相关论文: Isotropic PCA and Affine-Invariant Clustering

We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…

In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA…

Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace…

We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…

Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional…

Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience.…

Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…

We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between…

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Single-particle cryo-electron microscopy (cryo-EM) is a leading technology to resolve the structure of molecules. Early in the process, the user detects potential particle images in the raw data. Typically, there are many false detections…

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

We present an algorithm using Principal Component Analysis (PCA) to subtract galaxies from imaging data, and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is…

We compare the performance of different clustering algorithms applied to the task of unsupervised text categorization. We consider agglomerative clustering algorithms, principal direction divisive partitioning and (for the first time)…