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Clustering High-Dimensional Noisy Categorical Data

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2024年第548期119卷 3008-3019页

作者： Tian, Zhiyi Xu, Jiaming Tang, Jen IQVIA Wayne PA USA Duke Univ Fuqua Sch Business Durham NC USA Purdue Univ Daniels Sch Business W Lafayette IN USA

Clustering is a widely used unsupervised learning technique that groups data into homogeneous clusters. However, when dealing with real-world data that contain categorical values, existing algorithms can be computationally costly in high dimensions and can struggle with noisy data that has missing values. Furthermore, except for one algorithm, no others provide theoretical guarantees of clustering accuracy. In this article, we propose a general categorical data encoding method and a computationally efficient spectral-based algorithm to cluster high-dimensional noisy categorical data (nominal or ordinal). Under a statistical model for data on m attributes from n subjects in r clusters with missing probability E, we show that our algorithm exactly recovers the true clusters with high probability when mn(1-epsilon) >= CMr(2) log(3) M, with M = max(n,m) and a fixed constant C. In addition, we show that mn(1-epsilon)(2) >= r delta/2 with 0 < delta < 1 is necessary for any algorithm to succeed with probability at least (1 + delta)/2. In cases where m = n and r are fixed, the sufficient condition matches with the necessary condition up to a polylog(n) factor. In numerical studies our algorithm outperforms several existing algorithms in both clustering accuracy and computational efficiency. Supplementary materials for this article are available online.

关键词： Categorical values Clustering Clustering accuracy High dimensions Noisy and sparse data spectral algorithm

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CONSISTENCY OF spectral HYPERGRAPH PARTITIONING UNDER PLANTED PARTITION MODEL

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ANNALS OF STATISTICS 2017年第1期45卷 289-315页

作者： Ghoshdastidar, Debarghya Dukkipati, Ambedkar Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random nonuniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning nonuniform hypergraphs.

关键词： Hypergraph stochastic block model spectral algorithm

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spectral methods for testing membership in certain post classes and the class of forcing functions

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IEEE SIGNAL PROCESSING LETTERS 2004年第2期11卷 289-292页

作者： Shmulevich, I Lähdesmäki, H Egiazarian, K Univ Texas MD Anderson Canc Ctr Canc Genom Lab Houston TX 77030 USA Tampere Univ Technol Inst Signal Proc FIN-33720 Tampere Finland

Forcing functions represent an important class of Boolean functions that have been extensively studied in the analysis of the dynamics of random Boolean networks as models of genetic regulatory systems. Several other so-called Post classes of Boolean functions are closely related to forcing functions and have been used in learning theory as well as in control systems. We develop novel spectral algorithms to test membership of a Boolean function in these classes. These algorithms are highly efficient and are essential in learning problems, especially in the context of genetic regulatory networks, where the same learning procedures are applied repeatedly.

关键词： forcing function PoA class spectral algorithm

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SPLITTING LANDAU LEVELS ON THE 2D TORUS BY PERIODIC PERTURBATIONS

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2008年第11期19卷 1753-1761页

作者： Onofri, E. Univ Montpellier 2 Lab Phys Theor & Astroparticules F-34095 Montpellier 05 France Univ Parma Dept Phys I-43100 Parma Italy Ist Nazl Fis Nucl Grp Collegato Parma I-43100 Parma Italy

We study the spectrum of the Schroedinger operator for a particle constrained on a two-dimensional flat torus under the combined action of a transverse magnetic field and a conservative force. A numerical method is presented which allows to compute the spectrum with high accuracy. The method employs a fast Fourier transform to accurately represent the momentum variables and takes into account the twisted boundary conditions required by the presence of the magnetic field. An accuracy of 12 digits is attained even with coarse grids. Landau levels are reproduced in the case of a uniform magnetic field satisfying Dirac's condition. A new fine structure of levels within the single Landau level is formed when the field has a sinusoidal component with period commensurable to the integer magnetic charge. This fact is interpreted in terms of the peculiar symmetry Z(N) x Z(N) which holds in the unperturbed case.

关键词： Landau levels spectral algorithm periodic perturbations

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Nearly Linear Time algorithm for Mean Hitting Times of Random Walks on a Graph 20

Nearly Linear Time Algorithm for Mean Hitting Times of Rando...

