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Also known as min-max scaling or min-max normalization, rescaling is the simplest method and consists in rescaling the range of features to scale the range in or . Selecting the target range depends on the nature of the data. The general formula for a min-max of is given as:
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is the normalized value. For example, suppose that we have the students' weight data, and the students' weights span . To rescale this data, we first subtract 160 from each student's weight and divide the result by 40 (the difference between the maximum and minimum weights).
991:. If one of the features has a broad range of values, the distance will be governed by this particular feature. Therefore, the range of all features should be normalized so that each feature contributes approximately proportionately to the final distance.
1012:. In support vector machines, it can reduce the time to find support vectors. Feature scaling is also often used in applications involving distances and similarities between data points, such as clustering and similarity search. As an example, the
1565:. Feature standardization makes the values of each feature in the data have zero-mean (when subtracting the mean in the numerator) and unit-variance. This method is widely used for normalization in many machine learning algorithms (e.g.,
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2468:{\displaystyle \left({\frac {v_{1}}{(|v_{1}|^{p}+|v_{2}|^{p}+|v_{3}|^{p})^{1/p}}},{\frac {v_{2}}{(|v_{1}|^{p}+|v_{2}|^{p}+|v_{3}|^{p})^{1/p}}},{\frac {v_{3}}{(|v_{1}|^{p}+|v_{2}|^{p}+|v_{3}|^{p})^{1/p}}}\right)}
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is the mean of that feature vector. There is another form of the means normalization which divides by the standard deviation which is also called standardization.
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for each feature. Next we subtract the mean from each feature. Then we divide the values (mean is already subtracted) of each feature by its standard deviation.
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Ioffe, Sergey; Christian
Szegedy (2015). "Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift".
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The effect of z-score normalization on k-means clustering. 4 gaussian clusters of points are generated, then squashed along the
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1759:. It scales features using the median and IQR as reference points instead of the mean and standard deviation:
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Juszczak, P.; D. M. J. Tax; R. P. W. Dui (2002). "Feature scaling in support vector data descriptions".
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Unit vector normalization regards each individual data point as a vector, and divide each by its
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is a method used to normalize the range of independent variables or features of data. In
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1282:{\displaystyle x'=a+{\frac {(x-{\text{min}}(x))(b-a)}{{\text{max}}(x)-{\text{min}}(x)}}}
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clustering was computed. Without normalization, the clusters were arranged along the
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1113:{\displaystyle x'={\frac {x-{\text{min}}(x)}{{\text{max}}(x)-{\text{min}}(x)}}}
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To rescale a range between an arbitrary set of values , the formula becomes:
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The
Elements of Statistical Learning: Data Mining, Inference, and Prediction
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1404:{\displaystyle x'={\frac {x-{\bar {x}}}{{\text{max}}(x)-{\text{min}}(x)}}}
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are the three quartiles (25th, 50th, 75th percentile) of the feature.
1577:). The general method of calculation is to determine the distribution
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Empirically, feature scaling can improve the convergence speed of
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Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome H. (2009).
1998:. Any vector norm can be used, but the most common ones are the
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algorithms, objective functions will not work properly without
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Since the range of values of raw data varies widely, in some
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converges much faster with feature scaling than without it.
16:
Method used to normalize the range of independent variables
1854:{\displaystyle x'={\frac {x-Q_{2}(x)}{Q_{3}(x)-Q_{1}(x)}}}
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List of datasets in computer vision and image processing
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Another reason why feature scaling is applied is that
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2650:Han, Jiawei; Kamber, Micheline; Pei, Jian (2011).
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1636:{\displaystyle x'={\frac {x-{\bar {x}}}{\sigma }}}
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987:calculate the distance between two points by the
1001:It's also important to apply feature scaling if
2598:. Sebastopol, CA: O'Reilly. pp. 99, 100.
1705:{\displaystyle {\bar {x}}={\text{average}}(x)}
1498:{\displaystyle {\bar {x}}={\text{average}}(x)}
900:List of datasets for machine-learning research
2652:"Data Transformation and Data Discretization"
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1934:{\displaystyle Q_{1}(x),Q_{2}(x),Q_{3}(x)}
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2680:Lecture by Andrew Ng on feature scaling
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1509:Standardization (Z-score Normalization)
26:
1743:, also known as standardization using
963:and is generally performed during the
2063:{\displaystyle x=(v_{1},v_{2},v_{3})}
7:
2656:Data Mining: Concepts and Techniques
2070:, then its Lp-normalized version is:
895:Glossary of artificial intelligence
14:
1025:Rescaling (min-max normalization)
2484:Normalization (machine learning)
1666:is the original feature vector,
2700:Statistical data transformation
2658:. Elsevier. pp. 111–118.
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315:Relevance vector machine (RVM)
1:
804:Computational learning theory
368:Expectation–maximization (EM)
761:Coefficient of determination
608:Convolutional neural network
320:Support vector machine (SVM)
1732:is its standard deviation.
