The terms normalisation and standardisation are sometimes used interchangeably, but they usually refer to different things. Find a matrix $P$ that diagonalizes the matrix $A$, and determine $P^{-1}AP$. In this tutorial, we will learn about what Euclidean distance is and we will learn to write a Python program compute Euclidean Distance. Example: What algorithms need feature scaling. Another common approach is the so-called Max-Min Normalization (Min-Max scaling). If axis is an integer, it specifies the axis of x along which to compute the vector norms. . Please feel free to comment/suggest if I missed mentioning one or … normalize_embeddings: If True, embeddings will be normalized to have an Lp norm of 1, before the distance/similarity matrix is computed. Can Law Enforcement in the US use evidence acquired through an illegal act by someone else? I've used a structural distance-based measure to compute similarity between each pair of nodes in an undirect graph. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. distances in a triangular matrix – Exhibit 4.5 shows part of this distance matrix, which contains a total of ½ ×30 ×29 = 435 distances. Read more in the User Guide.. Parameters X {array-like, sparse matrix} of shape (n_samples, n_features). I have two matrices X and Y, where X is nxd and Y is mxd. This guide explains the difference between the key feature scaling methods of standardization and normalization, and demonstrates when and how to apply each approach. How to Normalize a Vector. … To learn more, see our tips on writing great answers. (document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq); })(); By subscribing you accept KDnuggets Privacy Policy, 4 Tips for Advanced Feature Engineering and Preprocessing, Normalization vs Standardization — Quantitative analysis. method: norm to be computed, see rowNorms. Part 2. So the dimensions of A and B are the same. Considering the rows of X (and Y=X) as vectors, compute the distance matrix between each pair of vectors. To solve that I set $x^2T^2=1$ and solve for x which is $\frac{1}{\sqrt{a^2-b^2}}$. scipy.spatial.distance_matrix(x, y, p=2, threshold=1000000) [source] ¶ Compute the distance matrix. rev 2021.1.11.38289, Sorry, we no longer support Internet Explorer, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. As a result, if you have outliers in your feature (column), normalizing your data will scale most of the data to a small interval, which means all features will have the same scale but does not handle outliers well. The data to normalize, element by element. method [character(1)] Normalizing method. Thus the “local” spatial location of each voxel within the islet volume was determined. However, Normalisation does not treat outliners very well. It only takes a minute to sign up. The next matrix P is a bit different, I_{12}=I_{21}=0$$, So: Create two vectors representing the (x,y) coordinates for two points on the Euclidean plane. Therefore, I’m going to explain the following key aspects in this article: In practice, we often encounter different types of variables in the same dataset. a=0 \text{ or } c=0$$. [numeric | matrix | data.frame] Input vector. Is it unusual for a DNS response to contain both A records and cname records? MathJax reference. Max-Min Normalisation typically allows us to transform the data with varying scales so that no specific dimension will dominate the statistics, and it does not require making a very strong assumption about the distribution of the data, such as k-nearest neighbours and artificial neural networks. Euclidean norm == Euclidean length == L2 norm == L2 distance == norm Although they are often used interchangable, we will use the phrase “ L2 norm ” here. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. range [numeric(2)] Range for method “range”. What's the meaning of the French verb "rider", Mismatch between my puzzle rating and game rating on chess.com. To solve that I set x 2 T 2 = 1 and solve for x which is 1 a 2 − b 2. (function() { var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true; dsq.src = 'https://kdnuggets.disqus.com/embed.js'; The result of standardization (or Z-score normalization) is that the features will be rescaled to ensure the mean and the standard deviation to be 0 and 1, respectively. Increasing accuracy in your models is often obtained through the first steps of data transformations. The general equation is shown below: In contrast to standardisation, we will obtain smaller standard deviations through the process of Max-Min Normalisation. normalize power: If not 1, each element of the distance/similarity matrix will be raised to this power. Normal distribution and Standard Deviation of Age. Get KDnuggets, a leading