Sparse subspace clustering via Low-Rank structure propagation
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Yao Sui↗
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Results for “Subspace clustering”
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Scaling Subspace-Driven Approaches Using Information Fusion
In this work, we seek to exploit the deep structure of multi-modal data to robustly exploit the group subspace distribution of the information using the Convolutional Neural Networks (CNNs) formalism. Upon unfolding the set of subspaces constituting each data modality, and learning their corresponding encoders, an optimized integration of the generated inherent information is carried out to yield a characterization of various classes. Referred to as deep Multimodal Robust Group Subspace Clustering (DRoGSuRe), this approach is compared against the independently developed state-of-the-art approach named Deep Multimodal Subspace Clustering (DMSC). Experiments on different multimodal datasets show that our approach is competitive and more robust in the presence of noise.
Ghanem, Sally↗
Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion
Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. In this work, we build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors’ data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.
47 OTHER INSTRUMENTATION↗
Cluster analysis of multiple planetary flow regimes
A modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them. This method was applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data. The dynamical model is governed by the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere. Clusters of point in the model's phase space are associated with either a few persistent or with many transient events. Two stationary clusters have patterns similar to unstable stationary model solutions, zonal, or blocked. Transient clusters of wave trains serve as way stations between the stationary ones. For the NH data, cluster analysis was performed in the subspace of the first seven empirical orthogonal functions (EOFs). Stationary clusters are found in the low-frequency band of more than 10 days, and transient clusters in the bandpass frequency window between 2.5 and 6 days. In the low-frequency band three pairs of clusters determine, respectively, EOFs 1, 2, and 3. They exhibit well-known regional features, such as blocking, the Pacific/North American (PNA) pattern and wave trains. Both model and low-pass data show strong bimodality. Clusters in the bandpass window show wave-train patterns in the two jet exit regions. They are related, as in the model, to transitions between stationary clusters.
Mo, Kingtse↗
Emulating ab initio computations of infinite nucleonic matter
We construct efficient emulators for the computation of the infinite nuclear matter equation of state. These emulators are based on the subspace-projected coupled-cluster method for which we here develop a new algorithm called small-batch voting to eliminate spurious states that might appear when emulating quantum many-body methods based on a non-Hermitian Hamiltonian. The efficiency and accuracy of these emulators facilitate a rigorous statistical analysis within which we explore nuclear matter predictions for > 10 6 different parametrizations of a chiral interaction model with explicit Δ -isobars at next-to-next-to leading order. Constrained by nucleon-nucleon scattering phase shifts and bound-state observables of light nuclei up to He 4 , we use history matching to identify nonimplausible domains for the low-energy coupling constants of the chiral interaction. Within these domains we perform a Bayesian analysis using sampling and importance resampling with different likelihood calibrations and study correlations between interaction parameters, calibration observables in light nuclei, and nuclear matter saturation properties. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Unsupervised learning in neurodynamics using example-interaction approach
A new concept for unsupervised learning based upon examples introduced to the neural network is proposed. Each example is considered as an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines diverge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from the minimization of the strength energy, while the node velocities play the role of constraints.
Zak, Michail↗
Unsupervised learning in neurodynamics using example-interaction approach
A new concept for unsupervised learning based upon examples introduced to the neural network is proposed. Each example is considered as an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines diverge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from the minimization of the strength energy, while the node velocities play the role of constraints.
Zak, Michail↗
Cluster analysis of multiple planetary flow regimes
A modified cluster analysis method developed for the classification of quasi-stationary events into a few planetary flow regimes and for the examination of transitions between these regimes is described. The method was applied first to a simple deterministic model and then to a 500-mbar data set for Northern Hemisphere (NH), for which cluster analysis was carried out in the subspace of the first seven empirical orthogonal functions (EOFs). Stationary clusters were found in the low-frequency band of more than 10 days, while transient clusters were found in the band-pass frequency window between 2.5 and 6 days. In the low-frequency band, three pairs of clusters determined EOFs 1, 2, and 3, respectively; they exhibited well-known regional features, such as blocking, the Pacific/North American pattern, and wave trains. Both model and low-pass data exhibited strong bimodality.