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13th Annual ACM International Conference on Web Search and Data Mining (WSDM)

作者： Zhang, Zuobai Xu, Wanyue Zhang, Zhongzhi Fudan Univ Sch Comp Sci Shanghai Key Lab Intelligent Informat Proc Shanghai Peoples R China

ISBN: (纸本)9781450368223

For random walks on a graph, the mean hitting time H-j from a vertex i chosen from the stationary distribution to the target vertex j can be used as a measure of importance for vertex j, while the Kemeny constant K is the mean hitting time from a vertex i to a vertex j selected randomly according to the stationary distribution. Both quantities have found a large variety of applications in different areas. However, their high computational complexity limits their applications, especially for large networks with millions of vertices. In this paper, we first establish a connection between the two quantities, representing K in terms of H-j for all vertices. We then express both quantities in terms of quadratic forms of the pseudoinverse for graph Laplacian, based on which we develop an efficient algorithm that provides an approximation of H-j for all vertices and K in nearly linear time with respect to the edge number, with high probability. Extensive experiment results on real-life and model networks validate both the efficiency and accuracy of the proposed algorithm.

关键词： Random walk hitting time Kemeny constant spectral algorithm complex network node centrality

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Real-time multispectral data collection, processing, downlink and display: Test and demonstration

Real-time multispectral data collection, processing, downlin...

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Airborne Intelligence, Surveillance, Reconnaissance (ISR) Systems and Applications

作者： Runnes, Denise Peterman, Scott Powell, Jonathan Leflore, Chad Martin, Addison Schoonmaker, Jon Henderson, Paula Dirbas, Joseph Crowley, Michael Davies, Adam Radiance Technol Inc 775 N Univ Blvd Mobile AL 36608 USA Adv Coherent Technol San Diego CA 92106 USA PAR Govt Syst Corp La Jolla CA 92037 USA

ISBN: (纸本)9780819471376

Radiance Technologies, Inc. has tested and demonstrated real-time collection and on-board processing of Multispectral Imagery (MSI). Further, the test and demonstration consisted of a real-time downlink from the aircraft to the ground station and real-time display of the processed data product. The multispectral imagery was collected with a low-cost, low-profile MSI sensor, MANTIS-3T, from PAR Government Systems. The data product was created from output of a novel spectral algorithm combination that increases the probability of detection and decreases the false alarm rates for specific objects of interest. The display product was a compressed true color image in which the detected objects were delineated with red pixels. A description of the end-to-end solution, issues encountered as well as their resolution, and results will be discussed.

关键词： real-time spectral processing multispectral remote sensing spectral algorithm reconnaissance MANTIS data downlink

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Improved Cheeger's Inequality: Analysis of spectral Partitioning algorithms through Higher Order spectral Gap 13

Improved Cheeger's Inequality: Analysis of Spectral Partitio...

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45th Annual ACM Symposium on the Theory of Computing (STOC)

作者： Kwok, Tsz Chiu Lau, Lap Chi Lee, Yin Tat Gharan, Shayan Oveis Trevisan, Luca CUHK Hong Kong Peoples R China Stanford Univ Stanford CA 94305 USA

Let phi(G) be the minimum conductance of an undirected graph G, and let 0 = lambda(1) = 2, phi(G) = O(kappa) lambda(2)/root lambda(kappa) , and this performance guarantee is achieved by the spectral partitioning algor... 详细信息

ISBN: (纸本)9781450320290

Let phi(G) be the minimum conductance of an undirected graph G, and let 0 = lambda(1) <= lambda(2) <= . . . <= lambda(n) <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any kappa >= 2, phi(G) = O(kappa) lambda(2)/root lambda(kappa) , and this performance guarantee is achieved by the spectral partitioning algorithm. This improves Cheeger's inequality, and the bound is optimal up to a constant factor for any kappa. Our result shows that the spectral partitioning algorithm is a constant factor approximation algorithm for finding a sparse cut if lambda(kappa) is a constant for some constant k. This provides some theoretical justification to its empirical performance in image segmentation and clustering problems. We extend the analysis to spectral algorithms for other graph partitioning problems, including multi-way partition, balanced separator, and maximum cut.

