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Thematic map visualizing multiple variables
A bivariate map or multivariate map is a type of thematic map that displays two or more variables on a single map by combining different sets of symbols
Multivariate_map
Type of map that visualizes data
with each other (forming a bivariate or multivariate map) and with one or more reference map layers in a single map. For example, a cartogram technique could
Thematic_map
Thematic map based on symbol size
according to an overall total amount. This approach is thus a form of multivariate map. The most common technique, first appearing in the 1850s, is to start
Proportional_symbol_map
Statistical linear model
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models
General_linear_model
Specifies a range of position-dependent colors
color-blind people ( colorblind-friendly) color space color depth 1D 2D: Multivariate map, bivariate or trivariate 3D An axial color gradient (sometimes also
Color_gradient
Field of asymmetric cryptographic primitives
Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field F {\displaystyle
Multivariate_cryptography
Association of one output to each input
whether 0 belongs to its domain of definition (see Halting problem). A multivariate function, multivariable function, or function of several variables is
Function_(mathematics)
Process of designing maps
An interesting map will no doubt engage a reader. Information richness or a map that is multivariate shows relationships within the map. Showing several
Cartographic_design
Data visualization technique
A heat map (or heatmap) is a two-dimensional data visualization technique that represents the magnitude of individual values within a dataset as a color
Heat_map
Map distorting size to show another value
cartogram (also called a value-area map or an anamorphic map, the latter common among German speakers) is a thematic map of a set of features (countries,
Cartogram
Machine learning technique useful for dimensionality reduction
(2006-11-01). "Application of a self-organizing map to select representative species in multivariate analysis: A case study determining diatom distribution
Self-organizing_map
Visualization technique for multivariate data
reasoning is a single question: Compared to what? Small multiple designs, multivariate and data bountiful, answer directly by visually enforcing comparisons
Small_multiple
Measure of covariance of components of a random vector
Multivariate Statistics: a Vector Space Approach. John Wiley and Sons. pp. 116–117. ISBN 0-471-02776-6. W J Krzanowski "Principles of Multivariate Analysis"
Covariance_matrix
The multivariate ENSO index, abbreviated as MEI, is a method used to characterize the intensity of an El Niño Southern Oscillation (ENSO) event. Given
Multivariate_ENSO_index
Statistical modeling method
variables is a multiple linear regression. This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables
Linear_regression
In mathematics, invariant of square matrices
derived via the formula for the Kullback–Leibler divergence between two multivariate normal distributions. Also, n tr ( A − 1 ) ≤ det ( A ) 1 n ≤ 1 n tr
Determinant
Method of estimating the parameters of a statistical model
statistics, the maximum a posteriori (MAP) estimate of an unknown quantity is the mode of the posterior density. The MAP can be used to obtain a point estimate
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Sequential locally weighted global linear maps (S-Map) projection, Multivariate embedding in Simplex or S-Map, Convergent cross mapping (CCM), and Multiview
Empirical_dynamic_modeling
Human-face shaped display of data
mathematician, statistician, and physicist Herman Chernoff in 1973, display multivariate data in the shape of a human face. The individual parts, such as eyes
Chernoff_face
Complex-differentiable (mathematical) function
each point in U {\displaystyle U} . Osgood's lemma shows (using the multivariate Cauchy integral formula) that, for a continuous function f {\displaystyle
Holomorphic_function
Algebraic structure
polynomial rings are defined up to a unique isomorphism.) In other words, a multivariate polynomial ring can be considered as a univariate polynomial over a smaller
Polynomial_ring
Mathematical construct in computer algebra
algebraic varieties under projections or rational maps. Gröbner basis computation can be seen as a multivariate, non-linear generalization of both Euclid's
Gröbner_basis
Chart displaying multivariate data
