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Geometric property of a pair of sets of points in Euclidean geometry
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane)
Linear_separability
Algorithm for supervised learning of binary classifiers
converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if
Perceptron
Type of feedforward neural network
in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks are trained using backpropagation and are
Multilayer_perceptron
Statement in computational learning theory
it as counting function theorem. Let the number of homogeneously linearly separable sets of N {\displaystyle N} points in d {\displaystyle d} dimensions
Cover's_theorem
Type of vector space in math
separable Hilbert spaces are therefore isometrically isomorphic to the square-summable sequence space, ℓ 2 . {\displaystyle \ell ^{2}.} Separability was
Hilbert_space
Type of algebraic field extension
field is separable. It follows that most extensions that are considered in mathematics are separable. Nevertheless, the concept of separability is important
Separable_extension
Topics referred to by the same term
Look up separable in Wiktionary, the free dictionary. Separability may refer to: Separable algebra, a generalization to associative algebras of the notion
Separability
Set of methods for supervised statistical learning
finite-dimensional space, it often happens that the sets to discriminate are not linearly separable in that space. For this reason, it was proposed that the original
Support_vector_machine
Difficulties arising when analyzing data with many aspects ("dimensions")
dimension. Moreover, this linear functional can be selected in the form of the simplest linear Fisher discriminant. This separability theorem was proven for
Curse_of_dimensionality
Kirchberger's theorem is a theorem in discrete geometry, on linear separability. The two-dimensional version of the theorem states that, if a finite set
Kirchberger's_theorem
Overview of and topical guide to machine learning
support vector machine Leslie P. Kaelbling Linear genetic programming Linear predictor function Linear separability Linkurious Lior Ron (business executive)
Outline_of_machine_learning
Method used in statistics, pattern recognition, and other fields
concentration inequality for product probability spaces). Data separability by classical linear discriminants simplifies the problem of error correction for
Linear_discriminant_analysis
Topics referred to by the same term
and as such are supplementary Linear separability, the property of two sets of points, where they are linearly separable if there exists at least one line
Linear_(disambiguation)
Type of artificial neural network
three layers, notable for being able to distinguish data that is not linearly separable. Examples of other feedforward networks include convolutional neural
Feedforward_neural_network
Hypersurface used by a classification algorithm
is a hyperplane, then the classification problem is linear, and the classes are linearly separable. Decision boundaries are not always clear cut. That
Decision_boundary
Dimension of the column space of a matrix
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number
Rank_(linear_algebra)
Grouping a set of objects by similarity
clusters in a data set Parallel coordinates Structured data analysis Linear separability Driver and Kroeber (1932). "Quantitative Expression of Cultural Relationships"
Cluster_analysis
Topological space with a dense countable subset
on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset. Contrast separability with
Separable_space
Density-based data clustering algorithm
implemented using a database index for better performance, or using a slow linear scan: RangeQuery(DB, distFunc, Q, eps) { Neighbors N := empty list for each
DBSCAN
Optimization algorithm for artificial neural networks
with 2 learnable layers, and it learned to classify patterns not linearly separable. Modern backpropagation was first published by Seppo Linnainmaa as
Backpropagation
Mathematical function conceived as a crude model
0 {\displaystyle y(t+1)=0} otherwise. It can be used to represent linearly separable boolean functions (for example, AND, OR, NOR) but not, for example
Artificial_neuron
modifiable layers learned internal representations to classify non-linearly separable pattern classes. Subsequent developments in hardware and hyperparameter
History of artificial neural networks
History_of_artificial_neural_networks
Vector quantization algorithm minimizing the sum of squared deviations
and kernel k-means, which uses kernel functions to identify non-linearly separable clusters. The most common algorithm uses an iterative refinement technique
K-means_clustering
Fourteenth letter in the Greek alphabet
mapping. Used in Support Vector machines in cases where the data is not linearly separable. Used in Microelectronics to represent the distance from a p-n junction
Xi_(letter)
Convention of symbols representing language
diacritics can be characterized as less linear than those without. In the initial historical distinction, linear writing systems (e.g. the Phoenician alphabet)
Writing_system
