the main computational bottleneck over matrix--vector multiplications, where the block power method can effectively reduce the total number of times to pass over the matrix. To further reduce the overall computational cost, we combine the block power method with a sliding window scheme, taking advantage of the subsequent vectors of the latest $s$ iterations to assemble the block matrix. The sliding window scheme correlates vectors in the sliding window to quickly remove the influences from the eigenvalues whose magnitudes are smaller than $|λ_{s}|$ to reduce the overall number of matrix--vector multiplications to reach convergence. Finally, we compare the effectiveness of these methods in a Markov chain model representing a stochastic luminal calcium release site.

Ji Fang, Vincent CS Lee, Hao Ji et al.

The utilization of digital health has increased recently, and these services provide extensive guidance to encourage users to exercise frequently by setting daily exercise goals to promote a healthy lifestyle. These comprehensive guides evolved from the consideration of various personalized behavioral factors. Nevertheless, existing approaches frequently neglect the users dynamic behavior and the changing in their health conditions. This study aims to fill this gap by developing a machine learning algorithm that dynamically updates auto-suggestion exercise goals using retrospective data and realistic behavior trajectory. We conducted a methodological study by designing a deep reinforcement learning algorithm to evaluate exercise performance, considering fitness-fatigue effects. The deep reinforcement learning algorithm combines deep learning techniques to analyse time series data and infer user exercise behavior. In addition, we use the asynchronous advantage actor-critic algorithm for reinforcement learning to determine the optimal exercise intensity through exploration and exploitation. The personalized exercise data and biometric data used in this study were collected from publicly available datasets, encompassing walking, sports logs, and running. In our study, we conducted The statistical analyses/inferential tests to compare the effectiveness of machine learning approach in exercise goal setting across different exercise goal setting strategies.

David Ge, Hao Ji

Self-organizing systems consist of autonomous agents that can perform complex tasks and adapt to dynamic environments without a central controller. Prior research often relies on reinforcement learning to enable agents to gain the skills needed for task completion, such as in the box-pushing environment. However, when agents push from opposing directions during exploration, they tend to exert equal and opposite forces on the box, resulting in minimal displacement and inefficient training. This paper proposes a model called Shared Pool of Information (SPI), which enables information to be accessible to all agents and facilitates coordination, reducing force conflicts among agents and enhancing exploration efficiency. Through computer simulations, we demonstrate that SPI not only expedites the training process but also requires fewer steps per episode, significantly improving the agents' collaborative effectiveness.

Puyu Yang, Laifa Tao, Zijian Huang et al.

With the rapid advancement of generative artificial intelligence, large language models (LLMs) are increasingly adopted in industrial domains, offering new opportunities for Prognostics and Health Management (PHM). These models help address challenges such as high development costs, long deployment cycles, and limited generalizability. However, despite the growing synergy between PHM and LLMs, existing evaluation methodologies often fall short in structural completeness, dimensional comprehensiveness, and evaluation granularity. This hampers the in-depth integration of LLMs into the PHM domain. To address these limitations, this study proposes PHM-Bench, a novel three-dimensional evaluation framework for PHM-oriented large models. Grounded in the triadic structure of fundamental capability, core task, and entire lifecycle, PHM-Bench is tailored to the unique demands of PHM system engineering. It defines multi-level evaluation metrics spanning knowledge comprehension, algorithmic generation, and task optimization. These metrics align with typical PHM tasks, including condition monitoring, fault diagnosis, RUL prediction, and maintenance decision-making. Utilizing both curated case sets and publicly available industrial datasets, our study enables multi-dimensional evaluation of general-purpose and domain-specific models across diverse PHM tasks. PHM-Bench establishes a methodological foundation for large-scale assessment of LLMs in PHM and offers a critical benchmark to guide the transition from general-purpose to PHM-specialized models.

Eitan Rothberg, Tingting Chen, Luo Jie et al.

Today's state-of-the-art image classifiers fail to correctly classify carefully manipulated adversarial images. In this work, we develop a new, localized adversarial attack that generates adversarial examples by imperceptibly altering the backgrounds of normal images. We first use this attack to highlight the unnecessary sensitivity of neural networks to changes in the background of an image, then use it as part of a new training technique: localized adversarial training. By including locally adversarial images in the training set, we are able to create a classifier that suffers less loss than a non-adversarially trained counterpart model on both natural and adversarial inputs. The evaluation of our localized adversarial training algorithm on MNIST and CIFAR-10 datasets shows decreased accuracy loss on natural images, and increased robustness against adversarial inputs.

Bin Liu, Hao Ji, Yi Dai

In this paper, we describe work in progress towards a real-time vision-based traffic flow prediction (TFP) system. The proposed method consists of three elemental operators, that are dynamic texture model based motion segmentation, feature extraction and Gaussian process (GP) regression. The objective of motion segmentation is to recognize the target regions covering the moving vehicles in the sequence of visual processes. The feature extraction operator aims to extract useful features from the target regions. The extracted features are then mapped to the number of vehicles through the operator of GP regression. A training stage using historical visual data is required for determining the parameter values of the GP. Using a low-resolution visual data set, we performed preliminary evaluations on the performance of the proposed method. The results show that our method beats a benchmark solution based on Gaussian mixture model, and has the potential to be developed into qualified and practical solutions to real-time TFP.