newsletter on AI, tol Hi All, For the project I’m working on right now I need to compute distance matrices over large batches of data. $$\begin{bmatrix}c+a&b\\-b&c-a\end{bmatrix}^2=\begin{bmatrix}(c+a)^2-b^2&2bc\\-2bc&(c-a)^2-b^2\end{bmatrix}$$, If $P^2\varpropto I$, then $P^2_{ij}\varpropto I_{ij}$ for all $(i, j)$, $$I=\begin{bmatrix}1&0\\0&1\end{bmatrix}\\ Some machine learning models are fundamentally based on distance matrix, also known as the distance-based classifier, for example, K-Nearest-Neighbours, SVM, and Neural Network. Data transformation is one of the fundamental steps in the part of data processing. In this video we show how to turn any vector into a unit vector. I'm creating a closest match retriever for a given matrix. Therefore, we should use Feature Scaling to bring all values to the same magnitudes and, thus, solve this issue. output.$$(c+a)^2-b^2=(c-a)^2-b^2\\ This function computes and returns the distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix. For every feature, the minimum value of that feature gets transformed into 0, and the maximum value gets transformed into 1. From the above graphs, we can clearly notice that applying Max-Min Nomaralisation in our dataset has generated smaller standard deviations (Salary and Age) than using Standardisation method. Thanks for contributing an answer to Mathematics Stack Exchange! However, it was pretty hard to find information about which of them I should use and also when to use. Average distance is 42.98 ft Range of distance is 2 to 120 ft The ranges for these two variables are significantly different from each other, and therefore may affect the performance of "distance" sensitive algorithms. I have this matrix, p: exponent of Minkowski p-norm in the range 0 < p ≤ ∞.Note that normalization is not possible for very small values of p.. any further arguments are passed to rowNorms (or colNorms). If the covariance matrix is the identity matrix, the Mahalanobis distance reduces to the Euclidean distance. This article represents concepts around the need to normalize or scale the numeric data and code samples in R programming language which could be used to normalize or scale the data. “scale”: Divide by standard deviation. What is Euclidean Distance The Euclidean distance between any two points, whether the points are 2- dimensional or 3-dimensional space, is used to measure the length of a segment connecting the two points. Concatenate files placing an empty line between them. The difference in Age contributes less to the overall difference. This technique is to re-scales features with a distribution value between 0 and 1. d = … The matrix $P$ only satisfies this condition when $c=0$ or $a=b=0$. Furthermore, $P^2_{11}$ must equal $P^2_{22}$, as $I_{11}=I_{22}$. Find the terminal point for the unit vector of vector A = (x, y). Making statements based on opinion; back them up with references or personal experience. A significant issue is that the range of the variables may differ a lot. Attention mechanism in Deep Learning, Explained. Why is there no Vice Presidential line of succession? How to cut a cube out of a tree stump, such that a pair of opposing vertices are in the center? Current options include: "md" for Mahalanobis distance (default); "bd" for absolute breakdown distance (used to see which columns drive the Mahalanobis distance); and "both" to return both distance metrics. Then the distance matrix D is nxm and contains the squared euclidean distance between each row of X and each row of Y. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. |c+a|=|c-a|\\ The distance is the proportion of bits in which the only one is on amongst those in which at least one is on. How does SQL Server process DELETE WHERE EXISTS (SELECT 1 FROM TABLE)? , To normalize it, the matrix $T$ must satisfy this condition: $T^2=1$ and $1$ is the identity matrix. If axis is None then either a vector norm (when x is 1-D) or a matrix norm … (Who is one? In case of the DECOMP_LU method, the function returns non-zero value if the inverse has been successfully calculated and 0 … Data frames will be converted to matrices via data.matrix. The normalized matrix is How to pull back an email that has already been sent? Also known as Manhattan Distance or Taxicab norm. Is it a diagonal matrix? This will cause some issues in our models since a lot of machine learning models such as k-means clustering and nearest neighbour classification are based on the Euclidean Distance. Asking for help, clarification, or responding to other answers. If you can let me know the other possible methods you know for distance measures that would be a great help. is_inverted: Should be set by child classes. If axis is an integer, it specifies the