Related papers: Exploiting Low-Dimensional Structure in Astronomic…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
This work addresses a procedure to estimate fundamental stellar parameters such as T eff , logg, [Fe/H], and v sin i using a dimensionality reduction technique called Principal Component Analysis (PCA), applied to a large database of…
We study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA(Principal Component Analysis). We believe that…
Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…
Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…
We present a data-driven method - heteroscedastic matrix factorization, a kind of probabilistic factor analysis - for modeling or performing dimensionality reduction on observed spectra or other high-dimensional data with known but…
We have developed a web tool to perform Principal Component Analysis (PCA, Murtagh & Heck 1987; Kendall 1980) onto spectral data. The method is especially designed to perform spectral classification of galaxies from a sample of input…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
In this work, we are trying to extent the existing photometric redshift regression models from modeling pure photometric data back to the spectra themselves. To that end, we developed a PCA that is capable of describing the input…
High-resolution stellar spectra offer valuable insights into atmospheric parameters and chemical compositions. However, their inherent complexity and high-dimensionality present challenges in fully utilizing the information they contain. In…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
This paper addresses the challenge of spectral-spatial feature extraction for hyperspectral image classification by introducing a novel tensor-based framework. The proposed approach incorporates circular convolution into a tensor structure…
Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
Astronomical observations typically provide three-dimensional maps, encoding the distribution of the observed flux in (1) the two angles of the celestial sphere and (2) energy/frequency. An important task regarding such maps is to…