a common method of visualizing high-dimensional datasets to analyze multivariate data having multiple variables, or attributes. To plot, or visualize
Parallel_coordinates
Nonparametric spectral estimation method
It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. Its roots
Singular_spectrum_analysis
Elliptic-curve cryptography Lattice-based cryptography McEliece cryptosystem Multivariate cryptography Isogeny-based cryptography Corinne Bernstein. "cryptosystem"
List_of_cryptosystems
Branch of mathematics
approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point
Linear_algebra
Method of data analysis
of the data matrix. PCA is the simplest of the true eigenvector-based multivariate analyses and is closely related to factor analysis. Factor analysis typically
Principal_component_analysis
Statistical concept
different parametric family of distributions, for example, a mixture of a multivariate normal distribution and a generalized hyperbolic distribution. N random
Mixture_model
Topics referred to by the same term
distribution for two variables Bivariate map, a single map that displays two variables Two-dimensional curve Multivariate (disambiguation) This disambiguation
Bivariate
Type of mathematical expression
x_{n-1}]\right)[x_{n}].} So, most of the theory of the multivariate case can be reduced to an iterated univariate case. The map from R to R[x] sending r to itself considered
Polynomial
Operation on mathematical functions
numerous programming languages. Partial composition is possible for multivariate functions. The function resulting when some argument xi of the function
Function_composition
Field of mathematics and science based on non-linear systems and initial conditions
Kyrtsou C., Labys W.; Labys (2007). "Detecting positive feedback in multivariate time series: the case of metal prices and US inflation". Physica A. 377
Chaos_theory
Random variable with multiple component dimensions
In probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown
Multivariate_random_variable
Type of polynomial
In algebra, a multilinear polynomial is a multivariate polynomial that is linear (meaning affine) in each of its variables separately, but not necessarily
Multilinear_polynomial
Unscrambler X is a commercial software product for multivariate data analysis, used for calibration of multivariate data which is often in the application of analytical
The_Unscrambler
Sequence of data points over time
analysis may also be divided into linear and non-linear, and univariate and multivariate. A time series is one type of panel data. Panel data is the general class
Time_series
Large stellar association
Robin, Annie C.; Doyon, René (March 2018). "BANYAN. XI. The BANYAN Σ Multivariate Bayesian Algorithm to Identify Members of Young Associations with 150
Tucana–Horologium_association
Mathematical concept in polynomial theory
The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's resultant for distinguishing it from the usual
Resultant
Mathematical function for the probability a given outcome occurs in an experiment
called multivariate. A univariate distribution gives the probabilities of a single random variable taking on various different values; a multivariate distribution
Probability_distribution
Analysis of datasets using techniques from topology
entropies. The information cohomology is an example of ringed topos. Multivariate k-Mutual information appear in coboundaries expressions, and their vanishing
Topological_data_analysis
Categorization of data using statistics
early work assumed that data-values within each of the two groups had a multivariate normal distribution. The extension of this same context to more than
Statistical_classification
Statistical data-visualization software
High-D: Multivariate continuous: Scatterplot matrix, Parallel coordinates Multivariate categorical: Mosaic plot (see also Treemapping) Geographical: Map Special:
Mondrian_(software)
Technique in signal processing
it by a fraction of the sampling interval. It is often used also for multivariate interpolation, for example to resize or rotate a digital image. It has
Lanczos_resampling
Mathematical concept
the Pareto front for three-objective problems are known as the decision maps. They give a clear picture of tradeoffs between the three criteria. The disadvantages
Multi-objective_optimization
Statistical model for a binary dependent variable
not true, however, because logistic regression does not require the multivariate normal assumption of discriminant analysis. The assumption of linear
Logistic_regression
Multivariate statistical technique
