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Process of reducing the number of random variables under consideration
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the
Dimensionality_reduction
Projection of data onto lower-dimensional manifolds
Nonlinear dimensionality reduction (NLDR), also known as manifold learning, is any of various related techniques that aim to project high-dimensional data
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector x {\displaystyle
Sufficient dimension reduction
Sufficient_dimension_reduction
Theoretical effect in physics
Dynamical dimensional reduction or spontaneous dimensional reduction is the apparent reduction in the number of spacetime dimensions as a function of the
Dynamical dimensional reduction
Dynamical_dimensional_reduction
or quantum field theory, dimensional reduction is the limit of a compactified theory where the size of the compact dimension(s) goes to zero. For a system
Dimensional_reduction
Partial differential equations whose solutions are instantons
surpassed by Seiberg–Witten invariants. Through the process of dimensional reduction, the Yang–Mills equations may be used to derive other important
Yang–Mills_equations
Subset of artificial intelligence
hypothesis proposes that high-dimensional data sets lie along low-dimensional manifolds, and many dimensionality reduction techniques make this assumption
Machine_learning
Posits ability to interpolate within latent manifolds
many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space. As
Manifold_hypothesis
Difficulties arising when analyzing data with many aspects ("dimensions")
high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression
Curse_of_dimensionality
Multifactor dimensionality reduction (MDR) is a statistical approach, also used in machine learning automatic approaches, for detecting and characterizing
Multifactor dimensionality reduction
Multifactor_dimensionality_reduction
Method of data analysis
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data
Principal_component_analysis
Simplifying data to facilitate analysis
meaningful. Dimensionality reduction helps reduce noise in the data and allows for easier visualization, such as the example below where 3-dimensional data is
Data_reduction
Non-parametric classification method
feature vectors in reduced-dimension space. This process is also called low-dimensional embedding. For very-high-dimensional datasets (e.g. when performing
K-nearest_neighbors_algorithm
Set of related ordination techniques used in information visualization
dimensions, N, an MDS algorithm places each object into N-dimensional space (a lower-dimensional representation) such that the between-object distances are
Multidimensional_scaling
Study of vector bundles, principal bundles, and fibre bundles
Werner Nahm, are obtained as the dimensional reduction of the anti-self-duality in four dimensions to one dimension, by imposing translational invariance
Gauge_theory_(mathematics)
Technique for dimensionality reduction
It is a nonlinear dimensionality reduction technique for embedding high-dimensional data for visualization in a low-dimensional space of two or three
T-distributed stochastic neighbor embedding
T-distributed_stochastic_neighbor_embedding
American ice hockey executive
Inorganic chemistry, Solid-state chemistry, Nanotechnology Thesis Dimensional reduction: directed synthesis of metal-anion frameworks and heterometallic
Eric_Tulsky
General relativity in M-theory
could consider the 10-dimensional theory on a nontrivial circle bundle over M9. Dimensional reduction still leads to a 9-dimensional theory on M9, but with
Higher-dimensional supergravity
Higher-dimensional_supergravity
Neural network that learns efficient data encoding in an unsupervised manner
representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine
Autoencoder
Supergravity in eleven dimensions
four-dimensional supergravity with one gravitino. One important direction in the supergravity program was to try to construct four-dimensional N = 8
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Method in natural language processing
numbers. Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models, explainable
Word_embedding
Topics referred to by the same term
or treatment Urea reduction ratio (URR), a dimensionless number used to quantify hemodialysis treatment adequacy Dimensional reduction, the limit of a compactified
Reduction
Overview of and topical guide to machine learning
classifier Binary classifier Linear classifier Hierarchical classifier Dimensionality reduction Canonical correlation analysis (CCA) Factor analysis Feature extraction
Outline_of_machine_learning
Circle on Earth's surface enclosing majority of the human population
circles can be used for studying population changes over time, dimensional reduction and measuring population centralization. The world’s tightest cluster
Valeriepieris_circle
Measurable property or characteristic
feature space. In order to reduce the dimensionality of the feature space, a number of dimensionality reduction techniques can be employed. Higher-level
Feature_(machine_learning)
Set of learning techniques in machine learning
learning is often to discover low-dimensional features that capture some structure underlying the high-dimensional input data. When the feature learning
Feature_learning
Type of large language model
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
Generative pre-trained transformer
Generative_pre-trained_transformer