Mo, Kingtse↗
Latent code-based fusion: A Volterra neural network approach
We propose a deep structure encoder using Volterra Neural Networks (VNNs) to seek a latent representation of multi-modal data whose features are jointly captured by a union of subspaces. The so-called self-representation embedding of the latent codes leads to a simplified fusion which is driven by a similarly constructed decoding. The Volterra Filter architecture achieved reduction in parameter complexity is primarily due to controlled non-linearities being introduced by the higher-order convolutions in lieu of generalized activation functions. Experimental results on two different datasets have shown a significant improvement in the clustering performance for VNNs auto-encoder over conventional Convolutional Neural Networks (CNNs) auto-encoder. In addition, we also show that the proposed approach demonstrates a much-improved sample complexity over CNN-based auto-encoder with a robust classification performance.
97 MATHEMATICS AND COMPUTING↗
Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
Costiner, Sorin↗
Regional surrogates for predictive control of digital twins
Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.
Data-driven model↗
A unified exploration of the chronology of the Galaxy
The Milky Way has distinct structural stellar components linked to its formation and subsequent evolution, but disentangling them is non-trivial. With the recent availability of high-quality data for a large numbers of stars in the Milky Way, it is a natural next step for research in the evolution of the Galaxy to perform automated explorations with unsupervised methods of the structures hidden in the combination of large-scale spectroscopic, astrometric, and asteroseismic data sets. We determine precise stellar properties for 21 076 red giants, mainly spanning 2–15 kpc in Galactocentric radii, making it the largest sample of red giants with measured asteroseismic ages available to date. We explore the nature of different stellar structures in the Galactic disc by using Gaussian mixture models as an unsupervised clustering method to find substructure in the combined chemical, kinematic, and age subspace. The best-fitting mixture model yields four distinct physical Galactic components in the stellar disc: the thin disc, the kinematically heated thin disc, the thick disc, and the stellar halo. We find hints of an age asymmetry between the Northern and Southern hemisphere, and we measure the vertical and radial age gradient of the Galactic disc using the asteroseismic ages extended to further distances than previous studies.
79 ASTRONOMY AND ASTROPHYSICS↗
Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons
We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor \nu=2/3 ν = 2 / 3 . The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body M M -clustering property within any given number of Landau levels, that is, wave functions with M M th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the M=3 M = 3 case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Molecular dynamics analysis of particle number fluctuations in the mixed phase of a first-order phase transition
Molecular dynamics simulations are performed for a finite nonrelativistic system of particles with Lennard-Jones potential. We study the effect of liquid-gas mixed phase on particle number fluctuations in coordinate subspace. A metastable region of the mixed phase, the so-called nucleation region, is analyzed in terms of a noninteracting cluster model. Large fluctuations due to spinodal decomposition are observed. They arise due to the interplay between the size of the acceptance region and that of the liquid phase. These effects are studied with a simple geometric model. The model results for the scaled variance of particle number distribution are compared with those obtained from the direct molecular dynamic simulations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations
Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled-cluster Ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point-group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit by a factor of 4–8. With these strategies, VQE calculations on a noise-free quantum simulator achieve energies within a few meVs of those obtained with the full unitary coupled-cluster Ansatz with single and double excitations for the H 4 -square, H 4 -chain, and H 6 -hexagon molecules, while the number of cnot gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore, we introduced an efficient “score” parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first. Using the H 4 square and H 4 chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational Ansatz.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Solving Coupled Cluster Equations by the Newton Krylov Method
We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm
The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.
Chemistry↗
Short-range order parameter expansions for simple configurational energetics
Local chemical environments of multicomponent crystals are parametrized according to basis vectors of their irreducible invariant subspaces. These short-range order parameters enable Taylor expansions of configurational properties that easily incorporate additional couplings. As one example, expansions including long-range composition can describe the energies of many alloys more accurately than conventional cluster expansions while using far fewer neighbors and basis functions.
36 MATERIALS SCIENCE↗