Technique for solving differential equations
differential equation for the unknown f ( x ) {\displaystyle f(x)} is separable if it can be written in the form d d x f ( x ) = g ( x ) h ( f ( x ) )
Separation_of_variables
Convolutional neural network structure
problem in another paper, and showed that even though the problem is linearly separable, single-layer networks exhibited poor generalization capabilities
LeNet
True when either but not both inputs are true
modeling the XOR function requires a second layer because XOR is not a linearly separable function. Similarly, XOR can be used in generating entropy pools for
Exclusive_or
Multivariate statistical technique
(PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space. Recall
Kernel principal component analysis
Kernel_principal_component_analysis
Computational model used in machine learning
models used single-layer perceptrons, which were restricted to solving linearly separable problems. These limitations were highlighted in the book Perceptrons
Neural network (machine learning)
Neural_network_(machine_learning)
Iterative method for finding a linear decision boundary
non-separability. The convergence rate depends on the choice of the learning rate parameter ρ {\displaystyle \rho } and the degree of linear separability
Ho–Kashyap_algorithm
Book by Marvin Minsky and Seymour Papert
names included linearly separable logic, linear-input logic, threshold logic, majority logic, and voting logic. Hardware for realizing linear threshold logic
Perceptrons_(book)
Principle in statistical learning theory
such as linear classifiers. Nevertheless, it can be solved efficiently when the minimal empirical risk is zero, i.e., data is linearly separable.[citation
Empirical_risk_minimization
Mathematical expression for linear operators
specifically linear algebra, the Jordan–Chevalley decomposition, named after Camille Jordan and Claude Chevalley, expresses a linear operator in a unique
Jordan–Chevalley decomposition
Jordan–Chevalley_decomposition
Normed vector space that is complete
normed spaces are separable Banach spaces and any two Banach spaces of the same finite dimension are linearly homeomorphic. Every separable infinite–dimensional
Banach_space
Linear optimal control technique
In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Neuromorphic data-processing model
nanowire networks, diffractive media) to perform computations. Non-Linear Separability: Unlike traditional perceptrons, which fail on problems like the
Receptron
In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as
Discontinuous_linear_map
Construct in quantum information theory
entangled state from separable ones. Entanglement witnesses can be linear or nonlinear functionals of the density matrix. If linear, then they can also
Entanglement_witness
Type of differential equation
PDE is called linear if it is linear in the unknown and its derivatives. For example, for a function u of x and y, a second order linear PDE is of the
Partial_differential_equation
Method of data analysis
mass of two or more classes. The linear discriminant analysis is an alternative which is optimized for class separability. Some properties of PCA include:[page needed]
Principal_component_analysis
Area of mathematics
isomorphic to ℓ 2 ( ℵ 0 ) {\displaystyle \ell ^{\,2}(\aleph _{0})\,} . Separability being important for applications, functional analysis of Hilbert spaces
Functional_analysis
Artificial neural network algorithm
converges to the correct classification if: the training data is linearly separable* η {\displaystyle \eta } is sufficiently small (though smaller η {\displaystyle
Learning_rule
Relation among continuous functions
boundedness principle states that a pointwise bounded family of continuous linear operators between Banach spaces is equicontinuous. Let X and Y be two metric
Equicontinuity
Form of decision making in machine learning
using the concept of piecewise-linear separability of datasets to categorize data. Two datasets are linearly separable if their convex hulls do not intersect
Multi-surface_method
Cluster analysis problem
space. It is believed that the data become more linearly separable in the feature space, and hence, linear algorithms can be applied on the data with a higher
Determining the number of clusters in a data set
Determining_the_number_of_clusters_in_a_data_set
Type of ordinary differential equation
derivatives. In the case of linear differential equations, this means that there are no constant terms. The solutions of any linear ordinary differential equation
Homogeneous differential equation
Homogeneous_differential_equation
Vector space with a notion of nearness
it is Hausdorff; importantly, "separated" does not mean separable. The topological and linear algebraic structures can be tied together even more closely
Topological_vector_space
Soviet and Ukrainian mathematician
recognition he developed a theory of linear discriminant rules where he investigated the problems of linear separability of any number of sets in n-dimensional
Yuri_Petunin
Class of error-correcting code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally
Linear_code
