arXiv subjects

Jiaji Su

Publications and source records attributed to Jiaji Su.

7 recordsLinked to original sources

arXiv2026

Manifold Fitting: A Review of Methods and Applications

With data growing in scale and complexity, traditional linear dimension reduction techniques are becoming inadequate in some settings. Manifold fitting offers an important alternative by capturing low-dimensional latent geometric structures within high-dimensional spaces. This capability allows it to support downstream analysis in complex data settings. In this review, we explore the development and applications of manifold fitting. First, we introduce the basic concepts of manifold fitting and distinguish it from related techniques such as manifold embedding and denoising. We review the development of manifold fitting with three distinct stages: early nonparametric statistical methods, insights from mathematical analysis, and contemporary practical statistical approaches. Furthermore, we present diverse applications of manifold fitting, particularly in neural networks and bioinformatics, which illustrate its utility in complex data scenarios. Despite considerable progress, manifold fitting remains a fertile area for research. Many theoretical and practical questions remain unanswered, and ongoing investigations will further clarify its role in modern data science as a geometric tool for a wide range of data analysis challenges.

stat.ME↗

arXiv2026

Data-centric Design of Learning-based Surgical Gaze Perception Models in Multi-Task Simulation

In robot-assisted minimally invasive surgery (RMIS), reduced haptic feedback and depth cues increase reliance on expert visual perception, motivating gaze-guided training and learning-based surgical perception models. However, operative expert gaze is costly to collect, and it remains unclear how the source of gaze supervision, both expertise level (intermediate vs. novice) and perceptual modality (active execution vs. passive viewing), shapes what attention models learn. We introduce a paired active-passive, multi-task surgical gaze dataset collected on the da Vinci SimNow simulator across four drills. Active gaze was recorded during task execution using a VR headset with eye tracking, and the corresponding videos were reused as stimuli to collect passive gaze from observers, enabling controlled same-video comparisons. We quantify skill- and modality-dependent differences in gaze organization and evaluate the substitutability of passive gaze for operative supervision using fixation density overlap analyses and single-frame saliency modeling. Across settings, MSI-Net produced stable, interpretable predictions, whereas SalGAN was unstable and often poorly aligned with human fixations. Models trained on passive gaze recovered a substantial portion of intermediate active attention, but with predictable degradation, and transfer was asymmetric between active and passive targets. Notably, novice passive labels approximated intermediate-passive targets with limited loss on higher-quality demonstrations, suggesting a practical path for scalable, crowd-sourced gaze supervision in surgical coaching and perception modeling.

cs.RO↗

arXiv2025

Principal Decomposition with Nested Submanifolds

Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To address this issue, we introduce a novel nonlinear decomposition technique called the principal nested submanifolds, which builds on the foundational concepts of principal component analysis. This method exploits the local geometric information of data sets by projecting samples onto a series of nested principal submanifolds with progressively decreasing dimensions. It effectively isolates complex information within the data in a backward stepwise manner by targeting variations associated with smaller eigenvalues in local covariance matrices. Unlike previous methods, the resulting subspaces are smooth manifolds, not merely linear spaces or special shape spaces. Validated through extensive simulation studies and applied to real-world RNA sequencing data, our approach surpasses existing models in delineating intricate nonlinear structures. It provides more flexible subspace constraints that improve the extraction of significant data components and facilitate noise reduction. This innovative approach not only advances the non-Euclidean statistical analysis of data with low-dimensional intrinsic structure within Euclidean spaces, but also offers new perspectives for dealing with high-dimensional noisy data sets in fields such as bioinformatics and machine learning.

stat.ME↗

arXiv2024

Three Degree-of-Freedom Soft Continuum Kinesthetic Haptic Display for Telemanipulation Via Sensory Substitution at the Finger