关键词： Graph partitioning spectral algorithm

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Simple Approximation algorithms for Balanced MAX 2SAT 12th

Simple Approximation Algorithms for Balanced MAX 2SAT

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12th Latin American Symposium on Theoretical Informatics (LATIN)

作者： Paul, Alice Poloczek, Matthias Williamson, David P. Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14850 USA

ISBN: (纸本)9783662495285

We study simple algorithms for the balanced MAX 2SAT problem, where we are given weighted clauses of length one and two with the property that for each variable x the total weight of clauses that x appears in equals the total weight of clauses for . We show that such instances have a simple structural property in that any optimal solution can satisfy at most the total weight of the clauses minus half the total weight of the unit clauses. Using this property and a novel analysis of the computation tree, we are able to show that a large class of greedy algorithms, including Johnson's algorithm, gives a -approximation algorithm for balanced MAX 2SAT;a similar statement is false for general MAX 2SAT instances. We further give a spectral 0.81-approximation algorithm for balanced MAX E2SAT instances (in which each clause has exactly 2 literals) by a reduction to a spectral algorithm of Trevisan for the maximum colored cut problem. We provide experimental results showing that this spectral algorithm performs well and is slightly better than Johnson's algorithm and the Goemans-Williamson semidefinite programming algorithm on balanced MAX E2SAT instances.

关键词： Maximum satisfiability Approximation algorithm Greedy algorithm spectral algorithm Balanced instances Priority algorithm

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Toward Model-Based Control of Near-Wall Turbulent Coherent Structures

Toward Model-Based Control of Near-Wall Turbulent Coherent S...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Tsolovikos, Alexandros Suryanarayanan, Saikishan Bakolas, Efstathios Goldstein, David Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

Coherent structures in wall-bounded flows, such as large-scale motions (LSMs), contribute significantly to the dynamics of turbulent boundary layers: they contain a large fraction of the turbulent kinetic energy, add to the average Reynolds shear stresses, and transport momentum. Therefore, one may wish to control turbulence by manipulating the movement of these LSMs in order to achieve a desired performance gain (such as drag reduction, noise reduction, or mixing enhancement). In the present work, we approach the above problem in an abstract way by developing a model-based approach of steering towards the wall isolated volumes of interest (that could be an LSM we wish to control) in a direct numerical simulation (DNS) of a three-dimensional laminar boundary layer using as an actuator a Gaussian-distributed force field applied in a region of the flow directly above the wall. In particular, we derive a reduced-order linear model of the actuator dynamics using a variant of dynamic mode decomposition that includes control inputs (dynamic mode decomposition with control - DMDc), which describes how the actuator input (i.e. the magnitude of the input force field) perturbs the velocity field (i.e. the output of the reduced-order model) downstream of the actuator. The identified linear model is then required to track a reference output that creates a downwash along the trajectory of the target volume. To that end, the control design is formulated as an output tracking linear-quadratic optimal control problem with input constraints in discrete time, which is reduced to an equivalent quadratic program with linear constraints. The solution to the constrained optimization problem yields an input signal that effectively drives the target volume towards the wall while minimizing the actuation energy.

关键词： Direct Numerical Simulation Actuators Boundary Layer Thickness Free Stream Velocity Optimal Control Quadratic Programming Shear Stress Kinetic Energy spectral algorithm Tracking Control

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Discriminative spectral learning of hidden markov models for human activity recognition 40

Discriminative spectral learning of hidden markov models for...

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40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015

作者： Nazabal, Alfredo Artes-Rodriguez, Antonio Department of Signal and Communications Theory Universidad Carlos III de Madrid Avenida de la Universidad 30 Leganés Spain

ISBN: (纸本)9781467369978

Hidden Markov Models (HMMs) are one of the most important techniques to model and classify sequential data. Maximum Likelihood (ML) and (parametric and non-parametric) Bayesian estimation of the HMM parameters suffers from local maxima and in massive datasets they can be specially time consuming. In this paper, we extend the spectral learning of HMMs, a moment matching learning technique free from local maxima, to discriminative HMMs. The resulting method provides the posterior probabilities of the classes without explicitly determining the HMM parameters, and is able to deal with missing labels. We apply the method to Human Activity Recognition (HAR) using two different types of sensors: portable inertial sensors, and fixed, wireless binary sensor networks. Our algorithm outperforms the standard discriminative HMM learning in both complexity and accuracy. © 2015 IEEE.

关键词： Discriminative learning Hidden Markov Models Human activity recognition Observable operator models spectral algorithm

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