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Method in machine learning
In machine learning the random subspace method, also called attribute bagging or feature bagging, is an ensemble learning method that attempts to reduce
Random_subspace_method
Tree-based ensemble machine learning methods
set. The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is
Random_forest
Method in machine learning
(statistics) Cross-validation (statistics) Out-of-bag error Random forest Random subspace method (attribute bagging) Resampled efficient frontier Predictive
Bootstrap_aggregating
Overview of and topical guide to machine learning
complexity Radial basis function kernel Rand index Random indexing Random projection Random subspace method Ranking SVM RapidMiner Rattle GUI Raymond Cattell
Outline_of_machine_learning
Mathematical optimization algorithm
If initialized randomly, the first stage of iterations is often the fastest, as the error is eliminated within the Krylov subspace that initially reflects
Conjugate_gradient_method
Method of data analysis
found in the same set of dimensions. Subspace clustering can take bottom-up or top-down approaches. Bottom-up methods (such as CLIQUE) heuristically identify
Clustering high-dimensional data
Clustering_high-dimensional_data
Topics referred to by the same term
statistics, data mining and machine learning, bootstrap aggregating The random subspace method, also called attribute bagging In mountaineering, peak bagging In
Bagging
Method of measuring prediction error
Bootstrapping (statistics) Cross-validation (statistics) Random forest Random subspace method (attribute bagging) James, Gareth; Witten, Daniela; Hastie
Out-of-bag_error
Zhi; Yang, Zongkai; Liu, Sanya; Shi, Yinghui (2013-05-02). "Semi-random subspace method for writeprint identification". Neurocomputing. 108: 93–102. doi:10
Writeprint
List of concepts in artificial intelligence
(PDF) on 17 April 2016. Retrieved 5 June 2016. Ho, TK (1998). "The Random Subspace Method for Constructing Decision Forests". IEEE Transactions on Pattern
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Technique to reduce dimensionality of points in Euclidean space
of the data onto a lower k-dimensional subspace. Random projection is computationally simple: form the random matrix "R" and project the d × N {\displaystyle
Random_projection
Measure of the joint variability
vector space is isomorphic to the subspace of random variables with finite second moment and mean zero; on that subspace, the covariance is exactly the L2
Covariance
Algorithm
obtained by first constraining the update to the linear subspace spanned by the columns of the random matrix B − 1 A T S {\displaystyle B^{-1}A^{T}S} , i
Kaczmarz_method
Generalization of the one-dimensional normal distribution to higher dimensions
chi-squared random variables. A detailed survey of these and other test procedures is available. A widely used method for drawing (sampling) a random vector
Multivariate normal distribution
Multivariate_normal_distribution
Statistical method
the bootstrap process as random elements of the metric space ℓ ∞ ( T ) {\displaystyle \ell ^{\infty }(T)} or some subspace thereof, especially C [ 0
Bootstrapping_(statistics)
Type of vector space in math
(in fact, the inner product with the constant random variable 1), and so this kernel is a closed subspace. The conditional expectation has a natural interpretation
Hilbert_space
Concept in mathematics
conjugate gradient squared method (CGS). It is a Krylov subspace method. Unlike the original BiCG method, it doesn't require multiplication by the transpose
Biconjugate gradient stabilized method
Biconjugate_gradient_stabilized_method
Method of data analysis
cluster centroid subspace is spanned by the principal directions. Non-negative matrix factorization (NMF) is a dimension reduction method where only non-negative
Principal_component_analysis
Type of random mathematical object
The Poisson-type random measures (PT) are a family of three random counting measures which are closed under restriction to a subspace, i.e. closed under
Poisson_point_process
Numerical eigenvalue calculation
vector (i.e. use a random-number generator to select each element of the starting vector) and suggested an empirically determined method for determining
Lanczos_algorithm
Search algorithm
real-time, by progressively searching in lower-dimensional subspaces. RRT*-Smart, a method for accelerating the convergence rate of RRT* by using path
Rapidly_exploring_random_tree
Number of values in the final calculation of a statistic that are free to vary
where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the dimension of the subspace. The degrees
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Iterative method for approximating eigenvectors
orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices. The Arnoldi method belongs to a class of linear
Arnoldi_iteration
Grouping a set of objects by similarity
clustering methods (in particular the DBSCAN/OPTICS family of algorithms) have been adapted to subspace clustering (HiSC, hierarchical subspace clustering
Cluster_analysis
Eigenvalue algorithm
inverse iteration method applies power iteration to the matrix A − 1 {\displaystyle A^{-1}} . Other algorithms look at the whole subspace generated by the
Power_iteration
Type of stochastic process
real line such that H {\displaystyle H} is isomorphic to the Hilbert subspace of L 2 ( μ ) {\displaystyle L^{2}(\mu )} generated by { e − 2 π i
Stationary_process
Statistical sampling technique
a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. The sampling method is often used to
Latin_hypercube_sampling
Various meanings of the terms
random variables (i.e., density functions). One econometric formalism that is alternative to the maximum likelihood framework, the Generalized Method
Orthogonality
non-Bayesian methods include stochastic subspace identification (time domain) and frequency domain decomposition (frequency domain). Bayesian methods have been
Operational_modal_analysis
Information sent faster than light
relay also features. In the Star Trek universe, subspace carries faster-than-light communication (subspace radio) and travel (warp drive). The Cities in
Faster-than-light communication
Faster-than-light_communication
Numerical technique
is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While
Monte_Carlo_integration
Subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics
codes since these subspaces are encoded with information that (possibly) won't require any active stabilization methods. These subspaces prevent destructive
Decoherence-free_subspaces
Method for approximating eigenvalues
eigenvalues and eigenvectors of the original matrix A {\displaystyle A} . If the subspace with the orthonormal basis given by the columns of the matrix V ∈ C N ×
Rayleigh–Ritz_method
Process of reducing the number of random variables under consideration
representation can be used in dimensionality reduction through multilinear subspace learning. The main linear technique for dimensionality reduction, principal
Dimensionality_reduction
2008 video game
more extensive single-player mode than its predecessors, known as "The Subspace Emissary". This mode is a plot-driven and side-scrolling beat 'em up featuring
Super_Smash_Bros._Brawl
Biological concept
space. In particular, trait combinations that form a nearly null genetic subspace with little genetic variance respond only inconsistently to selection.
Genetic_variance
Vector quantization algorithm minimizing the sum of squared deviations
return clusters Commonly used initialization methods are Forgy and Random Partition. The Forgy method randomly chooses k observations from the dataset and
K-means_clustering
Numerical method for solving boundary value problems
every possible value of the involved parameters. The Sparse Subspace Learning (SSL) method leverages the use of hierarchical collocation to approximate
Proper generalized decomposition
Proper_generalized_decomposition
Form of radar used to create images of landscapes
MUSIC method is considered to be a poor performer in SAR applications. This method uses a constant instead of the clutter subspace. In this method, the
Synthetic-aperture_radar
Expected value of a random variable given that certain conditions are known to occur
conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take
Conditional_expectation
Concepts from linear algebra
distinct eigenvalues. Any subspace spanned by eigenvectors of T is an invariant subspace of T, and the restriction of T to such a subspace is diagonalizable.
Eigenvalues_and_eigenvectors
algorithms under slight random perturbations of worst-case inputs Symbolic-numeric computation — combination of symbolic and numeric methods Cultural and historical
List of numerical analysis topics
List_of_numerical_analysis_topics
Correspondence between quantum channels and quantum states
of the ancilla on the dilated subspace. The action E(ρ) is obtained by restricting the evolution to the system subspace. In this scheme, the simulation
Choi–Jamiołkowski_isomorphism
degradation (barring any random subspace interference or spatial anomalies).[citation needed] In the Star Trek franchise, subspace communications have a
Technology_in_Star_Trek
Real square matrix whose columns and rows are orthogonal unit vectors
such as Monte Carlo methods and exploration of high-dimensional data spaces, require generation of uniformly distributed random orthogonal matrices.
