Euclidean distance excel. When you drop or double-click Cluster:Euclidean Distance. Euclidean distance excel

 
 When you drop or double-click Cluster:Euclidean DistanceEuclidean distance excel  Before we can predict using KNN, we need to find some way to figure out which data rows are "closest" to the row we're trying to predict on

Actually I have 60x3 values in two different excel sheets, I need to calculate the euclidean distance between these two sheets. put euclidean_dist =; run; Result - 46. 41 1. When a cluster gains or loses a data point, the K means clustering algorithm recalculates its centroid. We can now measure the lengths of each couple for both: AC = 1, BD = 1, BE = 2. 828. I have a data frame and would like to calculate the Euclidean distance between all rows and the last row and add the distance value as a new column to data frame using distance function. C. From Euclidean Distance - raw, normalized and double‐scaled coefficients. Longitude: 144° 25' 29. First, you should only need one set of variables for your Point class. In cell B2, enter the value of y1. Video ini menjelaskan tentang studi kasus algoritma klasifikasi. . However, the Commission Internationale de l’Éclairage (CIE) has extended upon and refined it (numerous times) to improve accuracy. B = Akram is positive and Ali is negative. You can help keep this site running by allowing ads on. . To calculate the Euclidean distance between two vectors in Excel, we can use the following function: =SQRT(SUMXMY2(RANGE1. Oct 28, 2018 at 18:28. The Euclidean distance between two vectors, A and B, is calculated as:. Below is a visualization of the Euclidean distance formula in a 2-dimensional space. The Euclidean distance between cluster 3 and the new wine is smaller. In the results, we can see the following facts; The distance between object 1 and 2 is 0. We used the reference form of the INDEX function to manipulate arrays into different dimensions (remove a column, select a row). h h is a real number such that h ≥ 1 h ≥ 1. Press Enter to calculate the Euclidean distance between the two points. 7,198 6 33 61. So the output array would be 3x3 aswell. There are various techniques to estimate the distance. Below is the implementation in R to calculate Minkowski distance by using a custom function. For different values of λ, we can calculate the distance in three different ways: λ = 1 — Manhattan distance (L¹ metric)The Minkowski distance is a distance between two points in the n -dimensional space. Using the 3D Distance Formula Calculator. The results showed that of the three methods compared had a good level of accuracy, which is 84. 8018 0. But what if we have distance is 0 that why we add 1 in the denominator. As most definitions of color difference are distances within a color space, the standard means of determining distances is the Euclidean distance. We will use the Euclidean distance formula to calculate the rest of the distances. Let's say we have these two rows (True/False has been. I am using Excel 2013. Change the Data range to C3:X24, then at Data type, click the down arrow, and select Distance Matrix. Thus, the Euclidean distance formula is given by: d =√ [ (x2 – x1)2 + (y2 – y1)2] Where, “d” is the Euclidean. I am using scipy distances to get these distances. The Pythagorean theorem states that c = sqrt {a^2+b^2} c = a2 +b2. Now, follow the steps below to calculate the distance. . When you drop or double-click Cluster:Euclidean Distance. Those observations are divided into two clusters - A and B. BTW; formula for a true distance computation in spatial coordinates is: square root of (the sum of the squares of (the coordinate difference)), not the sum of (square root of (the squares of (the coordinate difference))). I'm trying to use Excel to calculate Euclidean Distances between two people in a person x person matrix. I just need a formula that will get me 95% there. Standard_dev Required. I have attempted to use . Euclidean distance in R using two variables in a matrix. euclidean distance calculation for values from. Now I need to find out the distance : |d (i)|=sqrt ( (x (k)-x (j))^2+ (y (k)-y (j))^2+ (z (k)-z (j)^2)), where i=1:60 , j,k are end points of the line segment under. Learn step-by-step. Print the resultant euclidean distance. I want euclidean distance between A1. Now figure out how to plug the Excel values you already have into that formula. The Manhattan distance is longer, and you can find it with more than one path. y1, and so on. This metric is often called the Manhattan distance or city-block metric. Note that the formula treats the values of X and Y seriously:. 