Related papers: Manifold Learning for Dimensionality Reduction: Qu…
Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
Automatic image annotation is one of the most challenging problems in machine vision areas. The goal of this task is to predict number of keywords automatically for images captured in real data. Many methods are based on visual features in…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…
Quantum image processing (QIP) means the quantum based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency are theoretically higher than their corresponding classical schemes.…
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…
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
The growing demands of remote detection and increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles…
UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…
Non-linear spectral dimensionality reduction methods, such as Isomap, remain important technique for learning manifolds. However, due to computational complexity, exact manifold learning using Isomap is currently impossible from large-scale…
The Adam optimizer is the standard choice in deep learning applications. I propose a simple explanation of Adam's success: it makes each parameter's step size independent of the norms of the other parameters. Based on this principle I…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…
Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…
This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping…
In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…