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Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps.

ABSTRACT: Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often overlooked problem is what high-dimensional representation should be used to describe systems before dimensionality reduction. Here, we address this issue using a recently developed method called the reweighted diffusion map [J. Chem. Theory Comput. 2022, 18, 7179-7192]. We show how high-dimensional representations can be quantitatively selected by exploring the spectral decomposition of Markov transition matrices built from data obtained from standard or enhanced sampling atomistic simulations. We demonstrate the performance of the method in several high-dimensional examples.

SUBMITTER: Rydzewski J

PROVIDER: S-EPMC10041639 | biostudies-literature | 2023 Mar

REPOSITORIES: biostudies-literature

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Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps.

Rydzewski Jakub J

The journal of physical chemistry letters 20230310 11

Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often overlooked problem is what high-dimensional representation should be used to describe systems before dimensionality reduction. Here, we address this issue using a recently developed method called the reweighted diffusion map [<i>J. Chem. Theory Comput.</i> <b>2022< ...[more]

PMID: 36897996

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Project description:A perceptual space is a mental workspace of points in a sensory domain that supports similarity and difference judgments and enables further processing such as classification and naming. Perceptual spaces are present across sensory modalities; examples include colors, faces, auditory textures, and odors. Color is perhaps the best-studied perceptual space, but it is atypical in two respects. First, the dimensions of color space are directly linked to the three cone absorption spectra, but the dimensions of generic perceptual spaces are not as readily traceable to single-neuron properties. Second, generic perceptual spaces have more than three dimensions. This is important because representing each distinguishable point in a high-dimensional space by a separate neuron or population is unwieldy; combinatorial strategies may be needed to overcome this hurdle. To study the representation of a complex perceptual space, we focused on a well-characterized 10-dimensional domain of visual textures. Within this domain, we determine perceptual distances in a threshold task (segmentation) and a suprathreshold task (border salience comparison). In N=4 human observers, we find both quantitative and qualitative differences between these sets of measurements. Quantitatively, observers' segmentation thresholds were inconsistent with their uncertainty determined from border salience comparisons. Qualitatively, segmentation thresholds suggested that distances are determined by a coordinate representation with Euclidean geometry. Border salience comparisons, in contrast, indicated a global curvature of the space, and that distances are determined by activity patterns across broadly tuned elements. Thus, our results indicate two representations of this perceptual space, and suggest that they use differing combinatorial strategies.To move from sensory signals to decisions and actions, the brain carries out a sequence of transformations. An important stage in this process is the construction of a "perceptual space" - an internal workspace of sensory information that captures similarities and differences, and enables further processing, such as classification and naming. Perceptual spaces for color, faces, visual and haptic textures and shapes, sounds, and odors (among others) are known to exist. How such spaces are represented is at present unknown. Here, using visual textures as a model, we investigate this. Psychophysical measurements suggest roles for two combinatorial strategies: one based on projections onto coordinate-like axes, and one based on patterns of activity across broadly tuned elements scattered throughout the space.

Dataset Information

Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps.

Publications

Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps.

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