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At least 73 records · Page 4

Dimensionality Reduction Through Classifier Ensembles

In data mining, one often needs to analyze datasets with a very large number of attributes. Performing machine learning directly on such data sets is often impractical because of extensive run times, excessive complexity of the fitted model (often leading to overfitting), and the well-known "curse of dimensionality." In practice, to avoid such problems, feature selection and/or extraction are often used to reduce data dimensionality prior to the learning step. However, existing feature selection/extraction algorithms either evaluate features by their effectiveness across the entire data set or simply disregard class information altogether (e.g., principal component analysis). Furthermore, feature extraction algorithms such as principal components analysis create new features that are often meaningless to human users. In this article, we present input decimation, a method that provides "feature subsets" that are selected for their ability to discriminate among the classes. These features are subsequently used in ensembles of classifiers, yielding results superior to single classifiers, ensembles that use the full set of features, and ensembles based on principal component analysis on both real and synthetic datasets.

Oza, Nikunj C.↗

Robust training of machine learning interatomic potentials with dimensionality reduction and stratified sampling

Abstract Machine learning interatomic potentials (MLIPs) enable accurate simulations of materials at scales beyond that accessible by ab initio methods and play an increasingly important role in the study and design of materials. However, MLIPs are only as accurate and robust as the data on which they are trained. Here, we present DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling as an approach to select a robust training set of structures from a large and complex configuration space. By applying DIRECT sampling on the Materials Project relaxation trajectories dataset with over one million structures and 89 elements, we develop an improved materials 3-body graph network (M3GNet) universal potential that extrapolates more reliably to unseen structures. We further show that molecular dynamics (MD) simulations with the M3GNet universal potential can be used instead of expensive ab initio MD to rapidly create a large configuration space for target systems. We combined this scheme with DIRECT sampling to develop a reliable moment tensor potential for titanium hydrides without the need for iterative augmentation of training structures. This work paves the way for robust high-throughput development of MLIPs across any compositional complexity.

Qi, Ji (ORCID:0000000158089931)↗

Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: classical and quantum computing perspective

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub- systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be defined at the level of the CC Ansatz defined by selected classes of cluster amplitudes, which define the wave function ”memory” of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.

Electron correlation, quantum chemistry, quantum c↗

Dimensional reduction upon calcium incorporation in Cs 0.3 (Ca 0.3 Ln 0.7 )PS 4 and Cs 0.5 (Ca 0.5 Ln 0.5 )PS 4

A series of Ca-containing lanthanide thiophosphates has been obtained and their structural evolution from 3D for LnPS 4 and Cs 0.3 (Ln 0.7 Ca 0.3 )PS 4 to 2D in Cs 0.5 (Ln 0.5 Ca 0.5 )PS 4 was shown as a function of Ca content. The first series with an idealized formula of Cs 0.3 (Ca 0.3 Ln 0.7 )PS 4 crystallizes in the R3¯m with combining macron]m space group and belongs to a new structure type that consists of a channel containing [(Ca 0.3 Ln 0.7 )PS 4 ] 0.3– framework, where the channels are occupied by severely disordered Cs + cations. A second new series with formula Cs 0.5 (Ca 0.5 Ln 0.5 )PS 4 crystallizes in the monoclinic C2/c space group and exhibits a layered structure consisting of [(Ca 0.5 Ln 0.5 )PS 4 ] 0.5– layers with Cs + cations located between the layers for charge balance. Together with the parent structure type, LnPS 4 , these three structure types illustrate how the LnPS 4 structure changes with Cs + cation incorporation, reducing its dimensionality from 3D to 2D. The magnetic properties of Cs 0.3 [(Ca 0.3 Ce 0.7 )PS 4 ] and Cs 0.3 [(Ca 0.3 Pr 0.7 )PS 4 ] were studied and revealed no magnetic transition down to 2 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analytical Dimensional Reduction of a Fuel Optimal Powered Descent Subproblem

Current renewed interest in exploration of the moon, Mars, and other planetary objects is driving technology development in many fields of space system design. In particular, there is a desire to land both robotic and human missions on the moon and elsewhere. The landing guidance system must be able to deliver the vehicle to a desired soft landing while meeting several constraints necessary for the safety of the vehicle. Due to performance limitations of current launch vehicles, it is desired to minimize the amount of fuel used. In addition, the landing site may change in real-time in order to avoid previously undetected hazards which become apparent during the landing maneuver. This complicated maneuver can be broken into simpler subproblems that bound the full problem. One such subproblem is to find a minimum-fuel landing solution that meets constraints on the initial state, final state, and bounded thrust acceleration magnitude. With the assumptions of constant gravity and negligible atmosphere, the form of the optimal steering law is known, and the equations of motion can be integrated analytically, resulting in a system of five equations in five unknowns. It is shown that this system of equations can be reduced analytically to two equations in two unknowns. With an additional assumption of constant thrust acceleration magnitude, this system can be reduced further to one equation in one unknown. It is shown that these unknowns can be bounded analytically. An algorithm is developed to quickly and reliably solve the resulting one-dimensional bounded search, and it is used as a real-time guidance applied to a lunar landing test case.

Rea, Jeremy R.↗

Quantifying and connecting atomic and crystallographic grain boundary structure using local environment representation and dimensionality reduction techniques

In this paper, the relationship between grain boundary crystallography and grain boundary atomic structure is examined, using [100] - symmetric tilt grain boundaries in nickel. The structural unit model is used as a benchmark to evaluate the atomic structure description capacities of an emerging structural descriptor, the local environment representation, which itself is a refinement of the Smooth Overlap of Atomic Positions (SOAP) descriptor. We show that the local environment representation encodes both the information of the structural unit model and additional information, such as distortion in the structural units and the arrangement of the structural units at the interface. The use of the local environment representation permits the use of a visualization tool known as SPRING to represent structural similarities between grain boundaries. With the SPRING representation, we produce objective evidence of a relationship between crystallography and atomic structure, at least for [100] - symmetric tilt grain boundaries.

36 MATERIALS SCIENCE↗

Improvements of pre-emptive identification of particle accelerator failures using binary classifiers and dimensionality reduction

In this paper we look at the properties of the Spallation Neutron Source (SNS) Differential Beam Current Monitor (DCM) data and various methods of data transformation to improve pre-emptive detection of machine trips. In this study, the foundation of the approach is the analysis of new underlying data and understanding various properties with the goal of faster classification, higher precision and higher recall with the aim to reduce false positives as low as required. The result of the research presented in this paper are a binary classifier capable of predicting accelerator failures with millisecond classification time, 96% precision, 58% true positive and 0% false positive rate and optimization techniques enabling real-time implementations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