5 each, and down 2 spaces of . What I have is thousands of coordinates in 3 dimensional Euclidean space (this isn't a question about distance on Earth or in spherical coordinates). Task 2: Locate and Process The Data Files. Maka, Euclidean Distance antara titik A dan B dapat dihitung menggunakan rumus berikut: d = sqrt ( (x2 – x1) 2 + (y2 – y1) 2) Di mana sqrt adalah simbol untuk square root atau akar kuadrat. Add a comment. 49691. 0. When the sink is on the center, it forms concentric circles around the center. array([2, 6, 7, 7,. Euclidean Distance. See this question on Cros Validated to better understand the difference between a loss function and a metric: a loss function is generally based on a reference metric. There are many such formulas that could be used; the following formula will suffice for our purposes: =ACOS (SIN (Lat1)*SIN (Lat2)+COS (Lat1)*COS (Lat2)*COS (Lon2-Lon1))*180/PI ()*60. Insert the coordinates in the Excel sheet as shown above. Step 2. Click here for the Excel Data File a. 0, 1. The example of computation shown in the Figure below. Distance matrices are sometimes called. The arithmetic mean of the distribution. Mahalanobis vs. . Share. 0. hamming(array1, array2) Note that this function returns the percentage of corresponding elements that differ between the two arrays. We have a great community of people providing excel help here. Then, the Euclidean metric coincides with one's geometric intuition of distance, and the Mahalanobis metric coincides with costliness of traveling along that distance, say, treating distance along one axis as. 46 4. The euclidean distance is computed between pairs of rows and then averaged for the group. E. The basis of many measures of similarity and dissimilarity is euclidean distance. Using the original values, compute the Euclidean distance for all possible pairs of the first three observations. If you were to rewrite the Pythagorean theorem for the Manhattan distance, it would instead be c = a + b c = a +b. Imagine a scenario for two US counties, where most of the diabetes variables have a measurement scale from 0 to 1, but one of the variables has a measurement scale from 0 to 10. The Euclidean Distance between point A and B is. SquaredEuclideanDistance [u, v] gives the squared Euclidean distance between vectors u and v. 9 Statistical distance between records can be measured in several ways. Distance between 2 coordinates 2D array. 23. Beta diversity is another name for sample dissimilarity. a. Since it returns the distance in metres, we need to divide it by 1609. If one presently has an RGB (red, green, blue) tuple and wishes to find the color difference, computationally one of the easiest is to consider R, G, B linear dimensions defining the. As you can see in this scatter graph, each. 8 miles. I want euclidean distance between A1. So the dimensions of A and B are the same. Euclidean space was originally devised by the Greek mathematician Euclid around 300 B. This video demonstrates how to calculate Euclidean distance in Excel to find similarities between two observations. #initializing two pandas series. 4142135623730951] If you only want points that lie within a certain distance from (x1, y1), you could write:Well, only the OP can really know what he wants. sir, I have values in an excel sheet, which contains 60x3 values, they are x,y,z cordinates for all the 60 points. Aplicando essa fórmula como distância, o espaço euclidiano torna-se um espaço métrico . We saw how to classify data using K-nearest neighbors (KNN) in Excel. The issue I have is that the number of. 0. Distance Matrix: Diagonals will be 0 and values will be symmetric. in G Lee & Y Jin (eds), Proceedings of 34th International Conference on Computers and Their Applications, CATA 2019. I think the Mahalanobis metric is perhaps best understood as a weighted Euclidean metric. How to calculate Euclidian distance between two points defined by matrix containing x, y? 6. Write the Excel formula in any one of the cells to calculate the Euclidean distance. Euclidean Distance. The Minkowski distance is a distance between two points in the n -dimensional space. 1609 metres is equal to 1 mile. The idea of a norm can be generalized. That is why, when performing k-means, it is important to run diagnostic checks for determining the number of clusters in the data set. So here are some of the distances used: Minkowski Distance – It is a metric intended for real-valued vector spaces. Equivalent to having 2s equations with 2s unknowns Implementing Reed-Solomon – p. linalg. X₁= Existing entry's brightness. Since we are using complete linkage clustering, the distance between "35" and every other item is the maximum of the distance between this item and 3 and this item and 5. Orthogonal matrices and euclidean distances. Euclidean space diperkenalkan oleh Euclid, seorang matematikawan dari Yunani sekitar tahun 300 B. The formula for this distance between a point X (X 1, X 2, etc. The Minkowski distance is a distance between two points in the n -dimensional space. Euclidean Distance Euclidean Distance digunakan untuk mengukur tingkat kemiripan jarak antara data dengan rumus euclidean (Nishom 2019). 