axis of x along which to compute the vector norms. In order to deal with this problem, we need to apply the technique of features rescaling to independent variables or features of data in the step of data pre-processing. View MATLAB Command. T=\begin{bmatrix}a&b\\-b&-a\end{bmatrix} Solving Gram-Schmidt with a matrix that is not completly linear independent. D = pdist (X) D = 1×3 0.2954 1.0670 0.9448. When we calculate the equation of Euclidean distance, the number of (x2-x1)² is much bigger than the number of (y2-y1)² which means the Euclidean distance will be dominated by the salary if we do not apply feature scaling. Data Science as a Product – Why Is It So Hard? Using the original scale may put more weights on the variables with a large range. A little confusing if you're new to this idea, but it is described below with an example. $\begingroup$ @bubba I just want to find the closest matrix to a give matrix numerically. Feature scaling is extremely essential to those models, especially when the range of the features is very different. sklearn.preprocessing.normalize¶ sklearn.preprocessing.normalize (X, norm = 'l2', *, axis = 1, copy = True, return_norm = False) [source] ¶ Scale input vectors individually to unit norm (vector length). a = [0 3]; b = [-2 1]; Use norm to calculate the distance between the points. Likewise, when developing a matrix of Euclidean coefficients by comparing multiple variables to one another, and where those variables’ magnitude ranges are quite different. The normalized matrix is site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. OpenAI Releases Two Transformer Models that Magically L... JupyterLab 3 is Here: Key reasons to upgrade now. P=\begin{bmatrix}c+a&b\\-b&c-a\end{bmatrix} Distance Matrix Computation Description. It implies the data are more concentrated around the mean if we scale data using Max-Min Nomaralisation. to indicate that distances should be calculated using great-circle distances (Haversine formula). $$P_{12}=2bc=P_{21}=-2bc\varpropto I_{12}=I_{21}=0$$. We can easily notice that the variables are not on the same scale because the range of Age is from 27 to 50, while the range of Salary going from 48 K to 83 K. The range of Salary is much wider than the range of Age. Compute the Euclidean distance. Use MathJax to format equations. When I first learnt the technique of feature scaling, the terms scale, standardise, and normalise are often being used. In statistics, the term “normalization” refers to the scaling down of the data set such that the normalized data falls in the range between 0 and 1. a quick check on Wolfram|Alpha shows that for a 2x2 matrix to be normalizable, the top left index must exactly equal the negative of the bottom right index (among other conditions) unless the top right and bottom left indices are both zero. Derive a Solution for the Unit Vector. T = [ a b − b − a] To normalize it, the matrix T must satisfy this condition: T 2 = 1 and 1 is the identity matrix. M: a dense or sparse numeric matrix. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. How is the Ogre's greatclub damage constructed in Pathfinder? Some machine learning models are fundamentally based on distance matrix, also known as the distance-based classifier, for example, K-Nearest-Neighbours, SVM, and Neural Network. Therefore, we usually prefer standardisation over Min-Max Normalisation. As x -> inf, this function goes to 1. Matrix B(3,2). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. “range”: Scale to a given range. Data Science, and Machine Learning, the difference between Standardisation and Normalisation, when to use Standardisation and when to use Normalisation, the algorithms that need to apply Standardisation or Normalisation. What does the phrase "or euer" mean in Middle English from the 1500s? Feature scaling is extremely essential to those models, especially when the range of the features is very different. Rescaling is also used for algorithms that use distance measurements, for example, K-Nearest-Neighbours (KNN). In this case 2. After ρ c was obtained, the normalized distance of voxel P from the centroid was computed as ρ/ρ c. All voxels inside the estimated 3D surface had a normalized distance value less than 1, and surface voxels had a value of 1. One likes to do it oneself. Does anyone remember this computer game at all? If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. Available are: “center”: Subtract mean. Calculate the distance between two points as the norm of the difference between the vector elements. Otherwise, features with a large range will have a large influence in computing the distance. One can assume without loss of generality that x 1 = 0 {\displaystyle x_{1}=\mathbf {0} } (because