Mathematical result
of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded
Johnson–Lindenstrauss_lemma
Type of database that uses vectors to represent other data
are mathematical representations of data in a high-dimensional space. In this space, each dimension corresponds to a feature of the data, with the number
Vector_database
Technique to reduce dimensionality of points in Euclidean space
projection, the original d {\displaystyle d} -dimensional data is projected to a k {\displaystyle k} -dimensional subspace, by multiplying on the left by a
Random_projection
Technique in mathematical modeling
numerical simulations, due to complexity and large size (dimension). Model order reduction aims to lower the computational complexity of such problems
Model_order_reduction
Embedding of data within a manifold based on a similarity function
drawn, making the construction of a latent space an example of dimensionality reduction, which can also be viewed as a form of data compression. Latent
Latent_space
Principle in theoretical physics
distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description from
Holographic_principle
Superconformal Yang–Mills theory
N=1 dimensional super Yang–Mills theory, and the lower dimensional cases D=6, N=2 and D=4, N=4 may be derived from this via dimensional reduction. In
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Machine learning technique useful for dimensionality reduction
learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher-dimensional data set while preserving the topological
Self-organizing_map
Nonlinear dimensionality reduction method
Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods. Isomap is used for computing
Isomap
Indication of topological symmetry groups to topological condensed matter
fact equivalent to a d + 1 {\displaystyle d+1} sphere wedged with lower-dimensional spheres), which are not included in this table. Furthermore, the table
Periodic table of topological insulators and topological superconductors
Periodic_table_of_topological_insulators_and_topological_superconductors
Similarity measure for number sequences
techniques available to any Euclidean space, notably standard dimensionality reduction techniques. This normalised form distance is often used within
Cosine_similarity
Deep learning generative model to encode data representation
variational distribution. As it maps from a known input space to the low-dimensional latent space, it is called the encoder. The decoder is the second neural
Variational_autoencoder
Ten-dimensional supergravity
discovery of eleven-dimensional supergravity in 1978 led to the derivation of many lower dimensional supergravities through dimensional reduction of this theory
Type_IIA_supergravity
Technique to summarize characteristic components of a video recording
Video fingerprinting or video hashing are a class of dimension reduction techniques in which a system identifies, extracts and then summarizes characteristic
Digital_video_fingerprinting
Dimensionality reduction method
In computational mechanics, Guyan reduction, is a dimensionality reduction method which reduces the number of degrees of freedom by ignoring the inertial
Guyan_reduction
Reverse-engineering neural networks
subfield combined various techniques such as feature visualization, dimensionality reduction, and attribution with human-computer interaction methods to analyze
Mechanistic_interpretability
Modern theory of gravitation that combines supersymmetry and general relativity
higher-dimensional supergravity theories via dimensional reduction (e.g. N=1, 11-dimensional supergravity is dimensionally reduced on T7 to 4-dimensional, ungauged
Supergravity
2018 text-generating language model
decoder-only transformer, using twelve masked self-attention heads, with 64-dimensional states each (for a total of 768). Rather than simple stochastic gradient
GPT-1
Grouping a set of objects by similarity
high-dimensional data, many methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high-dimensional spaces
Cluster_analysis
Representation learning technique
representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. It also denotes the
Embedding_(machine_learning)
German mathematician
Maryland, College Park, where he received his PhD in 1989. His thesis Dimensional Reduction for Elliptic Boundary Value Problems was written under the supervision
Christoph_Schwab
Least variables needed to represent data
intrinsic dimension can be used as a lower bound of what dimension it is possible to compress a data set into through dimension reduction, but it can
Intrinsic_dimension
Smooth approximation of one-hot arg max
cutting the dimension by one (the range is a ( K − 1 ) {\displaystyle (K-1)} -dimensional simplex in K {\displaystyle K} -dimensional space), due to
Softmax_function
Deep learning architecture
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
Mamba (deep learning architecture)
Mamba_(deep_learning_architecture)
Multivariate statistical technique
captured by each principal component. This is useful for data dimensionality reduction and it could also be applied to KPCA. However, in practice there
Kernel principal component analysis
Kernel_principal_component_analysis
Framework of superstring theory
eleven-dimensional supergravity. Although a complete formulation of M-theory is not known, such a formulation should describe two- and five-dimensional objects
M-theory
Dimensionality reduction algorithm