1010:stochastic gradient descent
912:Outline of machine learning
809:Empirical risk minimization
2716:
2489:Normalization (statistics)
1991:{\displaystyle x'=x/\|x\|}
1575:artificial neural networks
1512:
549:Feedforward neural network
300:Artificial neural networks
2596:Data Science from Scratch
1945:Unit vector normalization
1751:(IQR), is designed to be
1459:is the normalized value,
532:Artificial neural network
1318:are the min-max values.
841:Journals and conferences
788:Mathematical foundations
698:Temporal difference (TD)
554:Recurrent neural network
474:Conditional random field
397:Dimensionality reduction
145:Dimensionality reduction
107:Quantum machine learning
102:Neuromorphic engineering
62:Self-supervised learning
57:Semi-supervised learning
2566:"Min Max normalization"
2000:L1 norm and the L2 norm
1725:{\displaystyle \sigma }
1567:support vector machines
250:Apprenticeship learning
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1992:
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1434:is an original value,
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1143:is an original value,
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959:, it is also known as
799:Bias–variance tradeoff
681:Reinforcement learning
657:Spiking neural network
67:Reinforcement learning
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180:Structured prediction
52:Unsupervised learning
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983:. For example, many
824:Statistical learning
722:Learning with humans
514:Local outlier factor
2594:Grus, Joel (2015).
1749:interquartile range
1571:logistic regression
1546:{\displaystyle k=4}
1311:{\displaystyle a,b}
667:Electrochemical RAM
574:reservoir computing
305:Logistic regression
224:Supervised learning
210:Multimodal learning
185:Feature engineering
130:Generative modeling
92:Rule-based learning
87:Curriculum learning
47:Supervised learning
22:Part of a series on
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1583:standard deviation
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1452:{\displaystyle x'}
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1322:Mean normalization
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1161:{\displaystyle x'}
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1014:K-means clustering
989:Euclidean distance
965:data preprocessing
961:data normalization
235: •
150:Density estimation
2632:978-0-387-84884-6
2605:978-1-491-90142-7
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755:Model diagnostics
738:Human-in-the-loop
581:Boltzmann machine
494:Anomaly detection
290:Linear regression
205:Ontology learning
200:Grammar induction
175:Semantic analysis
170:Association rules
155:Anomaly detection
97:Neuro-symbolic AI
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2695:Machine learning
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2572:. Archived from
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2005:For example, if
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996:gradient descent
977:machine learning
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889:Related articles
766:Confusion matrix
519:Isolation forest
464:Graphical models
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195:Learning to rank
190:Feature learning
28:Machine learning
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2570:ml-concepts.com
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953:Feature scaling
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160:Data cleaning
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2625:. Springer.
2621:
2614:
2595:
2589:
2578:. Retrieved
2574:the original
2569:
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2535:
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2004:
1953:, to obtain
1948:
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819:PAC learning
506:
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350:Hierarchical
282:
236:
230:
1951:vector norm
985:classifiers
703:Multi-agent
640:Transformer
539:Autoencoder
295:Naive Bayes
33:data mining
2689:Categories
2580:2022-12-14
2526:1502.03167
2506:References
1563:dimensions
1513:See also:
971:Motivation
688:Q-learning
586:Restricted
384:Mean shift
333:Clustering
310:Perceptron
238:regression
140:Clustering
135:Regression
2546:CiteSeerX
2544:: 25–30.
1986:‖
1980:‖
1827:−
1784:−
1720:σ
1680:¯
1629:σ
1622:¯
1613:−
1473:¯
1382:−
1360:¯
1351:−
1260:−
1235:−
1209:−
1091:−
1058:−
847:ECML PKDD
829:VC theory
776:ROC curve
708:Self-play
628:DeepDream
469:Bayes net
260:Ensembles
41:Paradigms
2478:See also
1965:′
1771:′
1757:outliers
1600:′
1446:′
1338:′
1187:′
1155:′
1045:′
270:Boosting
119:Problems
1690:average
1483:average
1020:Methods
852:NeurIPS
669:(ECRAM)
623:AlexNet
265:Bagging
2662:
2629:
2602:
2548:
1861:where
1753:robust
1745:median
1646:Where
1573:, and
1414:where
1292:where
1123:where
967:step.
645:Vision
501:RANSAC
379:OPTICS
374:DBSCAN
358:-means
165:AutoML
2521:arXiv
2499:fMLLR
867:IJCAI
693:SARSA
652:Mamba
618:LeNet
613:U-Net
439:t-SNE
363:Fuzzy
340:BIRCH
2660:ISBN
2627:ISBN
2600:ISBN
1747:and
1581:and
1579:mean
877:JMLR
862:ICLR
857:ICML
743:RLHF
559:LSTM
345:CURE
31:and
1755:to
1386:min
1369:max
1264:min
1247:max
1213:min
1095:min
1078:max
1062:min
603:SOM
593:GAN
569:ESN
564:GRU
509:-NN
444:SDL
434:PGD
429:PCA
424:NMF
419:LDA
414:ICA
409:CCA
285:-NN
2691::
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2568:.
2002:.
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872:ML
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