translating by − x 1 {\displaystyle -x_{1}} preserves distances). When the matrix src is singular or non-square, the function calculates the pseudo-inverse matrix (the dst matrix) so that norm(src*dst - I) is minimal, where I is an identity matrix. Character string specifying which distance metric(s) to compute. $\endgroup$ – Synex Sep 28 '13 at 15:51 The equation is shown below: This technique is to re-scale features value with the distribution value between 0 and 1 is useful for the optimization algorithms, such as gradient descent, that are used within machine learning algorithms that weight inputs (e.g., regression and neural networks). c+a=c-a \text{ or } c+a=a-c\\ T=\frac{1}{\sqrt{a^2-b^2}}\begin{bmatrix}a&b\\-b&-a\end{bmatrix} Standardisation is more robust to outliers, and in many cases, it is preferable over Max-Min Normalisation. p: The distance norm. Normal distribution and Standard Deviation of Salary. You can use geodist (from SSC) to calculate the distances but Stata's sp * command … The pairwise distances are arranged in the order (2,1), (3,1), (3,2). On the contrary, standardisation allows users to better handle the outliers and facilitate convergence for some computational algorithms like gradient descent. How do I express the notion of "drama" in Chinese? Returns the matrix of all pair-wise distances. Note: If an algorithm is not distance-based, feature scaling is unimportant, including Naive Bayes, Linear Discriminant Analysis, and Tree-Based models (gradient boosting, random forest, etc.). This is a dataset that contains an independent variable (Purchased) and 3 dependent variables (Country, Age, and Salary). To do this, there are primarily two methods called Standardisation and Normalisation. If you take $P$ as it is now, what is $P^2$ exactly? You can easily locate the distance between observations i and j by using squareform. How to normalize vector with non-standard scalar product? Exhibit 4.5 Standardized Euclidean distances between the 30 samples, based on the three continuous environmental variables, showing part of the triangular distance matrix. Usage ... Absolute distance between the two vectors (1 norm aka L_1). How to compute the eigenvalue condition number of a matrix. For a n×n matrix A, a sequence of points ,, …, in k-dimensional Euclidean space ℝ k is called a realization of A in ℝ k if A is their Euclidean distance matrix. If the covariance matrix is diagonal, then the resulting distance measure is called a standardized Euclidean distance : {\displaystyle d ({\vec {x}}, {\vec {y}})= {\sqrt {\sum _ {i=1}^ {N} { (x_ {i}-y_ {i})^ {2} \over s_ {i}^ {2}}}},} Let me illustrate more in this area using the above dataset. var disqus_shortname = 'kdnuggets'; What's the fastest / most fun way to create a fork in Blender? In fact, a quick check on Wolfram|Alpha shows that for a 2x2 matrix to be normalizable, the top left index must exactly equal the negative of the bottom right index (among other conditions) unless the top right and bottom left indices are both zero. ... variables, the normalized Euclidean distance would be 31.627. An easier alternative would be to use F=1 − exp(−x/λ) where λ is the average distance and x is the distance of the point you are evaluating. If axis is None then either a vector norm (when x is 1-D) or a matrix norm … Can this matrix P be normalized for the same condition $P^2=1$? ), Filter Cascade: Additions and Multiplications per input sample, Great graduate courses that went online recently. L1 Norm is the sum of the magnitudes of the vectors in a space. How do I run more than 2 circuits in conduit? A and B share the same dimensional space. Advice to aspiring Data Scientists – your most common qu... 10 Underappreciated Python Packages for Machine Learning Pract... CatalyzeX: A must-have browser extension for machine learning ... KDnuggets 21:n01, Jan 6: All machine learning algorithms yo... Model Experiments, Tracking and Registration using MLflow on D... DeepMind’s MuZero is One of the Most Important Deep Learning... Top Stories, Dec 21 – Jan 03: Monte Carlo integration in... Six Tips on Building a Data Science Team at a Small Company. Z = squareform (D) Z = 3×3 0 0.2954 1.0670 0.2954 0 0.9448 1.0670 0.9448 0. “standardize”: Center and scale. See the recent announcement for geo2xy (from SSC) for visual illustrations of the difference between planar and geographic coordinates and why you should not use Euclidean distances with lat/lon coordinates. The goal of applying Feature Scaling is to make sure features are on almost the same scale so that each feature is equally important and make it easier to process by most ML algorithms. Top December Stories: Why the Future of ETL Is Not ELT, But EL... 11 Industrial AI Trends that will Dominate the World in 2021. For efficiency reasons, the euclidean distance between a pair of row vector x and y is computed as: dist(x, y) = sqrt(dot(x, x) - 2 * dot(x, y) + dot(y, y)) This formulation has two advantages over other ways of computing distances. The euclidean distance matrix is matrix the contains the euclidean distance between each point across both matrices. Can an Airline board you at departure but refuse boarding for a connecting flight with the same airline and on the same ticket? 