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The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
High-dimensional astronomical data cubes provide a wealth of spectral and structural information that can be used to study astrophysical and chemical processes. The complexity and sheer size of these datasets pose significant challenges in…
Selecting the appropriate dimensionality reduction (DR) technique and determining its optimal hyperparameter settings that maximize the accuracy of the output projections typically involves extensive trial and error, often resulting in…
To perform visual data exploration, many dimensionality reduction methods have been developed. These tools allow data analysts to represent multidimensional data in a 2D or 3D space, while preserving as much relevant information as…
This paper presents an extensive empirical study on the integration of dimensionality reduction techniques with advanced unsupervised time series anomaly detection models, focusing on the MUTANT and Anomaly-Transformer models. The study…
The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…
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…
We consider the problem of nonlinear dimensionality reduction: given a training set of high-dimensional data whose ``intrinsic'' low dimension is assumed known, find a feature extraction map to low-dimensional space, a reconstruction map…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
In this paper, we present a Mirroring Neural Network architecture to perform non-linear dimensionality reduction and Object Recognition using a reduced lowdimensional characteristic vector. In addition to dimensionality reduction, the…
Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and…
This paper presents a deep nonlinear metric learning framework for data visualization on an image dataset. We propose the Triangular Similarity and prove its equivalence to the Cosine Similarity in measuring a data pair. Based on this novel…
In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and…
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…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
Deep metric learning (DML) is a popular approach for images retrieval, solving verification (same or not) problems and addressing open set classification. Arguably, the most common DML approach is with triplet loss, despite significant…
This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…
During the last decades, learning a low-dimensional space with discriminative information for dimension reduction (DR) has gained a surge of interest. However, it's not accessible for these DR methods to achieve satisfactory performance…
Intrinsic dimension and differential entropy estimators are studied in this paper, including their systematic bias. A pragmatic approach for joint estimation and bias correction of these two fundamental measures is proposed. Shared steps on…