Related papers: DREAMS: Preserving both Local and Global Structure…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…
In this paper, we propose a novel ensembling technique for deep neural networks, which is able to drastically reduce the required memory compared to alternative approaches. In particular, we propose to extract multiple sub-networks from a…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard…
To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…
Neural implicit representations have had a significant impact on simultaneous localization and mapping (SLAM) by enabling robots to build continuous, differentiable, and high-fidelity 3D maps from sensor data. However, as the scale and…
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…
We present a new technique called "DSNE" which learns the velocity embeddings of low dimensional map points when given the high-dimensional data points with its velocities. The technique is a variation of Stochastic Neighbor Embedding,…
Suppose the data consist of a set $S$ of points $x_j$, $1\leq j \leq J$, distributed in a bounded domain $D\subset R^N$, where $N$ is a large number. An algorithm is given for finding the sets $L_k$ of dimension $k\ll N$, $k=1,2,...K$, in a…
Dimensionality reduction (DR) techniques map high-dimensional data into lower-dimensional spaces. Yet, current DR techniques are not designed to explore semantic structure that is not directly available in the form of variables or class…
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…
Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…
Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…
The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…
Eye image segmentation is a critical step in eye tracking that has great influence over the final gaze estimate. Segmentation models trained using supervised machine learning can excel at this task, their effectiveness is determined by the…
Applying dimensionality reduction (DR) to large, high-dimensional data sets can be challenging when distinguishing the underlying high-dimensional data clusters in a 2D projection for exploratory analysis. We address this problem by first…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
We present DREAM, a novel training framework representing Diffusion Rectification and Estimation Adaptive Models, requiring minimal code changes (just three lines) yet significantly enhancing the alignment of training with sampling in…
Dimensionality reduction is a critical step in scaling machine learning pipelines. Principal component analysis (PCA) is a standard tool for dimensionality reduction, but performing PCA over a full dataset can be prohibitively expensive. As…
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…