In data science, dynamic mode decomposition (DMD) is a dimensionality reduction algorithm developed by Peter J. Schmid and Joern Sesterhenn in 2008. Given
Dynamic_mode_decomposition
Science fiction book trilogy by Liu Cixin
eleven-dimensional protons dimensionally unfolded down to two-dimensional protons with Trisolaran particle accelerators. While in the two-dimensional form
Remembrance_of_Earth's_Past
Statistical technique
the corresponding k {\displaystyle k} dimensional derived covariates. Thus the k {\displaystyle k} dimensional principal components provide the best linear
Principal component regression
Principal_component_regression
Computational technique
the methods. Typically, the steps in the algorithm consist of dimensionality reduction to reduce the complexity of the data, trajectory building to determine
Trajectory_inference
Paradigm in machine learning that uses no classification labels
unsupervised learning, such as clustering algorithms like k-means, dimensionality reduction techniques like principal component analysis (PCA), Boltzmann machine
Unsupervised_learning
Clustering methods
(eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is
Spectral_clustering
Algorithm for modelling sequential data
low-dimensional spaces ("latent space"), one for query and one for key-value (KV vector). This design minimizes the KV cache, as only the low-dimensional
Transformer_(deep_learning)
Signal processing computational method
signals. Given M signal mixtures in an M-dimensional space, GSO project these data points onto an (M-1)-dimensional space by using the weight vector. We can
Independent component analysis
Independent_component_analysis
Academic conference in machine learning
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
International Conference on Learning Representations
International_Conference_on_Learning_Representations
Personality model consisting of five broad dimensions
"messy", all three traits are grouped under conscientiousness. Using dimensionality reduction techniques, psychologists showed that most (though not all) of
Big_Five_personality_traits
Vector quantization algorithm minimizing the sum of squared deviations
through manual inspection. K-means has also been combined with dimensionality reduction techniques to classify large numbers of unlabeled survey objects
K-means_clustering
Machine learning strategy
User-centered labeling strategies: Learning is accomplished by applying dimensionality reduction to graphs and figures like scatter plots. Then the user is asked
Active learning (machine learning)
Active_learning_(machine_learning)
Class of algorithms for pattern analysis
products. The feature map in kernel machines is infinite dimensional but only requires a finite dimensional matrix from user-input according to the representer
Kernel_method
Computational methods in biology
graph. Joint dimension reduction aims to reduce the complexity of multi-omics data by projecting observations onto a lower dimensional latent space such
Single-cell multi-omics integration
Single-cell_multi-omics_integration
Method for dimension reduction in statistics
exponentially with high-dimensional data (as p grows), reducing the number of dimensions can make the operation computable. Dimensionality reduction aims to achieve
Sliced_inverse_regression
Type of artificial neural network
first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution;
Residual_neural_network
Process in machine learning and statistics
which finds low-dimensional projections of the data that score highly: the features that have the largest projections in the lower-dimensional space are then
Feature_selection
Method used in statistics, pattern recognition, and other fields
combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification. LDA is closely related to analysis
Linear_discriminant_analysis
Data analysis process
several football teams over several years is a two-dimensional data set. In many disciplines, two-dimensional data sets are also called panel data. While, strictly
Multidimensional_analysis
Set of statistical processes for estimating the relationships among variables
underdetermined. Alternatively, one can visualize infinitely many 3-dimensional planes that go through N = 2 {\displaystyle N=2} fixed points. More generally
Regression_analysis
Statistical method in data analysis
Steffen; Ertl, Thomas (2016). Visual Clutter Reduction through Hierarchy-based Projection of High-dimensional Labeled Data (PDF). Graphics Interface. Graphics
Hierarchical_clustering
3D reconstruction technique
is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications
Neural_radiance_field
Analysis of datasets using techniques from topology
contains relevant information. Real high-dimensional data is typically sparse, and tends to have relevant low dimensional features. One task of TDA is to provide
Topological_data_analysis
Middle quantile of a data set or probability distribution
generalization of the median to data in higher-dimensional Euclidean space. Given a set of points in d-dimensional space, a centerpoint of the set is a point
Median
Model-free reinforcement learning algorithm
data. Sample efficiency is especially useful for complicated and high-dimensional tasks, where data collection and computation can be costly. Reinforcement
Proximal_policy_optimization
Range to estimate an unknown parameter
Concept in statistics Confidence region – Multi-dimensional version of a confidence interval, a higher dimensional generalization Credence (statistics) – Measure
Confidence_interval