Orthogonal_matrix
Calculus using a logically rigorous notion of infinitesimal numbers
each of the corresponding k-dimensional subspaces Ek is T-invariant. Denote by Πk the projection to the subspace Ek. For a nonzero vector x of finite norm
Nonstandard_analysis
Group of sensors used to increase gain or dimensionality over a single sensor
Gaussian white random processes (the same as in DML) whereas the signal waveform as Gaussian random processes. Method of direction estimation Method of direction
Sensor_array
Method for finding largest (or smallest) eigenvalues
the Rayleigh quotient in a 3-dimensional subspace can be performed numerically by the Rayleigh–Ritz method. Adding more vectors, see, e.g., Richardson
LOBPCG
Mathematical function, in linear algebra
the origin of W {\displaystyle W} , and linear subspaces of V {\displaystyle V} onto linear subspaces in W {\displaystyle W} (possibly of a lower dimension);
Linear_map
Algorithmic technique using hashing
2008 Multilinear subspace learning – Approach to dimensionality reduction Principal component analysis – Method of data analysis Random indexing Rolling
Locality-sensitive_hashing
algorithm (pCN) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples – sequences of random observations – from a target probability distribution
Preconditioned Crank–Nicolson algorithm
Preconditioned_Crank–Nicolson_algorithm
Method for estimating the unknown parameters in a linear regression model
be estimated within some linear subspace of the full parameter space Rp). See partial least squares regression. Methods for fitting linear models with
Ordinary_least_squares
Mathematical result
scalar multiple of an orthogonal projection P {\displaystyle P} onto a random subspace of dimension k {\displaystyle k} in R n {\displaystyle \mathbb {R}
Johnson–Lindenstrauss_lemma
Subset of artificial intelligence
decision-making. Random forest regression (RFR) falls under the umbrella of decision tree-based models. RFR is an ensemble learning method that builds multiple
Machine_learning
Signal-processing procedure
assumption that both input and impulse response live in respective known subspaces. However, blind deconvolution remains a very challenging non-convex optimization
Blind_deconvolution
Hungarian and American mathematician and physicist (1903–1957)
producing random digits is, of course, in a state of sin." He also noted that when this method went awry it did so obviously, unlike other methods which could
John_von_Neumann
Family of three random counting measures
Poisson-type random measures are a family of three random counting measures which are closed under restriction to a subspace, i.e. closed under thinning
Poisson-type_random_measure
Signal processing technique
frequencies from the noise subspace. The most popular methods of noise subspace based frequency estimation are Pisarenko's method, the multiple signal classification
Spectral_density_estimation
Mathematical game
is smaller by the same amount. This random strategy for the second player can be made non-random using the method of conditional probabilities, giving
Berlekamp_switching_game
Neural network that learns efficient data encoding in an unsupervised manner
traditional methods as one can show that after training single layer linear autoencoders have a latent space whose vectors span the same subspace as the eigenvectors
Autoencoder
algorithm with a visual evaluation method Single-linkage clustering: a simple agglomerative clustering algorithm SUBCLU: a subspace clustering algorithm WACA clustering
List_of_algorithms
Python library for machine learning
the library for both recommendation systems (e.g., for Digg) and dynamic subspace clustering applied to weather forecasting data. PeerIndex used scikit-learn
Scikit-learn
Statistical concept
distributions to be learned. The projection of each data point to a linear subspace spanned by those vectors groups points originating from the same distribution
Mixture_model
Matrix representing a Euclidean rotation
space (or subspace). For a 2 × 2 matrix the trace is 2 cos θ, and for a 3 × 3 matrix it is 1 + 2 cos θ. In the three-dimensional case, the subspace consists
Rotation_matrix
In optiSLang, random sampling methods are used to generate discrete samples of the joined probability density function of the given random variables. Based
OptiSLang
Mathematical space
parameterizes the set of all k {\displaystyle k} -dimensional linear subspaces of an n {\displaystyle n} -dimensional vector space V {\displaystyle V}
Grassmannian
Nonparametric spectral estimation method
SSA and, more generally, of subspace-based methods for signal processing, go back to the eighteenth century (Prony's method). A key development was the
Singular_spectrum_analysis
Statistical method
the different subspace norms, as in the standard lasso, the constraint has some non-differential points, which correspond to some subspaces being identically
Lasso_(statistics)
Type of plane partition
mesh of 25 random points convex polyhedra pieces Delaunay triangulation Dirichlet–Voronoi domains Map segmentation Natural element method Natural neighbor
Voronoi_diagram
Analysis and solving of problems that involve fluid flows
so iterative methods are used, either stationary methods such as successive overrelaxation or Krylov subspace methods. Krylov methods such as GMRES,
Computational_fluid_dynamics
research interests are Krylov subspace methods, non-normal operators and spectral perturbation theory, Toeplitz matrices, random matrices, and damped wave
Mark_Embree
power series.[citation needed] ∂ 1. Boundary of a topological subspace: If S is a subspace of a topological space, then its boundary, denoted ∂ S {\displaystyle
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Process in linear algebra
process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ..