1. 15, as some earlier/later versions seem to require a full distance matrix to be computed. 4142135623730951, 1. Rumus yang dapat digunakan dapat dilihat pada persamaan (3). Note: Round intermediate calculations to at least 4 decimal places and your final answers to 2 decimal places. Euclidean distance in R using two variables in a matrix. Then repeat this process for each point in columns X1, Y1. microsoft excel - Euclidean distance between two points with coordinates stored as strings - Super User Euclidean distance between two points with coordinates stored as strings Ask Question. In such a space, the distance formulas for points in rectangular coordinates are based on the Pythagorean theorem. The number of clusters k is an input parameter: an inappropriate choice of k may yield poor results. But unlike Euclidean, Mahalanobis uses a. If A (X1, Y1, Z1) and B (X2, Y2, Z2) are two vector points on a plane. Before we can predict using KNN, we need to find some way to figure out which data rows are "closest" to the row we're trying to predict on. 5) This well-known distance measure, which generalizes our notion of physical distance in two- or three-dimensional space to multidimensional space, is called the Euclidean distance (but often referred to as the ‘Pythagorean distance. Decoding (Syndromes) Step 1: Calculate the first 2s syndromes Syndromes are defined for all l: s l = Xs i=1 Y iX l i For the first 2s, it reduces to: s l = E(αl) = Xs i=1 Y iα lj i 1 ≤ l ≤ 2s s l = R(αl) = E(αl) for the first 2s powers of α. z-scores are computed from the centered data by dividing by the SD. ide rumus ini dari rumus pythagoras. Because of this, it represents the Pythagorean Distance between two points, which is calculated using: d = √ [ (x2 – x1)2 + (y2 – y1)2] We can easily calculate the distance of points of more than two dimensions by simply finding the difference between the two. 2. The above code gives Euclidean distance between the two Vectors for given p and q array is 6. XLSTAT provides a PCoA feature with several standard options that will let you represent. 8805 0. Notice that the resulting Euclidean Distance column values are not rounded up and they are spread across a range [29. If you’re interested in online or in. A distância euclidiana em duas dimensões. Let us assume two points, such as (x 1, y 1) and (x 2, y 2) in the two-dimensional coordinate plane. Copy the formula to other cells to calculate the distance between multiple points. For example, using a point layer of stores and a separate point layer of customers you could create a table or matrix of the drive times to the various stores. Euclidean distance is a metric, so it quantifies the distance between two observations. here is an example of data frame: df = data. Steps: First of all, go to the Developer tab. In this situation, the Euclidean distance will be dominated by variation in. Different algorithms There are different algorithms, as we can see in the document of the R implementation of k-means : Hartigan-Wong, Lloyd, Forgy and MacQueen. untuk mempelajari hubungan antara sudut dan jarak. The resulted value 46. There are a number of ways to create maps with Excel data. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer. 5. In fact, the elongated ellipsoid in the second figure in this post was. 04 whilst "A" corresponds to 10. When I compare an utterance with clustered speaker data I get (Euclidean distance-based) average distortion. The corresponding matrix or data. euclidean distance calculation for values from excel sheet. With Euclidean distance, we only need the (x, y) coordinates of the two points to compute the distance with the Pythagoras formula. 数学 における ユークリッド距離 (ユークリッドきょり、 英: Euclidean distance )または ユークリッド計量 (ユークリッドけいりょう、 英: Euclidean metric; ユークリッド距離函数)とは、人が定規で測るような二点間の「通常の」 距離 のこと. norm (sP - pA, ord=2, axis=1. 2 Calculating two dimensions Euclidean distance and adding it as a column in the data. For example, with a and c (see Figure 1) having coordinates: a = " a 1 a 2 # = " −4 0 # and c = " c 1 c 2 # = " 0 −3 # (3) the squared Euclidean distance d(a,c)is computed as d2(a,c) = (a. 这些名称来源于古希腊数学家欧几里得和毕达哥拉斯,尽管欧几里得. 