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

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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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48 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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Hyperplane data points

Would a single data point in the hyperplane (see below) correspond to a single cell in the data matrix or an entire row?
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28 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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3answers
412 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
37 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
125 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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25 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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26 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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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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35 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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21 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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21 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
19 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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40 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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1answer
45 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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6answers
6k views

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
41 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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37 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
105 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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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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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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2answers
113 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
38 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
34 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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37 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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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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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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119 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. ...
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Metric optimization on discrete learning sample

There are a set of ("artifical") not Minkovski (triangle inequality is not guaranteed) metrics defined on set of objects. There are one etalon ("natural") metric, which estimation is known only for ...
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Dealing with Euclidean distance and dimension independence

I'm not very well informed in terms of distance measures. What sort of distance measure would I use if I know that the various dimensions are not independent of each other? Because I think that ...
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2answers
30 views

How to cluster users based on search terms

How to cluster based on what users are searching on I'm working on an app which includes search functionality: a search box that allows a user to enter text and search the entire site. I have access ...
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80 views

String clustering and centroid computation

I have a text file document containing a set of words strings that I want to cluster. I want to use the K-means algorithm. As a ...
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1answer
68 views

How to measure the distance (or divergence - not sure) between data and a probability distribution?

If I have generated a set of random data and I wish to measure how well these data fit, e.g. a uniform probability distribution, what are the standard ways to do that? I am not very experienced with ...
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1answer
46 views

Calculating (dis)similarity between different types of features

Disclaimer: I understand that this question is specific to the types of data, the end goal, etc. but I just wanted to get some quick tips regarding calculating dissimilarity between different types of ...
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Limitations of using interpolated data

I have a data set that is composed of point locations in a landscape, lets call this dataset X. Some of the points in data set X need to be grouped together because they "function" together as a ...
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1answer
62 views

distortion function for k-means algorithm

I was reading Andrew Ng's ML lecture notes on K-mean clustering, in which the distortion function is defined as follow $$J(c,\mu) = \sum^m_{i=1} || x^{(i)} - \mu_{c^{(i)}}||^2$$ I am puzzled about ...
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Similarity Amongst Recipes Using Ingredients and Reviews/Descriptions

I'm still toying with things and just learning this, so please forgive any incorrect terminology. My toy data set is a collection of recipes with a fairly significant overlap in ingredients. I'm ...
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Multidimensional scaling of variables with multiple sub-features?

Let's say I have a year's worth of magazine issues (January, February, March, etc), and I want to visualize the differences among them. The classic example of multidimensional scaling (MDS) would have ...
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How to rank users?

I have a list of movies ranked out of 5 based on their income. I have users ranking the same movies. Not all users rank all movies. How can I find out which users have the best correlation between ...
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Making sense of the allele frequency weighted genetic distance

I found one formula to calculate the pairwise distance between samples according to their SNPs in the following paper: Siu, Jin and Xiong, Manifold Learning for Human Population Structure Studies, ...
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Dataset similarity measurement

Suppose: For each input data, I could obtain true result as well as experiment result from my algorithm, one example is The true result is A = {a, b, c}, ...
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3answers
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Why does k -means clustering algorithm use only euclidean distance metric?

Is there a specific purpose in terms of efficiency, functionality why k-means algorithm do not use cosine similarity as a distance metric and use the euclidean norm
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1answer
40 views

What is the relation between Kullback loss and L1 and L2 loss? [closed]

I tried to find some relation between these distance (loss) measures, but couldn't find any references. However, I think it must something like this: $$ \sqrt 2*D_{KL} < L_1 < L_2 $$ Is that ...
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2answers
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The right distance for the clustering. Maybe Mahalanobis?

I have to do a cluster analysis and I'm asking which distance should I used. I know that 99% of the clustering are made using a euclidean distance, but I heard about the Mahalanobis distance and it ...
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2answers
112 views

Radial basis function network - G function?

I'm trying to understand Radial Basis Function Network. I have (don' know how to write proper formatter mathematical functions here..): $x = [ -1.0000, -0.5000, 0,0.5000,1.0000]$ $y_i = f(x_i)$ ...
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1answer
121 views

similarity measures with missing values

How to handle missing values when computing similarity (or distances)? (I have binary feature values and do use the simple matching coefficient, but I feel that the answer to this question may be more ...
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36 views

A measure of distance that accounts for probabilities

I have a couple of vectors (each vector represents a student, each coordinate, a question) that I want to compare, to say if they are similar or not. I am using the cosine distance. I would like to ...