Related papers: Boundary Detection Algorithm Inspired by Locally L…

Boundary point detection aims to outline the external contour structure of clusters and enhance the inter-cluster discrimination, thus bolstering the performance of the downstream classification and clustering tasks. However, existing…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Extracting high-level structural information from 3D point clouds is challenging but essential for tasks like urban planning or autonomous driving requiring an advanced understanding of the scene at hand. Existing approaches are still not…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

Manifold structure learning is often used to exploit geometric information among data in semi-supervised feature learning algorithms. In this paper, we find that local discriminative information is also of importance for semi-supervised…

Rapid growth in the field of quantitative digital image analysis is paving the way for researchers to make precise measurements about objects in an image. To compute quantities from the image such as the density of compressed materials or…

Room geometry inference algorithms rely on the localization of acoustic reflectors to identify boundary surfaces of an enclosure. Rooms with highly absorptive walls or walls at large distances from the measurement setup pose challenges for…

Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of…

Most of the current boundary detection systems rely exclusively on low-level features, such as color and texture. However, perception studies suggest that humans employ object-level reasoning when judging if a particular pixel is a…

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and…

We present a lightweight network that infers grouping and boundaries, including curves, corners and junctions. It operates in a bottom-up fashion, analogous to classical methods for sub-pixel edge localization and edge-linking, but with a…

Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…

The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…

In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…

Samples from intimate (non-linear) mixtures are generally modeled as being drawn from a smooth manifold. Scenarios where the data contains multiple intimate mixtures with some constituent materials in common can be thought of as manifolds…

Incorporating boundaries of the imaging object as a priori information to imaging algorithms can significantly improve the performance of electromagnetic medical imaging systems. To avoid overly complicating the system by using different…