236. Step Two – If just two variables, use a scatter graph on Excel. e. Practice Section. The Euclidean distance d of two data cases (x 1, x 2) is defined as the square root of the sum of squared differences (dleft(x,y ight)= sqrt{sum {left|{x}_{i}-{y}_{i} ight|}^{2}}). answered Jan 22,. Apply the Euclidean distance formula to the table of transformed variables and calculate distance (similarity) between each pair of customers. A common mistake made by novice presenters is to present all the analysis that has been done for a project in the __________. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. Column X consists of the x-axis data points and column Y contains y-axis data points. Insert the coordinates in the excel sheet as shown above. In the attached Excel spreadsheet, I am trying to classify new visits in Table 2 into one of the three visits given in Table 1. The accompanying data file contains 10 observations with two variables, x1 and x2. (Round intermediate calculations to at least 4 decimal places and your. I want euclidean distance between A1. . Task 3: Understand The Result Dataset. ユークリッド距離. For example, suppose we have the following two vectors, A and B, in Excel: We can use the following function to calculate the Euclidean distance between the two vectors: The Euclidean distance between the two vectors turns out to be 12. norm (a-b) Firstly - this function is designed to work over a list and return all of the values, e. The prediction phase consists of. From Euclidean Distance - raw, normalized and double‐scaled coefficients. Using the Pythagorean theorem to compute two-dimensional Euclidean distance. In cell C2, enter the value of x2. SQL, Excel, Tableau . The Euclidean distance formula can be used to calculate distances in any number of dimensions. if p = 2, its called Euclidean Distance. Example 1: Find the distance between points P (3, 2) and Q (4, 1). The graphic below explains how to compute the euclidean distance between two points in a 2-dimensional space. The method you use to calculate the distance between data points will affect the end result. Function distancia (RangoA As Range, RangoB As Range) As Long Dim s () As Variant Dim t () As Variant Dim r () As Variant s = RangoA t = RangoB ReDim r. 773178, -79. To find the two points on a plane, the length of a segment connecting the two points is measured. spatial import distance dst = distance. The matrix will be created on the Euclidean Distance sheet. Use the euclidean_distances () function to calculate the euclidean distance between the given two input array elements by passing the input array 1, and input array 2 as arguments to it. Series (range (10)) series2 = pd. 1) and the (non-standardized) Euclidean distance (Eq. A simple way to do this is to use Euclidean distance. 1. Calculate the Euclidean distance between clusters A and B by using. We use this formula when we are dealing with 2 dimensions. So, D (1,"35")=11. I want euclidean distance between A1. Next video: is the first step in the cluster analysis process: selecting and calculating a distance measure. 10. The numpy. Cant You just do euclidean distance -> sqrt((lat1-lat2)^2+(lon1-lon2)^2)*110. 000000 1. xlsx sheets dpb on 17 Apr 2015Euclidean distance is calculated from the center of the source cell to the center of each of the surrounding cells. For the first two records in Table 2. The haversine can be expressed in trigonometric function as: The haversine of the central angle (which is d/r) is calculated by the following formula: where r is the radius of the earth (6371 km), d is the distance between two points, is the latitude of the two points, and is the longitude of the two points respectively. In these cases, we first need to define what point on this line or. Rumus Euclidean Distance dapat dituliskan sebagai berikut: d = √((x2 – x1)² + (y2 – y1)²) Di mana: d = jarak antara dua titik;# Statisticians Club, in this video, discussion about how to calculate Euclidean Distance with the help of Micro Soft ExcelGo to the Data tab > Click on Data Analysis (in the Analysis section). 027735 0. Introductory Book. Euclidean Distance. This system of geometry is still in use today and is the one that high school students study most often. sqrt((x1-x2)**2+(y1-y2)**2) for x2,y2 in p] Out[6]: [0. It evaluates each observation, assigning it to the closest cluster. the place: Σ is a Greek image that suggests “sum” A i is the i th price in vector A; B i is the i th. 97034 ms; they are (1. , v m ∈ X, the "Gram. For this example, 16 added to 121 added to 16 equals 153, and the square root of 153 is 12. It represents the Manhattan Distance when h = 1 h = 1 (i. sa import * lines = r"C:shapesLines. . AC = 1, AD = √2/2, BE = 2. Notes. Therefore, it can be said that the 2D graphics of the PCA and MDS applied dataset would have similar characteristics. Step 