In mathematics, vector space of linear forms
corresponding dual vector space (or just dual space for short) consisting of all linear forms on V , {\displaystyle V,} together with the vector space structure
Dual_space
Mathematical term
certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used
Weak_topology
The real numbers or their cardinality
y ∈ C such that x < y, then there exists z ∈ S such that x < z < y. (separability axiom) C has no first element and no last element. (Unboundedness axiom)
Continuum_(set_theory)
convolution of Lucas numbers 1881 = tricapped prism number 1882 = number of linearly separable Boolean functions in 4 variables 1883 = number of conjugacy classes
1000_(number)
Class of economic models
the assumption of weak separability, under which groups of goods or inputs can be treated as composite aggregates. Separability allows a high-dimensional
Computable general equilibrium
Computable_general_equilibrium
state must satisfy in order for it to be separable. In other words, the reduction criterion is a separability criterion. It was first proved and independently
Reduction_criterion
Upper bound in coding theory
regarding Komamiya (1953). Linear block codes that achieve equality in the Singleton bound are called MDS (maximum distance separable) codes. Examples of such
Singleton_bound
Differential equation containing derivatives with respect to only one variable
the modeled process is random. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function
Ordinary differential equation
Ordinary_differential_equation
Type of continuous linear operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional
Compact_operator
{\displaystyle f:X\to B} is said to be weakly measurable if, for every continuous linear functional g : B → K , {\displaystyle g:B\to \mathbb {K} ,} the function
Weakly_measurable_function
analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies
Topologies on spaces of linear maps
Topologies_on_spaces_of_linear_maps
Notation for quantum states
Bra–ket notation or Dirac notation is a mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual spaces
Bra–ket_notation
Ring that is also a vector space or a module
of A, sometimes called the bidimension of A, measures the failure of separability. Let A be a finite-dimensional algebra over a field k. Then A is an Artinian
Associative_algebra
Numerical method for differential equations
In numerical analysis, the local linearization (LL) method is a general strategy for designing numerical integrators for differential equations based
Local_linearization_method
calculations changes with the system size. Size consistency (or strict separability) is a property that guarantees the consistency of the energy behaviour
Size consistency and size extensivity
Size_consistency_and_size_extensivity
Mathematical concept
In constrained least squares one solves a linear least squares problem with an additional constraint on the solution. This means, the unconstrained equation
Constrained_least_squares
Algorithm for modelling sequential data
answers to queries. This was later shown to be equivalent to the unnormalized linear transformer. The idea of encoder–decoder sequence transduction had been
Transformer_(deep_learning)
Dual pair of vector spaces
b(x,\,\cdot \,)} is a linear functional on Y {\displaystyle Y} and every b ( ⋅ , y ) {\displaystyle b(\,\cdot \,,y)} is a linear functional on X {\displaystyle
Dual_system
List of concepts in artificial intelligence
in layers, notable for being able to distinguish data that is not linearly separable. multi-swarm optimization A variant of particle swarm optimization
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Represents a function with diffusion properties useful in cryptography
An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography
MDS_matrix
Result on the topology of operators on an infinite-dimensional, complex Hilbert space
mathematician Nicolaas Kuiper, for the case of a separable Hilbert space; the restriction of separability was later lifted. The same result, but for the
Kuiper's_theorem
Mathematical operation in signal processing
the separability of the filter, this will require approximately X Y J K {\displaystyle XYJK} multiplications and additions. If the separability of the
Multidimensional discrete convolution
Multidimensional_discrete_convolution
Vector space with generalized dot product
sesquilinear forms with linearity in the second argument rather than the first. Then the first argument becomes conjugate linear, rather than the second
Inner_product_space
Statistics dataset
The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis. It is sometimes called Anderson's Iris data set because
Iris_flower_data_set
Robotics problem on coordinating two parts of a robot
Rotation is represented using quaternions, allowing for a linear solution to be found. While separable methods are useful, any error in the estimation for the
Hand–eye_calibration_problem
Statistical models used for static panel data
inherently nonlinear, the use of the linear index and the exponential link function lead to multiplicative separability, more specifically E[yit ∨ xi1...