In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques
Kernel principal component analysis
Kernel_principal_component_analysis
Deep learning generative model to encode data representation
example, as a multivariate Gaussian distribution) that corresponds to the parameters of a variational distribution. Thus, the encoder maps each point (such
Variational_autoencoder
Measure of dependence between two variables
Besides, recently an estimation method accounting for continuous and multivariate outputs, Y {\displaystyle Y} , was proposed in . The Kullback-Leibler
Mutual_information
Public key cryptosystem
based on the hardness of the problem of finding solutions to a system of multivariate quadratic equations (the so-called MQ problem) since it uses private
Hidden_Field_Equations
Statistical error measure
| X − c | − | X | ) , {\displaystyle E(|X-c|-|X|),} as discussed at Multivariate median (and specifically at Spatial median). This optimization-based
Mean_absolute_error
Concept in linear algebra
(r-d)}.} R. Dennis Cook (2018). An Introduction to Envelopes : Dimension Reduction for Efficient Estimation in Multivariate Statistics. Wiley. p. 7. v t e
Reducing_subspace
Statistical method
PersonalityResearch". Sherman, Ryne A. (2 February 2015). "multicon: Multivariate Constructs". Huang, Francis (3 March 2015). "hornpa: Horn's (1965) Test
Parallel_analysis
Discrete analog of a derivative
denoted Δ {\displaystyle \Delta } (uppercase Delta), is the operator that maps a function f to the function Δ [ f ] {\displaystyle \Delta [f]} defined by
Finite_difference
Application of animation to add a temporal component to a map displaying change
natural disasters, and other multivariate data. Animated mapping is extensively used in the construction of animated maps to depict historical events in
Animated_mapping
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
Subset of artificial intelligence
advantage of the kernel trick to implicitly map input variables to higher-dimensional space. Multivariate linear regression extends the concept of linear
Machine_learning
Measures the relative position of nations' and regions' peacefulness
surveys and which from imputation. Appendix A states that IEP uses "multivariate imputation by chained equations to create country-level estimates" when
Global_Peace_Index
Method of statistical inference
"Admissible Bayes Character of T2-, R2-, and Other Fully Invariant Tests for Multivariate Normal Problems". Annals of Mathematical Statistics. 36 (3): 747–770
Bayesian_inference
Statistical model
space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint
Gaussian_process
Method of estimating the parameters of a statistical model, given observations
of the MLE apply to the restricted estimates also. For instance, in a multivariate normal distribution the covariance matrix Σ {\displaystyle \,\Sigma \
Maximum_likelihood_estimation
Directed graph representing overlaps between sequences of symbols
sequential dependencies in symbolic or discretized time series data. Multivariate De Bruijn graphs extend this idea by jointly encoding patterns across
De_Bruijn_graph
Degree of differentiability of a function or map
∞ {\displaystyle C^{\infty }} smoothness by regarding the function as a map between real vector spaces. This should be distinguished from complex differentiability:
Smoothness
Method used in statistics, pattern recognition, and other fields
smallest group must be larger than the number of predictor variables. Multivariate normality: Independent variables are normal for each level of the grouping
Linear_discriminant_analysis
Mathematical function with multiple real-number arguments
In mathematics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being
Function of several real variables
Function_of_several_real_variables
Statistical method
Analysis," from Statnotes: Topics in Multivariate Analysis. Retrieved on April 13, 2009, from StatNotes: Topics in Multivariate Analysis, from G. David Garson
Factor_analysis
binomial distribution. The multivariate normal distribution, a generalization of the normal distribution. The multivariate t-distribution, a generalization
List of probability distributions
List_of_probability_distributions
Statistics dataset
The Iris flower data set or Fisher's Iris data set is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher
Iris_flower_data_set
Multivariate kernel density estimation Multivariate normal distribution Multivariate Pareto distribution Multivariate Pólya distribution Multivariate
List_of_statistics_articles