4. Distance measure for asymmetric binary attributes – Click Here; Distance measure for symmetric binary variables – Click Here; Euclidean distance in data mining – Click Here Euclidean distance Excel file – Click Here; Jaccard coefficient similarity measure for asymmetric binary variables – Click HereThe choice of distance function typically doesn’t matter much. Number of Triangles that can be formed given a set of lines in Euclidean Plane; Program to calculate area of Circumcircle of an Equilateral Triangle;. Euclidean Distance Formula. g. 5 each, ending at Point 2. Edited: Andrew Newell on 15 Apr 2015. The norm () function calculates the Euclidean distance between the two vectors formed by the values of 'x' and 'y'. The accompanying data file contains 10 observations with two variables, x1 and x2. from scipy. xlsx sheets dpb il 17 Apr 2015Download Excel File Calculations. 5 Best Chrome. To find clusters in a view in Tableau, follow these steps. spatial. Euclidean distance. Using the original values, compute the Manhattan distance for all possible. 0, 1. Considering two points, X and Y, in n-dimensional space as a vector <x 1, x 2, x 3,. Theoretically, below are the clustering steps: P3, P4 points have the least distance and are merged. Euclidean distance adalah perhitungan jarak dari 2 buah titik dalam Euclidean space. Using the original values, compute the Euclidean distance for all possible pairs of the first three observations. ⏩ The Covariance dialog box opens up. 5387 0. This gives us the new distance matrix. Inserte las coordenadas en la hoja de Excel como se muestra arriba. We used SQRT and SUMXMY2 to calculate the Euclidean distance between two arrays of equal dimension, then selected the K-smallest distances. Euclidean distance adalah perhitungan jarak dari 2 buah titik dalam Euclidean space. 163k+ interested Geeks . For example; I have 2 arrays both of dimensions 3x3 (known as array A and array B) and I want to calculate the euclidean distance between value A[0,0] and B[0,0]. We find the attribute f f that gives the maximum difference in values between the two objects. I'm not sure if this is more of a math question than an excel question, but since my weapon of choice is Excel I thought I'd give this a try. 0, 1. Implementation :The functions used are :1. norm() function calculates the vector norm of a given array. xlsx sheets dpb on 17 Apr 2015Calculating pairwise Euclidean distance between all the rows of a dataframe. 3. I have two matrices, A and B, with N_a and N_b rows, respectively. Let’s discuss it one by one. The methods to compute the Euclidean distance matrix and accumulated cost matrix are defined below: def compute_euclidean_distance_matrix(x, y) -> np. M. I understand how to calculate the euclidean distance (utilizing the pythagoran theorem) but I am having trouble "matching the data" X Y 1 5 7 2 4 5 3 100 5. True Euclidean distance is calculated in each of the distance tools. Statistics and Probability questions and answers. Column X consists of the x-axis data points and column Y contains y-axis data points. Asad is object 1 and Tahir is in object 2 and the distance between both is 0. Access the Evaluate Formula Tool. . Escriba la fórmula de Excel en cualquiera de las celdas para calcular la distancia euclidiana. The accompanying data file contains 10 observations with two variables, x1 and x2. I understand how to calculate the euclidean distance (utilizing the pythagoran theorem) but I am having trouble "matching the data" X Y 1 5 7 2 4 5 3 100 5 4 80 2 5 25 16. @WolfyD So far as I saw, it's c = 2 * atan2 (sqrt (a), sqrt (1-a)), which is the same as c = 2 * asin (sqrt (a)) – Partha D. The resulting output is a single float value representing the Euclidean distance between the two Series objects. 5 each, and down 2 spaces of . Correlation analysis of numerical data – Click Here. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. You can find the Euclidean distance between two vectors v1 and v2 using norm: Theme. I have a tool that outputs the distance between two lat/long points. Further theoretical results are given in [10, 13]. The Euclidean Distance is actually the l2 norm and by default, numpy. In cell D2, enter the value of y2. To calculate the Euclidean distance between two vectors in R, we can define the following function: euclidean <- function (a, b) sqrt (sum ((a - b)^2)) We can then use this function to find the Euclidean distance between any two. linalg. It is a generalization of the Manhattan, Euclidean, and Chebyshev distances: where λ is the order of the Minkowski metric. Example 1: Determine the Euclidean distance between two points (a, b) and (-a, -b). Euclidean Distance: Is the shortest