Sensory substitution is an effective approach for displaying stable haptic feedback to a teleoperator under time delay. The finger is highly articulated, and can sense movement and force in many directions, making it a promising location for sensory substitution based on kinesthetic feedback. However, existing finger kinesthetic devices either provide only one-degree-of-freedom feedback, are bulky, or have low force output. Soft pneumatic actuators have high power density, making them suitable for realizing high force kinesthetic feedback in a compact form factor. We present a soft pneumatic handheld kinesthetic feedback device for the index finger that is controlled using a constant curvature kinematic model. \changed{It has respective position and force ranges of +-3.18mm and +-1.00N laterally, and +-4.89mm and +-6.01N vertically, indicating its high power density and compactness. The average open-loop radial position and force accuracy of the kinematic model are 0.72mm and 0.34N.} Its 3Hz bandwidth makes it suitable for moderate speed haptic interactions in soft environments. We demonstrate the three-dimensional kinesthetic force feedback capability of our device for sensory substitution at the index figure in a virtual telemanipulation scenario.

cs.RO↗

arXiv2023

Performance Analysis and Optimal Design of HARQ-IR-Aided Terahertz Communications

Terahertz (THz) communications are envisioned to be a promising technology for 6G thanks to its broad bandwidth. However, the large path loss, antenna misalignment, and atmospheric influence of THz communications severely deteriorate its reliability. To address this, hybrid automatic repeat request (HARQ) is recognized as an effective technique to ensure reliable THz communications. This paper delves into the performance analysis of HARQ with incremental redundancy (HARQ-IR)-aided THz communications in the presence/absence of blockage. More specifically, the analytical expression of the outage probability of HARQ-IR-aided THz communications is derived, with which the asymptotic outage analysis is enabled to gain meaningful insights, including diversity order, power allocation gain, modulation and coding gain, etc. Then the long term average throughput (LTAT) is expressed in terms of the outage probability based on renewal theory. Moreover, to combat the blockage effects, a multi-hop HARQ-IR-aided THz communication scheme is proposed and its performance is examined. To demonstrate the superiority of the proposed scheme, the other two HARQ-aided schemes, i.e., Type-I HARQ and HARQ with chase combining (HARQ-CC), are used for benchmarking in the simulations. In addition, a deep neural network (DNN) based outage evaluation framework with low computational complexity is devised to reap the benefits of using both asymptotic and simulation results in low and high outage regimes, respectively. This novel outage evaluation framework is finally employed for the optimal rate selection, which outperforms the asymptotic based optimization.

cs.IT↗

arXiv2023

Manifold Fitting

While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more complex objects, taking values in spaces that are naturally not (Euclidean) vector spaces but which still feature some geometric structure. Manifold fitting is a long-standing problem, and has finally been addressed in recent years by Fefferman et al. (2020, 2021a). We develop a method with a theory guarantee that fits a $d$-dimensional underlying manifold from noisy observations sampled in the ambient space $\mathbb{R}^D$. The new approach uses geometric structures to obtain the manifold estimator in the form of image sets via a two-step mapping approach. We prove that, under certain mild assumptions and with a sample size $N=\mathcal{O}(\sigma^{(-d+3)})$, these estimators are true $d$-dimensional smooth manifolds whose estimation error, as measured by the Hausdorff distance, is bounded by $\mathcal{O}(\sigma^2\log(1/\sigma))$ with high probability. Compared with the existing approaches proposed in Fefferman et al. (2018, 2021b); Genovese et al. (2014); Yao and Xia (2019), our method exhibits superior efficiency while attaining very low error rates with a significantly reduced sample size, which scales polynomially in $\sigma^{-1}$ and exponentially in $d$. Extensive simulations are performed to validate our theoretical results. Our findings are relevant to various fields involving high-dimensional data in machine learning. Furthermore, our method opens up new avenues for existing non-Euclidean statistical methods in the sense that it has the potential to unify them to analyze data on manifolds in the ambience space domain.

math.ST↗

arXiv2022

A Statistical Approach to Estimating Adsorption-Isotherm Parameters in Gradient-Elution Preparative Liquid Chromatography

Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. However, due to the ill-posedness, the high non-linearity, and the uncertainty quantification of the corresponding physical model, the existing deterministic inversion methods are usually inefficient in real-world applications. To overcome these difficulties and study the uncertainties of the adsorption-isotherm parameters, in this work, based on the Bayesian sampling framework, we propose a statistical approach for estimating the adsorption isotherms in various chromatography systems. Two modified Markov chain Monte Carlo algorithms are developed for a numerical realization of our statistical approach. Numerical experiments with both synthetic and real data are conducted and described to show the efficiency of the proposed new method.

stat.AP↗