Distance functions refer to functions used for quantifying the notion of distance between members of a set, or between objects.

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Similarity scoring to compare multi-dimensional datasets

I am trying to come up with a mechanism of scoring a set of multidimensional datasets based on a similarity with an ideal dataset. Each dataset will all have the same dimensions along with the ideal. ...
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29 views

Can I use k-means with a distance matrix composed of percentages? [duplicate]

I have objects o1, o2,...,on and for each pair I calculate a value that measures the pair's difference. This is a percentage, so for example o1o2 differ by 56%. Now I want to cluster this data. I can ...
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37 views

Distance measure for categorical attributes for k-Nearest Neighbor

For my class project, I am working on the Kaggle competition - Don't get kicked The project is to classify test data as good/bad buy for cars. There are 34 features and the data is highly skewed. I ...
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9 views

Find input image (ID,passport) in imagesDB based on similarity

I would like to decide if image is exists on DB images (pictures of IDs,passport,Stu. card,etc) I thought of KNN alghorithem that will plot the K closest images. Options for distance metric: 1) sum ...
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1answer
11 views

Why do two identical feature vectors (distance score 0) get different labels in DBSCAN?

I have two identical feature vectors. They have a distance score of 0. I perform DBSCAN Clustering (using sci-kit) and they get different labels. Is this expected behaviour?
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1answer
25 views

Multivariate nonparametric divergence (or distance) between distributions

For example, we could say I have two fruit classes (oranges and apples) and for each one I measured different statistics of interest, for example: width, height, sugar, water... of a lot of fruit ...
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39 views

Why is k-medians typically used with Manhattan rather than Euclidean distance?

K-medians is typically used with Manhattan distance rather than Euclidean distance. Why is this?
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1answer
35 views

Calculate PCoA scores for dataframe “x”, based on the distance matrix of dataframe “y”

I'm trying to use multivariate techniques to compare two datasets (same structure) that were collected using different sampling techniques. I'd like to compute a PCoA for the first dataset (D1), and ...
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1answer
13 views

Calculating distance comparing sets of frequencies

I have two sets of items, say A (with items a1, a2..) and B (with items b1,b2..). Each item in A appears with different frequency with items in B, so each item would have a list of B items with ...
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16 views

How to split a class which is not very cohesive?

Using the silhouette width metric I can find out as to how well each object lies within its class after classification is done. I next find the average silhouette width of objects within a class and ...
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1answer
68 views

Distances for binary and non binary categorical data

I am computing a matrix of distances for categorical data. I am using the Jaccard distance since as far as I understood it should be working properly with this kind of data. I have BOTH binary and ...
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28 views

Using Mantel to explore relationship between geographic distance and a multivariate character

I'm working with bird songs. A song is composed of many vocal parameters [highest frequency (Hz), lower frequency(Hz), bandwidth(Hz), duration (s), number of notes, and son on....] I'm interested in ...
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30 views

Mantel Test data assumptions

Does the Mantel Test works with non-normal distributed samples? I couldn't find anything clear enough about it.
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19 views

How do you deal with different distance based features?

If I have a model where the set of features where a cosign distance measure makes sense for some of the features, and a Euclidean distance measure makes sense for the others for example using a BOW ...
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1answer
42 views

Order of Matrix Operations in Mahalanobis Calculations

I'm teaching myself to translate equations to code after many years of letting my math skills atrophy, and am trying to do it on my own as much as possible. I've run into a couple of difficult ...
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74 views

Using relative frequency for Euclidean and cosine distance (dissimilarity)

How to calculate the Euclidean distance (dissimilarity) between two documents, e.g., D1 and D2 using relative frequency? Here is an example of both cosine and Euclidean distance between two ...
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57 views

Multidimensional Scaling: Interpreting output of different distance matrices (Euclidean or correlation)

I would like to understand the difference between using a Euclidean distance matrix or correlation matrix as input to a nMDS algorithm. I have completed MDS plots of both, and while similar, the ...
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14 views

Distribution of altered Mahalanobis distance [duplicate]

Let's say I have a set of i.i.d. samples $X_1,\ldots,X_N \sim N_p(\mu, \Sigma)$. Now define \begin{equation} d^2_i(b)=(X_i - b)'\Sigma^{-1}(X_i-b) \end{equation} which is essentially the Mahalanobis ...
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1answer
84 views

How to choose the right distance matrix for clustering?

I am attempting simple Ward type clustering. However, the R package is proving several choices to use for the distance matrix. I am wondering how I am supposed to determine the right distance matrix ...
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71 views

Distance between two random vectors

I have two random vectors, $A$ and $B$ with each consisting of $n$ geographical co-ordinates $(x_1,y_1),(x_2,y_2)\dots (x_n,y_n)$ and $(\tilde{x}_1,\tilde{y}_1),(\tilde{x}_2,\tilde{y}_2)\dots ...
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1answer
193 views

hclust, R and Euclidean distances: weird stuff

I have a table of similarities expressed through cosines and am trying to do some cluster analysis in R, using hclust and ...
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1answer
209 views

Cook's Distance

The formula of Cook's distance is $$D_i=\frac{(\hat Y-\hat Y(i))^{\prime}(\hat Y-\hat Y(i))}{p\times MSE}$$ where, $\hat Y$ is the prediction from the full regression model and $\hat Y$ is a ...
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98 views

advantage of euclidean distance for classification

Has euclidean distance any advantage in compare to another distance based methods like Manhatan distance or Maximum difference metric?
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841 views

Do the pdf and the pmf and the cdf contain the same information?