path between two geographic points on the surface of the earth. Recall that the Euclidean distance between two points x, y ∈ R^3 is |x − y|, where |z|^2 = z^T*z, for any z ∈ R^3 , thought of as a column vector. Finally, the observation labels are selected (STATE column) because the name of the state is specified for each observation. The idea is that I want to find the Euclidean distance between the user in df1 and all the users in df2. Euclidean distance matrix in excel. These data (along with immunopuncta IDs) are exported as an Excel file (. Solution: Let the point P be (a, b) and Q be (-a, -b) i. From the chapter 10 homework, normalize data and calculate euclidean distances I have a large set of XYZ Cartesian points in Excel (some 40k actually) and was looking for a formula or macro to compare every point to every other point to get the distances between them. I have been considering to use Word2vec for a problem. For rasters, the input type can be integer or floating point. import arcpy from arcpy. Pada artikel ini hanya dibahas 4 cara sebagai berikut : 1. In a two-dimensional field, the points and distance can be calculated as below:. Rescaling and Euclidean distance. vector2 is the second vector. For simplicity sake, i will narrow it down to few columns which are all in the same table. There are may be better ways to do it without writing for loops. 916666666666671 Distance: 0. The Euclidean distance formula is a mathematical formula used to calculate the distance between two points in. Compute the distance matrix between each pair from a vector array X and Y. In the case of determining the distance between two points (x1, y1) and (x2, y2), the Pythagorean theorem can be. e. (where H is the 7th city along the line). Euclidean Distance is a widely used distance measure in Machine Learning, which is essential for many popular algorithms like k-nearest neighbors and k-means clustering. spatial import distance # Calculate Manhattan distance between two points point1 = [1, 2, 3] point2 = [4, 5, 6] # Use the cityblock function from scipy's distance module to calculate the. 8 is far below than actual distance of 61 miles. 2 0. These metric axioms are as follows, where dab denotes the distance between objects a and b: 1. The distance (d) can then be defined as the length of. Learn more about distance, euclideanIn table 2, Asad, Bilal and Tahir are objects. Provide the necessary ranges such as F4:G14 ( Mean Difference Range) as Input Range, and I4 as Output Range. The following code shows how to compute a distance matrix that shows the Euclidean distance between each row of a matrix in R: #calculate Euclidean distance between. Principal Coordinate Analysis ( PCoA) is a powerful and popular multivariate analysis method that lets you analyze a proximity matrix, whether it is a dissimilarity matrix, e. The example of computation shown in the Figure below. To compute the length of a 2D line given the coordinates of two points on the line, you can use the distance formula, adapted for Excel's formula syntax. can express the distance between two J-dimensional vectors x and y as: ∑ = = − J j d xj yj 1, ()2 x y (4. 11603 ms and APHW = 0. Create a view. See the code below. Conceptually, the Euclidean algorithm works as follows: for each cell, the distance to each source cell is determined by calculating the hypotenuse with x_max. Consider Euclidean distance, measured as the square root of the sum of the squared differences. Euclidean distance The squared Euclidean distance between two vectors is computed from the Pythagorean theorem applied to the coordinates of the vectors. If A (X1, Y1, Z1) and B (X2, Y2, Z2) are two vector points on a plane. While this is true, it gives you the Euclidean distance. Euclidean distance is harder by hand bc you're squaring anf square rooting. Use the min-max transformation to normalize the values, and then compute the Euclidean distance between the first two observations. To troubleshoot any Excel formula, follow these steps: Select an appropriate cell to evaluate from a column (don't select a range of cells or the complete column) Click the Formulas tab. Cosine similarity in data mining – Click Here, Calculator Click Here. The cone of Euclidean distance matrices and its geometry is described in, for example, [11, 59, 71, 111, 112]. The K Nearest Neighbors dialog box appears. The green gene is actually now gone from the plot. I have the two image values G=[1x72] and G1 = [1x72]. For instance, think we have now refer to two vectors, A and B, in Excel: We will importance refer to serve as to calculate the Euclidean distance between the 2 vectors: The Euclidean distance between the 2 vectors seems to be 12. APHW = 1.