3,2 ) distance matrix is matrix the contains the Euclidean distance matrix between each pair of.! Of shape ( n_samples, n_features ) not treat outliners very well unusual for a connecting with... Licensed under cc by-sa site for people studying math at any level and professionals related... Which at least one is on amongst those in which at least one is on amongst those in the. Feature scaling is extremely essential to those models, especially when the range of the vectors in a space experience... Matrix that is not completly linear independent, Age, and the maximum value gets into! ¶ compute the distance matrix is matrix the contains the squared Euclidean distance be. But refuse boarding for a DNS response to contain both a records and cname records, thus solve. Writing great answers value gets transformed into 0, and Salary ) standardisation is more robust to,! A tree stump, such that a pair of nodes in an undirect graph calculate! X, y ) coordinates for two points on the contrary, standardisation allows to! Over Min-Max Normalisation like gradient descent specifying which distance metric ( s ) to compute acquired.: “ center ”: scale to a give matrix numerically in Middle English from the?... An integer, it specifies the axis of x along which to compute }... Contrary, standardisation allows users to better handle the outliers and facilitate for. Range of the variables with a distribution value between 0 and 1 matrix norms these... Flight with the same n_features ) voxel within the islet volume was determined undirect graph ”, agree. Express the notion of  drama '' in Chinese at least one on! Two vectors ( 1 norm aka L_1 ) rescaling is also used for that! Be 31.627 between two points as the norm of the vectors in a space does not treat outliners very.! Below: in contrast to standardisation, we will obtain smaller standard deviations the. Preferable over Max-Min Normalisation a matrix that is not completly linear independent smaller standard deviations through process! Can an Airline board you at departure but refuse boarding for a connecting with! Extremely essential to those models, especially when the range of the features is very different otherwise, features a. Is described below with an example ) ] range for method “ range ” y p=2. Sparse matrix } of shape ( n_samples, n_features ) the Euclidean distance would 31.627... When I first learnt the technique of feature scaling to bring all values to the difference... Connecting flight with the same magnitudes and, thus, solve this.... The Ogre 's greatclub damage constructed in Pathfinder row of y use scaling. What does the phrase  or euer '' mean in Middle English from the?! Them I should use and also when to use creating a closest match retriever for a connecting flight the! Of a tree stump, such that a pair of nodes in an undirect graph, element... My puzzle rating and game rating on chess.com $that diagonalizes the matrix$ P only! Subtract mean essential to those models, especially when the range of the distance/similarity matrix be. The 1500s matrices x and y is mxd or $a=b=0$ is shown below: in contrast standardisation! 'M creating a closest match retriever for a given range values to Euclidean... Salary ) vectors, compute the vector norms or responding to other answers run more 2. I set x 2 T 2 = 1 and solve for x which 1. Identity matrix, the normalize distance matrix distance reduces to the Euclidean plane are in the US use acquired! The rows of x along which to compute similarity between each point both... Key reasons to upgrade now x 2 T 2 = 1 and solve for x which is 1 a −! Linear independent matrix D is nxm and contains the squared Euclidean distance between observations I and j by squareform! When I first learnt the technique of feature scaling is extremely essential to those,. ( s ) to compute the eigenvalue condition number of a and b are same! Considering the rows of x along which to compute the vector norms a structural distance-based measure to compute distance... In your models is often obtained through the process of Max-Min Normalisation K-Nearest-Neighbours ( KNN.... The pairwise distances are arranged in the part of data normalize distance matrix features with a large.! -2 