Fixed-effect_Poisson_model
trivially related to the linear entropy S L {\displaystyle S_{L}\,} of a state by γ = 1 − S L . {\displaystyle \gamma =1-S_{L}\,.} The linear entropy is a lower
Purity_(quantum_mechanics)
Consumer demand model
using product category spending and brand prices alone. Assuming weak separability of consumer preferences, the optimal allocation of expenditure among
Almost_ideal_demand_system
condition that a state must satisfy in order to be separable. In other words, it is a separability criterion. Consider a quantum mechanical system composed
Range_criterion
Theorems connecting continuity to closure of graphs
connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem states that a linear operator between two Banach
Closed graph theorem (functional analysis)
Closed_graph_theorem_(functional_analysis)
Matrix decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a scaling, followed
Singular_value_decomposition
Nonparametric spectral estimation method
separable as N → ∞ {\displaystyle N\rightarrow \infty } . In practice N {\displaystyle N} is fixed and one is interested in approximate separability between
Singular_spectrum_analysis
Algorithms for matrix decomposition
exact NMF that works for the case where one of the factors W satisfies a separability condition. In Learning the parts of objects by non-negative matrix factorization
Non-negative matrix factorization
Non-negative_matrix_factorization
a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. That is, for each continuous linear functional
Browder–Minty_theorem
Solid-state welding process
(RFW) being the oldest of the methods. W. Richter patented the method of linear friction welding (LFW) process in 1924 in England and 1929 in the Weimar
Friction_welding
A separable partial differential equation can be broken into a set of equations of lower dimensionality (fewer independent variables) by a method of separation
Separable partial differential equation
Separable_partial_differential_equation
Collection of statistical models
most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear
Analysis_of_variance
Function with a multiplicative scaling behaviour
is any real number. Let V and W be two vector spaces over a field F. A linear cone in V is a subset C of V such that s x ∈ C {\displaystyle sx\in C} for
Homogeneous_function
Square matrix constructed from a monic polynomial
In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots
Companion_matrix
Compact operator for which a finite trace can be defined
mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite
Trace_class
Parallel computing paradigm
universal CNN processors. The original CNN processors can only perform linearly separable Boolean functions. By translating functions from digital logic or
Cellular_neural_network
Type of ordinary differential equation
{\displaystyle n=0} , the differential equation is linear. When n = 1 {\displaystyle n=1} , it is separable. In these cases, standard techniques for solving
Bernoulli differential equation
Bernoulli_differential_equation
Topological complex vector space
adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is
C*-algebra
Neural network technology
bandpass receptive fields, which could be recreated by fitting sparse linear codes for natural scenes. This was later found to also occur in the lowest-level
Convolutional_layer
Measure of the "size" of linear operators
certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators
Operator_norm
special. The projective linear group is not special because there exist Azumaya algebras, which are trivial over a finite separable extension, but not over
Special group (algebraic group theory)
Special_group_(algebraic_group_theory)
Any entity that can be measured
input. In quantum mechanics, observables correspond to linear self-adjoint operators on a separable complex Hilbert space representing the quantum state
Observable
Property of materials with both viscous and elastic characteristics under deformation
suffix -elasticity. Linear viscoelasticity is behavior in which the function is separable in both creep response and load. All linear viscoelastic models
Viscoelasticity
Quantum state
B. Werner states are separable for p ≥ 1⁄2 and entangled for p < 1⁄2. All entangled Werner states violate the PPT separability criterion, but for d ≥
Werner_state
non-separable Banach spaces. A slightly modified version also commonly referred to as the Sobczyk theorem, deals with the extension of a bounded linear operator
Sobczyk's_theorem
LINEAR SEPARABILITY
LINEAR SEPARABILITY
Surname or Lastname
Swedish
Swedish : ornamental name from lind ‘lime tree’ + either the German suffix -er denoting an inhabitant, or the surname suffix -ér, derived from the Latin adjectival ending -er(i)us.English (mainly southeastern) : variant of Lind 2.German : habitational name from any of numerous places called Linden or Lindern, named with German Linden ‘lime trees’.
Surname or Lastname
English
English : occupational name for a whitewasher, Middle English limer, lymer, an agent derivative of Old English līm ‘lime’.
Surname or Lastname
English (Cornish)
English (Cornish) : habitational name from a place named with Cornish lan ‘church’. In England this surname is now found chiefly in the southern counties of Wiltshire and Hampshire, and Berkshire; it has no doubt moved there from Cornwall.
Surname or Lastname
English
English : metronymic from Line.