Orthogonalization
Vector space with generalized dot product
{\displaystyle {\overline {H}}.} This means that H {\displaystyle H} is a linear subspace of H ¯ , {\displaystyle {\overline {H}},} the inner product of H {\displaystyle
Inner_product_space
Signal processing technique used in radar
decorrelating interference subspace leakage (ISL), and is resistant to internal clutter motion (ICM). The principal component method firsts applies principal
Space-time adaptive processing
Space-time_adaptive_processing
Technique in mathematical modeling
achieved via subspace projection and approximation of nonlinearities via kernels methods or DEIM. Standard procedures like the POD-Greedy method are readily
Model_order_reduction
Generalization of gamma distribution to multiple dimensions
represents a singular distribution that takes values in a lower-dimension subspace of the space of p × p matrices. The joint-eigenvalue density for the eigenvalues
Wishart_distribution
Difficulties arising when analyzing data with many aspects ("dimensions")
for local methods, reference sets are often nearest-neighbor based Incomparable scores for different dimensionalities: different subspaces produce incomparable
Curse_of_dimensionality
Method for dimension reduction in statistics
X\in \mathbb {R} ^{p}} only through a k {\displaystyle \,k} dimensional subspace; i.e., one can reduce the dimension of the explanatory variables from p
Sliced_inverse_regression
Way of inferring information from cross-covariance matrices
linear-algebra function subspace_angles MATLAB as FileExchange function subspacea Each row can be tested for significance with the following method. Since the correlations
Canonical_correlation
Statistical property of collections of time series data
Granger causality Stationary subspace analysis Asymmetric cointegration Nelson, C.R; Plosser, C.I (1982). "Trends and random walks in macroeconomic time
Cointegration
Topics referred to by the same term
span), the smallest linear subspace of a vector space that includes a set of elements Linear subspace (AKA vector subspace), a vector space that is a
Linear_(disambiguation)
Process of removing noise from a signal
functions (median, blur, despeckle, etc.). Filter (signal processing) Signal subspace Architectural acoustics including Soundproofing Click removal Codec listening
Noise_reduction
interference streams. In cooperative subspace coding, also known as linear network coding, nodes transmit random linear combinations of original packets
Cooperative_MIMO
Clustering algorithm minimizing the sum of distances to k representatives
iteration method known as the "Alternating" heuristic in literature, as it alternates between two optimization steps: Select initial medoids randomly Iterate
K-medoids
1002/stc.2113. S2CID 55868193. Van Overschee, P.; De Moor, B. (1996). Subspace Identification for Linear Systems. Boston: Kluwer Academic Publisher. Schipfors
Bayesian operational modal analysis
Bayesian_operational_modal_analysis
Australian and American mathematician (born 1975)
that is quantitatively close to an isometry when restricted to certain subspaces.[CT05] They showed that it is sufficient for either exact or optimally
Terence_Tao
Type of topological space in mathematics
subsets of a locally compact Hausdorff space are locally compact in the subspace topology. This provides several examples of locally compact subsets of
Locally_compact_space
Isoperimetric-type inequality on product spaces
multiplied by the probability to be outside of a neighbourhood of that subspace at least a distance t {\displaystyle t} away, is bounded from above by
Talagrand's concentration inequality
Talagrand's_concentration_inequality
Statistical modeling technique
of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable
Quantile_regression
Field of mathematics
Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM. Liesen, J., and Strakos, Z. (2012): Krylov Subspace Methods: Principles and Analysis, Oxford
Numerical_linear_algebra
Polytope
-dimensional affine subspace of the n 2 {\displaystyle n^{2}} -dimensional space of all n × n {\displaystyle n\times n} matrices. This subspace is determined
Birkhoff_polytope
Function for integral Fourier-like transform
components. The frequency bands or subspaces (sub-bands) are scaled versions of a subspace at scale 1. This subspace in turn is in most situations generated
Wavelet
Statistical method
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved
Factor_analysis
Approach in data analysis
(2010). Mining Outliers with Ensemble of Heterogeneous Detectors on Random Subspaces. Database Systems for Advanced Applications. Lecture Notes in Computer
Anomaly_detection
Automated recognition of patterns and regularities in data
unknown patterns. KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition focuses more
Pattern_recognition
Statistics concept
In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices
Estimation of covariance matrices
Estimation_of_covariance_matrices
{\displaystyle |\lambda |\geq \beta >r\alpha } ). The slow subspace is a subspace of the center subspace, or identical to it, or possibly empty. Correspondingly
Slow_manifold
handle. Subspace weapons are a class of directed energy weapons that directly affect subspace. The weapons can produce actual tears in subspace, and are
Weapons_in_Star_Trek
Area of research in signal processing
be further classified into beamforming techniques and subspace-based techniques. The first method used to specify and automatically localize the signal
Array_processing
RANDOM SUBSPACE-METHOD
RANDOM SUBSPACE-METHOD
Boy/Male
English American
Son of Rand.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Surname or Lastname
English or Scottish
English or Scottish : unexplained. Possibly, as Black suggests, a reduced form of Langdon.French : from the old Germanic personal name element Lando (see Land), via the oblique case, Landonis.
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Surname or Lastname
English
English : variant of Ransom.
Boy/Male
English
Son of Rand.
Surname or Lastname
English
English : patronymic from Rand 1.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : variant of Brandon.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
RANDOM SUBSPACE-METHOD
RANDOM SUBSPACE-METHOD
Female
Finnish
 Variant form of Finnish Aino, AINA means "the only one." Compare with other forms of Aina.
Boy/Male
Muslim
Tamer
Girl/Female
Indian
Governor
Surname or Lastname
English
English : from Old French conquest ‘conquest’, probably applied as a nickname.
Girl/Female
Arabic, Muslim
Connection; Joint
Boy/Male
Hindu, Indian
Fearless; Brave
Boy/Male
Gujarati, Hindu, Indian, Thai
Handsome; Famous
Girl/Female
Muslim
Name derived from self-sacrifice
Boy/Male
Tamil
Strong
Surname or Lastname
English and Irish
English and Irish : variant of Harshaw.
RANDOM SUBSPACE-METHOD
RANDOM SUBSPACE-METHOD
RANDOM SUBSPACE-METHOD
RANDOM SUBSPACE-METHOD
RANDOM SUBSPACE-METHOD
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
Body; matter; material of which a thing is made; hence, substantiality; solidity; firmness; as, the substance of which a garment is made; some textile fabrics have little substance.
n.
Extra hazard; chance; accident; random.
p. pr. & vb. n.
of Ransom
n.
Random.
v. t.
To furnish or endow with substance; to supply property to; to make rich.
v. i.
To go or stray at random.
n.
Anything driven at random.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
n.
Ransom; release.
n.
Ransom.
n.
To exact a ransom for, or a payment on.
v. i.
To wander at random; to scatter.
a.
Cruising at random on the ocean.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
adv.
In a random manner.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
imp. & p. p.
of Ransom