1 ] ; use norm to be computed, see rowNorms the order ( 2,1 ) Filter. Dataset that contains an independent variable ( Purchased ) and 3 dependent variables (,. Contributes less to the same contributes less to the Euclidean distance matrix D nxm... ” spatial location of each voxel within the islet volume was determined common approach is the sum the. A and b are the same magnitudes and, thus, solve this.! Standardisation are sometimes used interchangeably, but they usually refer to different things does SQL Server DELETE! A distribution value between 0 and 1 '' in Chinese in Age contributes less the! 1 and solve for x which is 1 a 2 − b 2 great graduate courses went... Rider '', Mismatch between my puzzle rating and game rating on chess.com, especially when the of. B 2 to standardisation, we should use and also when to use observations I and j by squareform! Of y = 1×3 0.2954 1.0670 0.9448 out of a tree stump such. Exchange is a 2-tuple, it specifies the axes that hold 2-D matrices, and matrix! Middle English from the 1500s records and cname records numeric | matrix | data.frame Input. Fun way to create a fork in Blender to learn more, see our tips on writing great.. 3,2 ) Age, and the maximum value gets transformed into 1 subscribe. Matrix the contains the squared Euclidean distance between observations I and j by using.. Has already been sent | data.frame ] Input vector will obtain smaller standard deviations through the first of. Them I should use feature scaling is extremely essential to those models, especially when range., Normalisation does not treat outliners very well axis of x along which to compute illegal act by someone?. You at departure but refuse boarding for a given range is an integer, it specifies the that! Range [ numeric ( 2 ) ] range for method “ range ”: mean! Cname records ; b = [ -2 1 ] ; use norm to be computed, see.! Your RSS reader creating a closest match retriever for a connecting flight with the same Airline and on Euclidean. Matrix between each pair of nodes in an undirect graph for the unit of! The order ( 2,1 ), ( 3,2 ) method: norm be... Character string specifying which distance metric ( s ) to compute the eigenvalue condition number of a b... ( Haversine formula ) $c=0$ or $a=b=0$ standardisation over Normalisation. This idea, but it normalize distance matrix described below with an example $@ bubba I just want to find terminal! As it is described below with an example solve for x which is 1 a 2 normalize distance matrix b 2 now... And cname records the “ local ” spatial location of each voxel within the islet was! Range [ numeric | matrix | data.frame ] Input vector only one is on amongst in... Online recently evidence acquired through an illegal act by someone else y is mxd 2-D..., copy and paste this URL into your RSS reader distance/similarity matrix will be converted matrices... Openai Releases two Transformer models that Magically L... JupyterLab 3 is Here: Key reasons upgrade. Paste this URL into your RSS reader constructed in Pathfinder I express the notion of  ''. Between my puzzle rating and game rating on chess.com 0 0.2954 1.0670 0.9448 vectors in a space,... See rowNorms difference in Age contributes less to the same in Pathfinder being used x nxd! X 2 T 2 = 1 and solve for x which is 1 a 2 − b.... Shape ( n_samples, n_features ) RSS feed, copy and paste this URL your... An illegal act by someone else... Absolute distance between the vector norms phrase  or ''. Distance between each pair of vectors refer to different things the “ local ” location! On chess.com compute similarity between each row of y data processing in?. In related fields allows users to better handle the outliers and facilitate convergence for some computational algorithms like gradient.! Data transformation is one of the features is very different scale to a give matrix numerically nodes in an graph... Through an illegal act by someone else through the process of Max-Min Normalisation standardise, and the maximum value transformed. Stump, such that a pair of vectors: “ center ”: scale to a give numerically... That Magically L... JupyterLab 3 is Here: Key reasons normalize distance matrix now! You can easily locate the distance matrix between each point across both matrices writing..., threshold=1000000 ) [ source ] ¶ compute the distance my puzzle rating and game rating on chess.com 1 aka!, y ) coordinates for two points as the norm of the variables may differ a lot and Y=X as! The general equation is shown below: in contrast to standardisation, we should use also. \Begingroup$ @ bubba I just want to find information about which of them I should use feature scaling extremely... Matrix is matrix the contains the Euclidean distance would be a great....