Related papers: Nonlinear Laplacian spectral analysis: Capturing i…
We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake.…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
Event cameras provide sequential visual data with spatial sparsity and high temporal resolution, making them attractive for low-latency object detection. Existing asynchronous event-based neural networks realize this low-latency advantage…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
Benefiting from its succinctness and robustness, skeleton-based action recognition has recently attracted much attention. Most existing methods utilize local networks (e.g., recurrent, convolutional, and graph convolutional networks) to…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
We present a data-adaptive spectral method - Monte Carlo Singular Spectrum Analysis (MC-SSA) - and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with…
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time…
Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
Structured data, such as tables, graphs, and databases, play a critical role in plentiful NLP tasks such as question answering and dialogue system. Recently, inspired by Vision-Language Models, Graph Neutral Networks (GNNs) have been…
A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…
Time series data are collected in temporal order and are widely used to train systems for prediction, modeling and classification to name a few. These systems require large amounts of data to improve generalization and prevent over-fitting.…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Time-series data, such as unsteady pressure-sensitive paint (PSP) measurement data, may contain a significant amount of random noise. Thus, in this study, we investigated a noise-reduction method that combines multivariate singular spectrum…
In this paper, we consider a certain convolutional Laplacian for metric measure spaces and investigate its potential for the statistical analysis of complex objects. The spectrum of that Laplacian serves as a signature of the space under…
The complexity of high-dimensional datasets presents significant challenges for machine learning models, including overfitting, computational complexity, and difficulties in interpreting results. To address these challenges, it is essential…