Related papers: Graph Regularized Autoencoder and its Application …
Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…
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…
Unsupervised learning-based anomaly detection in latent space has gained importance since discriminating anomalies from normal data becomes difficult in high-dimensional space. Both density estimation and distance-based methods to detect…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
Autoencoder and its variants have been widely applicated in anomaly detection.The previous work memory-augmented deep autoencoder proposed memorizing normality to detect anomaly, however it neglects the feature discrepancy between different…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…
Regularized autoencoders learn the latent codes, a structure with the regularization under the distribution, which enables them the capability to infer the latent codes given observations and generate new samples given the codes. However,…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps…
With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a…
Hyperspectral image analysis often requires selecting the most informative bands instead of processing the whole data without losing the key information. Existing band reduction (BR) methods have the capability to reveal the nonlinear…
In this paper, we address the problem of recovering arbitrary-shaped data clusters from datasets while facing \emph{high space constraints}, as this is for instance the case in many real-world applications when analysis algorithms are…