24 papers · ranked by Valyu relevance
Marcelo O. Magnasco, Andreas Keller, Leslie B. Vosshall
We recently presented an estimate of the number of mutually discriminable olfactory stimuli at one trillion (1). Subjects were asked to sniff mixtures of molecules with increasing component overlap selected from a panel of 128 isointense structurally and perceptually diverse monomolecular odorants (2). We considered…
Subhash Kak
We present an information-theoretic approach to the optimal representation of the intrinsic dimensionality of data and show it is a noninteger. Since optimality is accepted as a physical principle, this provides a theoretical explanation for why noninteger dimensions are useful in many branches of physics, where they…
Evgeny M. Mirkes, Jeza Allohibi, Alexander Gorban
The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using the Manhattan distance and even fractional $l_{p}$ quasinorms (for p less than 1) can help to overcome the curse of dimensionality in classification problems. In this study, we…
Ramon Bartolo, Richard C. Saunders, Andrew Mitz, Bruno B. Averbeck
Learning leads to changes in population patterns of neural activity. In this study we wanted to examine how these changes in patterns of activity affect the dimensionality of neural responses and information about choices. We addressed these questions by carrying out high channel count recordings in dorsal-lateral…
Christiane Ahlheim, Bradley C. Love
Recent advances in multivariate fMRI analysis stress the importance of information inherent to voxel patterns. Key to interpreting these patterns is estimating the underlying dimensionality of neural representations. Dimensions may correspond to psychological dimensions, such as length and orientation, or involve other…
Gabriel Nakamura, Larissa Oliveira Gonçalves, Leandro Duarte
Biodiversity can be represented by a variety of different dimensions (e.g. functional diversity, phylogenetic diversity, genetic diversity and taxonomic diversity). While the many different representations of biodiversity can lead to a more complete description of communities, they also lead to a degree of…
Erik Thordsen, Erich Schubert
The intrinsic dimensionality refers to the "true" dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower than the number of variables. Local intrinsic dimensionality refers to the…
Jean‐Pierre Eckmann, Tsvi Tlusty
The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data by distilling underlying principles and mechanisms—necessitates dimensional reduction. We propose that living systems achieve exquisite…
Evgeny M. Mirkes, Jeza Allohibi, Alexander N. Gorban
—The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using of the Manhattan distance and even fractional quasinorms lp (for p less than 1) can help to overcome the curse of dimensionality in classification problems. In this study, we…
Luana Fragoso, Tuhin Paul, Flaviu Vadan, Kevin G. Stanley + 3 more
'Scott Bell' 'Nathaniel D. Osgood' 'Federico Botta'] Patterns of spatial behavior dictate how we use our infrastructure, encounter other people, or are exposed to services and opportunities. Understanding these patterns through the analysis of data commonly available through commodity smartphones has become an…
Stefano Recanatesi, Serena Bradde, Vijay Balasubramanian, Nicholas A. Steinmetz + 1 more
A fundamental problem in science is uncovering the effective number of dynamical degrees of freedom in a complex system, a quantity that depends on the spatio-temporal scale at which the system is observed. Here, we propose a scale-dependent generalization of a classic enumeration of latent variables, the Participation…
Neda Pourali
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 order to calculate similarities between image samples. But the computation cost…
Maxwell P. Bobbin, Colin Jones, John Velkey, Tyler R. Josephson
Dimensional analysis is fundamental to the formulation and validation of physical laws, ensuring that equations are dimensionally homogeneous and scientifically meaningful. In this work, we use Lean 4 to formalize the mathematics of dimensional analysis. We define physical dimensions as mappings from base dimensions to…
David-Elias Künstle, Ulrike von Luxburg, Felix A. Wichmann
Vision researchers are interested in mapping complex physical stimuli to perceptual dimensions. Such a mapping can be constructed using multidimensional psychophysical scaling or ordinal embedding methods. Both methods infer coordinates that agree as much as possible with the observer’s judgments so that perceived…
Ravi Kashyap
| 1 | Abstract | | 2 | | --- | --- | --- | --- | | 2 | | Introduction | 2 | | 3 | | Literature Review of Methodological Fundamentals | 5 | | | 3.1 | Notation and Terminology for Key Results | 5 | | | 3.2 | Bhattacharyya Distance | 5 | | | 3.3 | Dimension Reduction | 9 | | 4 | | Intuition for Dimension Reduction | 10 |…
F. Patricia Medina, Linda Ness, Melanie Weber, Karamatou Yacoubou Djima
'Karamatou Yacoubou Djima'] Abstract When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold) of lower dimension than the ambient space.…
Yanguang Chen
The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical systems have characteristic scales. For a scale-free geographical system, the…
Karaj Khosla, Indra Prakash Jha, Vibhor Kumar
Dimension reduction is often used for several procedures of analysis of high dimensional biomedical data-sets such as classification or outlier detection. To improve performance of such data-mining steps, preserving both distance information and local topology among data-points could be more useful than giving priority…
Yanguang Chen
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal…
Authors not listed
We present a gridless framework for computing high-dimensional conformational free energy surfaces (FES) of flexible molecules using enhanced sampling trajectories. By combining concurrent well-tempered metadynamics with Density Peaks Advanced (DPA) clustering, our approach bypasses the dimensionality limitations of…
Brittany Story, Biswajit Sadhu, Henry Adams, Aurora Clark
Recent work (J. Chem. Phys. 154, 114114) has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in $3N$-dimensions. This includes information about all transition paths between local minima (connected by critical points of index > 1), and…
José L. Medina-Franco, Ana L. Chávez-Hernández, Edgar López-López, Fernanda I. Saldívar-González
Technological advances and practical applications of the chemical space concept in drug discovery, natural product research, and other research areas have attracted the scientific community´s attention. The large- and ultra-large chemical spaces are associated not only with the significant increase in the number of…
Jessica Braun, Paul Katzberger, Gregory A. Landrum, Sereina Riniker
Molecular flexibility is a commonly used, but not easily quantified term. It is at the core of understanding composition and size of a conformational ensemble and contributes to many molecular properties. For many computational workflows, it is necessary to reduce a conformational ensemble to meaningful…
Authors not listed
The influence of particle size on heterogeneous equilibria is investigated using Fe clusters as an example. Considering a thermodynamic cycle, the change in free enthalpy for the transfer of an Fe atom from a dispersed system to the bulk is analyzed with the aid of experimental data from molecular beam experiments.…