Related papers: A Comparative Study of UMAP and Other Dimensionali…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
Many data mining and data analysis techniques operate on dense matrices or complete tables of data. Real-world data sets, however, often contain unknown values. Even many classification algorithms that are designed to operate with missing…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We present a systematic and detailed construction of a metric…
Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Neighbor embedding is widely employed to visualize high-dimensional data; however, it frequently overlooks the global structure, e.g., intercluster similarities, thereby impeding accurate visualization. To address this problem, this paper…
Real-world data contains a vast amount of multimodal information, among which vision and language are the two most representative modalities. Moreover, increasingly heavier models, \textit{e}.\textit{g}., Transformers, have attracted the…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
We propose a novel approach to unsupervised learning by constructing a non-linear embedding of the data into a low-dimensional space followed by any conventional clustering algorithm. The embedding promotes clusterability of the data and is…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
Diffusion maps (DMAP) are often used as a dimensionality-reduction tool, but more precisely they provide a spectral representation of the intrinsic geometry rather than a complete charting method. To illustrate this distinction, we study a…
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric…
Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
Supervised learning depth estimation methods can achieve good performance when trained on high-quality ground-truth, like LiDAR data. However, LiDAR can only generate sparse 3D maps which causes losing information. Obtaining high-quality…