相关论文: K-Deep Simplex: Deep Manifold Learning via Local D…

While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization…

There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…

In this paper we show that the computational complexity of the Iterative Thresholding and K-residual-Means (ITKrM) algorithm for dictionary learning can be significantly reduced by using dimensionality-reduction techniques based on the…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

In this paper, we show that the popular K-means clustering problem can equivalently be reformulated as a conic program of polynomial size. The arising convex optimization problem is NP-hard, but amenable to a tractable semidefinite…

Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…

Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a…

Finding the densest subgraph (DS) from a graph is a fundamental problem in graph databases. The DS obtained, which reveals closely related entities, has been found to be useful in various application domains such as e-commerce, social…

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…

Clustering is a long-standing problem area in data mining. The centroid-based classical approaches to clustering mainly face difficulty in the case of high dimensional inputs such as images. With the advent of deep neural networks, a common…

Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise…

Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity…

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between…

In this paper, we investigate representation learning for low-resource keyword spotting (KWS). The main challenges of KWS are limited labeled data and limited available device resources. To address those challenges, we explore…

Variational Autoencoders and their many variants have displayed impressive ability to perform dimensionality reduction, often achieving state-of-the-art performance. Many current methods however, struggle to learn good representations in…

Recently, deep clustering methods have gained momentum because of the high representational power of deep neural networks (DNNs) such as autoencoder. The key idea is that representation learning and clustering can reinforce each other: Good…

In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large.…

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…