presenting large amounts of complex multivariate data that vary continuously across space, as is commonly encountered in maps, aerial photographs, satellite
Glossary of geography terms (N–Z)
Glossary_of_geography_terms_(N–Z)
Waleed. Temporal classification: Extending the classification paradigm to multivariate time series. Diss. The University of New South Wales, 2002. Graves, Alex
List of datasets for machine-learning research
List_of_datasets_for_machine-learning_research
water_quality_variables_on_a_map-_groundwater_and_surface_water_in_South_Africa.pdf Silberbauer, M.J., 2011. Multivariate Point Data Visualisation - Geographical
Maucha_diagram
{\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection
Matrix_regularization
Robin, Annie C.; Doyon, René (20 March 2018). "BANYAN. XI. The BANYAN Σ Multivariate Bayesian Algorithm to Identify Members of Young Associations with 150
List of software for astronomy research and education
List_of_software_for_astronomy_research_and_education
Number with a real and an imaginary part
many others. Important work (including a systematization) in complex multivariate calculus has been started at beginning of the 20th century. Important
Complex_number
Matrix decomposition
been applied for real time event detection from complex data streams (multivariate data with space and time dimensions) in disease surveillance. In astrodynamics
Singular_value_decomposition
Mathematical relation assigning a probability event to a cost
cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively
Loss_function
Array of numbers
Wiley, ISBN 0-471-50728-8. Krzanowski, Wojtek J. (1988), Principles of multivariate analysis, Oxford Statistical Science Series, vol. 3, The Clarendon Press
Matrix_(mathematics)
Coordinate change in linear algebra
terms of linear maps instead of coordinates. A function that has a vector space as its domain is commonly specified as a multivariate function whose variables
Change_of_basis
Grouping a set of objects by similarity
models: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the expectation-maximization algorithm.
Cluster_analysis
Study of health and disease within a population
condition in a particular location or time frame Disease diffusion mapping – Map of disease risk for a region Compartmental models in epidemiology – Type
Epidemiology
Measure of similarity between curves
to measure the difference between probability distributions. For two multivariate Gaussian distributions with means μ X {\displaystyle \mu _{X}} and μ
Fréchet_distance
Set of a matrix's eigenvalues
matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity). In many applications, such
Spectrum_of_a_matrix
Mathematical operation in linear algebra
p. 354–356, 1969. Styan, George P. H. (1973), "Hadamard Products and Multivariate Statistical Analysis" (PDF), Linear Algebra and Its Applications, 6:
Matrix_multiplication
Probability distribution
This follows from applying the additive logistic transformation to map a multivariate normal random variable y ∼ N ( μ , Σ ) , y ∈ R D − 1 {\displaystyle
Logit-normal_distribution
Statistical method in psychology
In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set
Exploratory_factor_analysis
Circular statistical graph of proportionality
The French engineer Charles Joseph Minard also used pie charts, in 1858. A map of his from 1858 used pie charts to represent the cattle sent from all around
Pie_chart
Biogeographical unit with a particular biological community
Abatzoglou, John T.; Dobrowski, Solomon Z.; Parks, Sean A. (2020-03-03). "Multivariate climate departures have outpaced univariate changes across global lands"
Biome
Canadian psychologist (born 1962)
included a debate over the gender pay gap in which Peterson claimed that a "multivariate analysis of the pay gap indicates that it doesn't exist" and that other
Jordan_Peterson
Regularization technique for ill-posed problems
knowledge of the underlying likelihood function is needed. For general multivariate normal distributions for x {\displaystyle \mathbf {x} } and the data
Ridge_regression
Branch of machine learning
performing shallow network. For instance, it was proved that sparse multivariate polynomials are exponentially easier to approximate with DNNs than with
Deep_learning
Extinct genus of bears
Larry (2010-08-13). "Esker, Wilkins, and Agenbroad—Multivariate Analysis Of Ursids: A multivariate analysis of the ecology of North American Pleistocene
Arctodus
Statistical technique
Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri
Correspondence_analysis
