Related papers: Multivariate $\alpha$-molecules
Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points…
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Data often are formed of multiple modalities, which jointly describe the observed phenomena. Modeling the joint distribution of multimodal data requires larger expressive power to capture high-level concepts and provide better data…
Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…
Mesoscale behavior of polymers is frequently described by universal laws. This physical property motivates us to propose a new modeling concept, grouping polymers into classes with a common long-wavelength representation. In the same class…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
The dipole moment is a physical quantity indicating the polarity of a molecule and is determined by reflecting the electrical properties of constituent atoms and the geometric properties of the molecule. Most embeddings used to represent…
Heterogeneity is an unwanted variation when analyzing aggregated datasets from multiple sources. Though different methods have been proposed for heterogeneity adjustment, no systematic theory exists to justify these methods. In this work,…
Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and…
It is proposed a complex valued channel encoding for multidimensional data. The basic approach contains overlapping of complex nonlinear mappings. Its development leads to sparse representation of multi-channel data, increasing their…
This paper studies deep network architectures to address the problem of video classification. A multi-stream framework is proposed to fully utilize the rich multimodal information in videos. Specifically, we first train three Convolutional…
Shape constraints enable us to reflect prior knowledge in regression settings. A unimodality constraint, for example, can describe the frequent case of a first increasing and then decreasing intensity. Yet, data shapes often exhibit…
Overcomplete representations and dictionary learning algorithms kept attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete representations. Despite…
3D volume rendering is widely used to reveal insightful intrinsic patterns of volumetric datasets across many domains. However, the complex structures and varying scales of volumetric data can make efficiently generating high-quality volume…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
We present a case study investigating feature descriptors in the context of the analysis of chemical multivariate ensemble data. The data of each ensemble member consists of three parts: the design parameters for each ensemble member, field…
In recent times, the field of unsupervised representation learning (URL) for time series data has garnered significant interest due to its remarkable adaptability across diverse downstream applications. Unsupervised learning goals differ…
Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal…
Recent molecular dynamics simulations show that thermal gradients can induce electric fields in water that are comparable in magnitude to electric fields seen in ionic thin films and biomembranes. This surprising non-equilibrium phenomenon…