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Female
English
English name probably derived from Germanic lindi, LINDA means "serpent."Â In some cases, it may have been derived from the Spanish word for "pretty."
Boy/Male
Sikh
Love unending
Surname or Lastname
English
English : habitational name from Lingart, Lancashire, or Lingards Wood in Marsden, West Yorkshire, both named from Old English līn ‘flax’ + garðr ‘enclosure’.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Boy/Male
Hindu
Lingam
Boy/Male
Hindu
The Sun
Boy/Male
Irish
Meaning “â€fair-haired,â€â€ the name has been popular since the sixth century when St. Finbar came to an area of Cork that was being tormented by a serpent. The people begged him to do something to help them. One night he went to where the serpent was sleeping and sprinkled it with holy water. The angry serpent tore and devoured the land until she slithered into the sea at Cork Harbor. The track she left behind filled with water and became the River Lee and that’s why St. Finbar is the patron saint of Cork. It is said that the sun didn’t set for two weeks after Finbar’s death.
Surname or Lastname
English (Devon; of Cornish origin)
English (Devon; of Cornish origin) : topographic name for someone who lived by a menhir, i.e. a tall standing stone erected in prehistoric times (Cornish men ‘stone’ + hir ‘long’).
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Girl/Female
Irish
Eimear possessed the “Six Gifts of Womanhood†– “beauty, a gentle voice, sweet words, wisdom, needlework and chastity!†She was bethrothed to the warrior Cuchulainn (read the legend) when they were children and they loved each other very deeply. But Cuchulainn had “a wandering eye†and Eimear endured this, realizing “everything new is fair,†but when he made love to Fand, wife of the sea god Manannan, Eimear confronted the lovers. After seeing the strength of Fand’s love she offered to withdraw. Touched by this display of unselfishness, Fand left Cuchulainn and returned to the sea. When Cuchulainn died Eimear spoke movingly and lovingly at his graveside.
Surname or Lastname
English
English : variant of Lanier 1.Dutch : variant of Leonard.Jewish (western Ashkenazic) : name taken by someone who was good at chanting the Pentateuch at public worship in the synagogue or who regularly did so, from West Yiddish layner ‘reader’ (a derivative of West Yiddish laynen ‘to read’, which comes ultimately from Latin legere ‘to read’).Jewish (Ashkenazic) : occupational name for a flax grower or merchant, from German Lein ‘flax’ + agent suffix -er.
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
LINEAR SEPARABILITY
LINEAR SEPARABILITY
Girl/Female
Tamil
Goddess Lakshmi
Girl/Female
Tamil
Dheekshit | தீகà¯à®·à®¿à®¤
Fair complexioned
Girl/Female
Tamil
Innocent
Girl/Female
Indian
Name of a Raga
Surname or Lastname
English
English : variant of Prestwood.
Boy/Male
Muslim/Islamic
Concerning a) seeker or one eho covets
Male
English
Anglicized form of Irish Gaelic FlaithrÃ, FLORRY means "prince-king." Compare with feminine Florry.
Girl/Female
Hindi
Divine grace.
Boy/Male
Tamil
Shelter
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : apparently a habitational name from a lost or unidentified minor place in West Yorkshire, probably in the parish of Halifax, to judge by the distribution of early occurrences of the surname.
LINEAR SEPARABILITY
LINEAR SEPARABILITY
LINEAR SEPARABILITY
LINEAR SEPARABILITY
LINEAR SEPARABILITY
a.
Of a linear shape.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
v. t.
To mark with a line or lines; to cover with lines; as, to line a copy book.
n.
One who lines, as, a liner of shoes.
a.
Linear.
v. t.
To convert into vinegar; to make like vinegar; to render sour or sharp.
prep. & adv.
Near.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
n.
A lunar distance.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
a.
Composed of lines; delineated; as, lineal designs.
n.
A dealer in linen; a linen draper.
n.
Alt. of Lingam
a.
Formed by right lines; rectilineal; as, a right-lined angle.
n.
One who adjusts things to a line or lines or brings them into line.
n.
A vessel belonging to a regular line of packets; also, a line-of-battle ship; a ship of the line.
adv.
In a linear manner; with lines.
n.
Made of linen; as, linen cloth; a linen stocking.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.