Do the pdf and the pmf and the cdf contain the same information? For me the pdf gives the whole probability to a certain point(basically the area under the probability). The pmf give the probability ...
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1answer
102 views

Jeffries Matusita distance for 14 variables

I wish to perform Jeffries-Matusita distance on 14 spectral bands. Is there anyone who can help with how it is done in R? Thank you.
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1answer
202 views

How to distance and to MDS-plot objects according their complex shape

Suppose I have four basal forms of signal (blue, purple, red, green). I also have created transition forms between each other. If you carefully look on the picture below, you can see that for example ...
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27 views

Representing a distance matrix in the plane [duplicate]

I've worked with observations as vectors with both continuous and categorical variables. In both cases one can use dimensionality reduction techniques such as PCA (in the latter case through ...
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28 views

Log likelihood - understand depper

I want to use log likelihood formula to relate between two items. The formula is: LLR = 2 sum(k) (H(k) - H(rowSums(k)) - H(colSums(k))) When this is the table: ...
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32 views

Way to Measure Groupings Using Distances Between Individuals?

I am working on a problem that requires me to measure groupings of people. I have the location of every individual in my sample at every point in time. It's therefore trivial to calculate the ...
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57 views

What is a good similarity measure to use when missing data is a significant issue?

I have a list of cities that I want to compare in terms of their similarity. Each city can described by a large but finite number of characteristics but most of them will have missing data for some ...
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36 views

Calculate number of standard deviations separating two multivariate Gaussians?

Given a set of multivariate Gaussian distributions (from fitting a Gaussian mixture model) I would like to be able to calculate the likelihood that a data point drawn from one Gaussian will improperly ...
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35 views

Histogram distance metric for extreme values only

I am interested in a histogram comparison method or histogram matching technique that takes into account only the tails of the distribution. Consider the following histograms: Histogram 1: ...
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1answer
34 views

calculate Levenshtein Distance for web click stream data

I want to calculate Levenshtein Distance between to web click paths. I have a web page list around 500. ...
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56 views

How does Gower distance work with free text?

The Gower distance measure is a good measure for mixed-type data (i.e., data attributes can be qualitative, categorical, ordinal or binary). But can data attributes be free-text (e.g., names of ...
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54 views

What is the $p$ in Cook's distance?

In the equation for Cook's distance: $$D_i = \frac{\sum_{j=1}^{n}(\hat{y}_j - \hat{y}_{j(i)})^2}{p MSE}$$ the value of $p$ is defined as "the number of fitted parameters in the model." What does ...
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Why is Euclidean distance not a good metric in high dimensions?

I read that 'Euclidean distance is not a good distance in high dimensions'. I guess this statement has something to do with the curse of dimensionality, but what exactly? Besides, what is 'high ...
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2answers
57 views

Is this a valid use case for Euclidean distance?

I have a set of points which is a count of links that users have clicked on : ...
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116 views

Negative Mahalanobis Distance

I would like to calculate a compound scores of several normal distributed continues standardized (z-score) variables. Some of these measures are correlated, some are not. Hence, I would like to take ...
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2answers
211 views

Building the connection between cosine similarity and correlation in R

According to some articles (e.g. here) correlation is just a centered version of cosine similarity. I use the following code to calculate the cosine similarity matrix of the column vectors of a matrix ...
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29 views

Comparing two distributions in Fourier space

There exist a number of tools that provide a distance between two continuous probability distributions. Most (semi)distances, like the Kullback-Leibler divergence, use probability density functions. ...
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41 views

Distance between a transition matrix and an instance

I am trying to put a number to the distance of a sequence and how close it is to the original training corpus. From the original training data, I got a markov transition matrix (TM). So from the ...
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353 views

Is there an advantage to squaring dissimilarities when using Ward clustering?

Is there a reason to prefer squaring or not squaring the dissimilarities when clustering with Ward's method? The question is motivated by the following statement in the documentation for R's ...
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1answer
49 views

One huge cluster + small ones with vector-space model + cosine distance

I'm trying to cluster meaningfully a set of objects characterized by a vector space (bag-of-words) model. Each of those 5000 objects has 1-8 features ("words") from a set of 5500 possible. I used a ...
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Average minimum distance between two random vectors

Let $\mathbf{y_1} =\begin{bmatrix}g_1x_1 & g_2x_1 & \dots & g_Nx_1 \end{bmatrix}$ and $\mathbf{y_2} = \begin{bmatrix} f_1x_2 & f_2x_2 & \dots & f_Nx_2\end{bmatrix}$. All the ...
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1answer
75 views

Silhouette scores for different distance metrics

I clustered a data set using PAM with a euclidean distance metric and a pearson correlation distance metric. The average silhouette value of the correlation clusters is higher at most points than the ...
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56 views

What is a good technique for grouping objects based on binary or dichotomous traits?

I have a set of objects each of which has a list of traits. Data on the traits is binary: an object has a trait or does not. The number of objects that I have is moderately greater than the number ...
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18 views

Why inverse of the sample covariance matrix is used in Mahalanobis distance calculation? [duplicate]

The Mahalanobis distance of an observation vector $X$ from a set of observations is defined as $d=\sqrt{(\vec{x}-\vec{\mu})^T S^{-1} (\vec{x}-\vec{\mu})}$ where $S$ is the sample covariance matrix and ...
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69 views

Facebook users similarities

I'm searching for a similarity metric such that given two Facebook users it returns a value that reflects how similar the two users are. The similarity metrics must take into account (at the same ...
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159 views

Compute Shannon entropy between every row of a large, sparse matrix

I have a sparse, binary matrix of user (rows) and items (columns). Each element of this matrix is either 0 or 1: ...
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20 views

Estimation based Distance observations

Let $X_1,\dots,X_n$ are i.i.d. copies of $X$, however I don't know the value of them. I only know the distance for every pair $(i,j)$. Now, assume that we are given $Y$ and $Z$ which are also i.i.d. ...