Method of interpolating functions on a 2D grid
and textures. An algorithm is used to map a screen pixel location to a corresponding point on the texture map. A weighted average of the attributes (color
Bilinear_interpolation
Matrix of partial derivatives of a vector-valued function
differential calculus with applications in the multivariate linear model and its diagnostics". Journal of Multivariate Analysis. 188 104849. doi:10.1016/j.jmva
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Partitioning a digital image into segments
the entropy of the model. The texture in each region is modeled by a multivariate normal distribution whose entropy has a closed form expression. An interesting
Image_segmentation
Personality model consisting of five broad dimensions
Personality: Re-Analysis, Comparison, And Interpretation Of Six Major Studies". Multivariate Behavioral Research. 16 (2): 149–170. doi:10.1207/s15327906mbr1602_2
Big_Five_personality_traits
Branch of mathematics
algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different
Algebraic_geometry
Overview of and topical guide to machine learning
Self-organizing map (SOM) Logistic regression Ordinary least squares regression (OLSR) Linear regression Stepwise regression Multivariate adaptive regression
Outline_of_machine_learning
Data models for IR probes
solvatochromism expressions, researchers frequently turn to employing multivariate leastsquare fitting. This technique involves fitting a sufficiently extensive
Vibrational_spectroscopic_map
f(x)} , sin ( x + y ) {\displaystyle \sin(x+y)} . In the case of a multivariate function, the parentheses contain several expressions separated by commas
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
MULTIVARIATE MAP
MULTIVARIATE MAP
Surname or Lastname
English
English : topographic name for someone who lived by a maple tree, Middle English mapel (Old English mapul).French : from Latin mapula, a diminutive of mappa ‘piece of cloth’, ‘napkin’, presumably a metonymic occupational name for a cloth merchant or a weaver.
Female
Native American
Native American Sioux name MAPIYA means "sky."
Boy/Male
Tamil
King of stars, Map
Boy/Male
Hindu
King of stars, Map
Girl/Female
Hindu
King of stars, Map
Girl/Female
Tamil
King of stars, Map
Surname or Lastname
English
English : habitational name from Great and Little Linford in Buckinghamshire or Lynford in Norfolk. The former may have Old English hlyn ‘maple’ as its first element; the latter is more likely to contain līn ‘flax’. The second element in each case is Old English ford ‘ford’.
Girl/Female
Indian, Marathi
Star; Map
Surname or Lastname
English
English : from a variant of the medieval female personal name Mab(be), a short form of Middle English, Old French Amabel (from Latin amabilis ‘loveable’). This has survived into the 20th century in the short form Mabel.English : possibly from an unattested Old English male personal name, Mappa.English : from Old Welsh map, mab ‘son’, which was used as a distinguishing epithet.
Surname or Lastname
English (Somerset and Gloucester)
English (Somerset and Gloucester) : unexplained. Perhaps a habitational name from a lost or unidentified place.
Surname or Lastname
English
English : metronymic from the medieval female personal name Mab(be) (see Mapp).
Surname or Lastname
English
English : variant of Maple.
Girl/Female
Hindu, Indian
Maple Tree
Surname or Lastname
English
English : variant spelling of Maple.
Surname or Lastname
German
German : nickname for someone with boils or lumpy skin, or perhaps for a hunchback, from Middle High German maser ‘lump’, ‘protuberance’.German and English : from Middle High Germanmaser, Middle English maser ‘maple-wood bowl’ (Old French masere, of Germanic origin), hence a metonymic occupational name for a wood-turner producing such ware.English : variant spelling of Macer, an occupational name for a mace-bearer, from Old French maissier, massier, a derivative of Old French masse ‘mace’.German (Maaser) : pet form of Thomas.
Surname or Lastname
English
English : of uncertain origin, perhaps, as Reaney suggests, from a pet form of the Old English personal name Wippa, or perhaps a topographic name for someone who lived by a whipple tree, whatever that may have been. Chaucer lists whippletree (probably a kind of dogwood) along with maple, thorn, beech, hazel, and yew.Matthew Whipple came from England to Ipswich, MA, in about 1638. His descendent William Whipple (1730–85) born in Kittery, ME, was a signer of the Declaration of Independence.
Boy/Male
Anglo Saxon
God of youth and music.