Stratification of a genetic population based on allele frequencies
interpretation as source populations. Genetic data are high dimensional and dimensionality reduction techniques can capture population structure. Principal
Population structure (genetics)
Population_structure_(genetics)
Academic conference in machine learning
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
International Conference on Machine Learning
International_Conference_on_Machine_Learning
Method of a dimension reduction
Count sketch is a type of dimensionality reduction that is particularly efficient in statistics, machine learning and algorithms. It was invented by Moses
Count_sketch
Technique in theoretical physics
vacua or type IIB string theory vacua with or without D-branes. Dimensional reduction Dean Rickles (2014). A Brief History of String Theory: From Dual
Compactification_(physics)
Machine learning methods using multiple input modalities
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
Multimodal_learning
Method used to normalize the range of independent variables
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
Feature_scaling
Algorithmic technique using hashing
as a way to reduce the dimensionality of high-dimensional data; high-dimensional input items can be reduced to low-dimensional versions while preserving
Locality-sensitive_hashing
Technique in numerical linear algebra
This problem was originally solved by Erhard Schmidt in the infinite dimensional context of integral operators (although his methods easily generalize
Low-rank_approximation
Type of convolutional neural network
(2023-02-14). "Deep learning based atomic defect detection framework for two-dimensional materials". Scientific Data. 10 (1): 91. Bibcode:2023NatSD..10...91C
U-Net
AI platform developed by IBM
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association
IBM_Watsonx
Algorithm used by recommender systems
– is taken as a third dimension (in addition to user and item) in advanced collaborative filtering to construct a 3-dimensional tensor structure for exploration
Collaborative_filtering
Probabilistic problem-solving algorithm
well-behaved, it can be estimated by randomly selecting points in 100-dimensional space, and taking some kind of average of the function values at these
Monte_Carlo_method
Technique for the generative modeling of a continuous probability distribution
distribution over images, one can first encode the images into a lower-dimensional space by an encoder, then use a diffusion model to model the distribution
Diffusion_model
Geometric algorithm
Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a
Diffusion_map
Statistical method
such as T-distributed stochastic neighbor embedding and nonlinear dimensionality reduction. The third group includes model-based ordination methods, which
Ordination_(statistics)
Approach to dimensionality reduction
hyperspectral cubes (3D/4D). The mapping from a high-dimensional vector space to a set of lower dimensional vector spaces is a multilinear projection. When
Multilinear_subspace_learning
Set of eigenvectors used in the computer vision problem of human face recognition
all images used to construct the covariance matrix. This produces dimension reduction by allowing the smaller set of basis images to represent the original
Eigenface
Nonparametric measure of rank correlation
{\displaystyle M[i,j]} stores the number of observations that fall into the two-dimensional cell indexed by ( i , j ) {\displaystyle (i,j)} . For streaming data
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Form of dimensional reduction
Freund–Rubin compactification is a form of dimensional reduction in which a field theory in d-dimensional spacetime, containing gravity and some field
Freund–Rubin_compactification
Deep learning library
rectangular arrays of numbers. PyTorch supports various sub-types of multi-dimensional arrays, or Tensors. PyTorch Tensors are similar to NumPy Arrays, but
PyTorch
Machine learning technique
Peter (25 April 2018). "Deep TAMER: Interactive Agent Shaping in High-Dimensional State Spaces". Proceedings of the AAAI Conference on Artificial Intelligence
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
DIMENSIONAL REDUCTION
DIMENSIONAL REDUCTION
Surname or Lastname
English and Scottish
English and Scottish : topographic name, a variant of Sell 1.English and Scottish : occupational name for a saddler, from Anglo-Norman French seller (Old French sellier, Latin sellarius, a derivative of sella ‘seat’, ‘saddle’).English and Scottish : metonymic occupational name for someone employed in the cellars of a great house or monastery, from Anglo-Norman French celler ‘cellar’ (Old French cellier), or a reduction of the Middle English agent derivative cellerer.English and Scottish : occupational name for a tradesman or merchant, from an agent derivative of Middle English sell(en) ‘to sell’ (Old English sellan ‘to hand over, deliver’).German : probably a habitational name from a place named Sella near Hoyerswerda.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Three Dimensions
Girl/Female
Hindu, Indian
Three Dimension
Surname or Lastname
English and Scottish
English and Scottish : nickname for a mild and gentle man, from Middle English do ‘doe’ (Old English dÄ).English (of Norman origin) : habitational name (Old French d’Eu) for someone from Eu in Seine-Maritime, France. The place name is either a dramatic reduction of Latin Augusta ‘(city of) Augustus’, or else derives from the Germanic element auwa ‘water meadow’, ‘island’.