Surname or Lastname
English (Norfolk)
English (Norfolk) : metronymic from the medieval female personal name Mab(be) (see Mapp 1).
Surname or Lastname
English and French
English and French : from the medieval personal name Masselin. This originated as an Old French pet form of Germanic names with the first element mathal ‘speech’, ‘counsel’. However, it was later used as a pet form of Matthew. Compare Mace. A feminine form, Mazelina, was probably originally a pet form of Matilda.English and French : possibly a metonymic occupational name for a maker of wooden bowls, from Middle English, Old French maselin ‘bowl or goblet of maple wood’ (a diminutive of Old French masere ‘maple wood’, of Germanic origin). In some cases it may derive from the homonymous dialect terms maslin, one of which means ‘brass’ (Old English mæslen, mæstling), the other ‘mixed grain’ (Old French mesteillon).
Surname or Lastname
English
English : from a short form of the female personal name Mabel (see Mapp).
MULTIVARIATE MAP
MULTIVARIATE MAP
Boy/Male
Biblical
Watchman; city; vision.
Boy/Male
Hindu, Indian, Punjabi, Sikh
Absorbed in the Lord's Essence
Boy/Male
English
Son of Hugh.
Girl/Female
Norse
Thor's fighter.
Girl/Female
Hindu, Indian
Sweet
Girl/Female
German
Temptress.
Boy/Male
Tamil
Kapeeshwara | கபீஷà¯à®µà®°
Lord of monkeys
Boy/Male
Indian, Punjabi, Sikh
Devotee of God
Girl/Female
Muslim
Praise of Allah, Hymn
Boy/Male
Australian, Chinese
Kingly
MULTIVARIATE MAP
MULTIVARIATE MAP
MULTIVARIATE MAP
MULTIVARIATE MAP
MULTIVARIATE MAP
n.
A zodiacal constellation, represented on maps and globes as a centaur shooting an arrow.
n.
A series of spaces marked by lines, and representing proportionately larger distances; as, a scale of miles, yards, feet, etc., for a map or plan.
n.
A description or plan of the heavens and the heavenly bodies; the construction of celestial maps, globes, etc.; uranology.
n.
The moosewood, or striped maple. See Maple.
n.
A dry, indehiscent, usually one-seeded, winged fruit, as that of the ash, maple, and elm; a key or key fruit.
n.
A tree of the genus Acer, including about fifty species. A. saccharinum is the rock maple, or sugar maple, from the sap of which sugar is made, in the United States, in great quantities, by evaporation; the red or swamp maple is A. rubrum; the silver maple, A. dasycarpum, having fruit wooly when young; the striped maple, A. Pennsylvanium, called also moosewood. The common maple of Europe is A. campestre, the sycamore maple is A. Pseudo-platanus, and the Norway maple is A. platanoides.
n.
The making, or study, of maps.
n.
That which runs or flows in the course of a certain operation, or during a certain time; as, a run of must in wine making; the first run of sap in a maple orchard.
v. t.
To represent by a map; -- often with out; as, to survey and map, or map out, a county. Hence, figuratively: To represent or indicate systematically and clearly; to sketch; to plan; as, to map, or map out, a journey; to map out business.
a.
Having many rays.
p. pr. & vb. n.
of Map
n.
Thick sirup made by boiling down the sap of the sugar maple, and then cooling.
n.
Relative dimensions, without difference in proportion of parts; size or degree of the parts or components in any complex thing, compared with other like things; especially, the relative proportion of the linear dimensions of the parts of a drawing, map, model, etc., to the dimensions of the corresponding parts of the object that is represented; as, a map on a scale of an inch to a mile.
a.
Having many streaks.
a.
Of or pertaining to an order of trees and shrubs (Sapindaceae), including the (typical) genus Sapindus, the maples, the margosa, and about seventy other genera.
a.
Many-keeled.
imp. & p. p.
of Map
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
a.
Having or consisting of lines resembling a map; as, the maplike figures in which certain lichens grow.