Girl/Female
Gujarati, Indian, Kannada
Dimension; Purity
Boy/Male
Tamil
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Controlling all three dimension
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Girl/Female
Tamil
Trikaya | தà¯à®°à®¿à®•à®¾à®¯à®¾
Three dimensional
Trikaya | தà¯à®°à®¿à®•à®¾à®¯à®¾
Boy/Male
Hindu, Indian
Shining in Three Dimensions
Boy/Male
Bengali, Hindu, Indian, Marathi
One who is Heard from Many Dimensions
Boy/Male
Sikh
Three/third dimension, Cross over worldy desires
Girl/Female
Hindu
Three dimensional
Girl/Female
Tamil
Triguni | தà¯à®°à¯€à®•à¯‚நீ
The three dimensions
Triguni | தà¯à®°à¯€à®•à¯‚நீ
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Three Dimentional
Boy/Male
Tamil
Dimensions
Boy/Male
Tamil
Trigun | தà¯à®°à®¿à®•à¯à®£
The three dimensions
Trigun | தà¯à®°à®¿à®•à¯à®£
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Three Dimensions
Boy/Male
Hindu, Indian
Dimensions
Girl/Female
Indian, Telugu
Uni-dimensional
Boy/Male
Hindu, Indian
Controlling All Three Dimension
DIMENSIONAL REDUCTION
DIMENSIONAL REDUCTION
Girl/Female
Muslim
Beautiful, Silk of heaven
Boy/Male
Indian, Telugu
Lord Vishnu
Girl/Female
Gujarati, Hindu, Indian
Goddess Durga; Grace; Favour; God has Shown Favour
Boy/Male
Indian, Punjabi, Sikh
Eyes of God
Girl/Female
Tamil
Impana | ஈமà¯à®ªà®¾à®¨à®¾
Girl with a melodious voice
Boy/Male
Hindu
The horizon, Appearance
Girl/Female
Arabic
Princess
Girl/Female
British, English, French, German
Bright Fame; Small Robin
Boy/Male
English
Rush
Girl/Female
American, British, English, Greek, Gujarati, Hindu, Indian, Jamaican, Kannada, Swedish
Strange; Bright Famous One
DIMENSIONAL REDUCTION
DIMENSIONAL REDUCTION
DIMENSIONAL REDUCTION
DIMENSIONAL REDUCTION
DIMENSIONAL REDUCTION
n.
Dimension.
n.
The manifoldness with which the fundamental units of time, length, and mass are involved in determining the units of other physical quantities.
n.
The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.
v. t.
The dimensions of a piece of timber with regard to its breadth and thickness; hence, the measure or dimensions of anything.
a.
Threefold; triple; as, trine dimensions, or length, breadth, and thickness.
a.
Having dimensions.
n.
Measure; dimension; size.
v. t.
The measure of a thing; dimensions; size.
n.
Measure in a single line, as length, breadth, height, thickness, or circumference; extension; measurement; -- usually, in the plural, measure in length and breadth, or in length, breadth, and thickness; extent; size; as, the dimensions of a room, or of a ship; the dimensions of a farm, of a kingdom.
n.
An instrument for measuring the dimensions of the pelvis.
n.
Extent; reach; scope; importance; as, a project of large dimensions.
a.
Without dimensions; marking dimensions or the limits.
a.
Having three dimensions; extended in three different directions.
n.
An imagined space having more than three dimensions.
a.
Pertaining to dimension.
a.
Without dimensions; having no appreciable or noteworthy extent.
a.
Pertaining to, or resembling, a mastodon; as, mastodontic dimensions.
a.
Having but one dimension. See Dimension.
n.
A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree.
n.
Measure; dimensions; estimate.