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

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4
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2answers
69 views

Looking for a robust, distribution-free/nonparametric distance between multivariate samples

There are many distance functions for distributions out there, but I'm having a hard time wading through them all to find one that is "distribution-free", or "nonparametric", by which I mean only ...
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1answer
20 views

Finding vectors with an extreme component

I'm looking for a function that measures if a vector component dominates all the rest. Let $$ \mathbf{v} = [v_1, v_2, \ldots, v_n] $$ and assume that it is L2 normalized, $|\mathbf{v}|_2 = ...
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0answers
5 views

Looking for a “(numerical) reliability index” for computed Bhattacharyya distances

The Bhattacharyya distance $D_B$ between two distributions $p_1$, $p_2$ is given by $$ D_B(p_1, p_2) = \frac{1}{8} (\mu_1 - \mu_2)^T \Sigma^{-1} (\mu_1 - \mu_2) + \frac{1}{2}\log\frac{\det ...
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1answer
108 views
+50

Beginner level : Unable to understand an application of Maximum Likelihood estimation from a paper

The paper "Distance Learning for Similarity Estimation" download link talks about finding distance measure for similarity estimation based on statistical analysis of distribution models and distance ...
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1answer
11 views

Is there a distance algorithm similar to Jaccard distance that handles scalar data?

we have the characteristics and (scalar) values of those characteristics for three (or more) people: ...
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0answers
14 views

calculating distance among unordered set partitions for k-mean clustering?

I have a dataset for which I construct unordered set partitions for each data point, e.g. {{1,2,3}{4,6}{5}} for one and {{1,3}{2,4,5}{6}} for the next. I would like to perform k-means clustering on ...
0
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1answer
29 views

Chosing optimal k and optimal distance-metric for k-means [duplicate]

I have a data-set with roughly 20-dimensions and millions of points which I want to cluster. The goal is to find a set of clusters which: Are as distinct as possible from each other (minimum ...
2
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1answer
31 views

Turn a distance measure into a kernel function

I have read here that an easy way to turn a distance function $d$ into a similarity function $s$ is to compute: $s = e^{-\gamma * d}$. I believe that this is also what is done with the RBF kernel. ...
2
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0answers
27 views

Calculate the Hamming Distance between the two same datasets

How to Calculate the Hamming Distance between two datasets of same points?Both the data sets look exactly the same. http://postimg.org/image/u11qnsolh/ There are two datasets of same number of ...
0
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1answer
27 views

FAMES in case of Dynamic Time Warping

I found this paper Using Pivots to Speed-Up k-Medoids Clustering in which authors explain how to use triangular geometry and cosine law to speed up search of new medoids in case of K-medoids. My ...
1
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2answers
36 views

Recommended/estimated number of radial basis functions in RBFN

thank you for taking the time to read my question. I am attempting to make a Radial Basis Function Network to see if a relationship exists between input/output data that I have been collecting. I ...
3
votes
1answer
136 views

What is the difference between graphs/networks? [closed]

Note: read down to below "Question" to find the question. Background: In a previous question I asked how to group what I would call nodes on a network graph based on a connectivity matrix. (link) ...
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0answers
20 views

Gaussian Mixture Model with Custom Distance Metric

I have some 1D data that I want to cluster using Mixture of Gaussian. However, the data "wraps around" at two extremes. Specifically, I have a list of angles from $-\pi$ to $\pi$ and the data near two ...
0
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0answers
39 views

Can I compare Mahalanobis distances from different distributions?

I have a multivariate dataset representing multiple locations, each of which has a set of reference observations and a single test observation. For each location, I would like to measure how anomalous ...
3
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2answers
93 views

How to measure similarity of bivariate probability distributions?

I have three different distributions of 2D data: or Now I like to know whether distribution two is more similar to distribution one (2 to 1) than distribution three is to distribution one (3 to ...
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0answers
22 views

evaluate the similarity between two time series

I have two time series, $\mathcal{T}_1$ and $\mathcal{T}_2$, each time series is of two dimensional. One time series is collected from two sensors (SA, SB), and the other is collected from other ...
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0answers
85 views

Hierarchical clustering, linkage methods and dynamic time warping

My goal is to cluster time series based on their DTW distance. Therefore I've calculated full distance matrices as input for several clustering algorithms. I first had a look at hierarchical methods, ...
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0answers
38 views

handling categorical data with a large amount of categories

I have data containing few categorical columns with a huge amount of categories at each (more than 1000 different categories at each column). I have to build a predictive model on this data, using the ...
1
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3answers
431 views

Ask for suggestions on clustering methods on a large dataset with mixed types of variables

I need to build segmentation on a large customer dataset with more than 300K records and many variables, including continuous like income and age, ordinal like education level and membership level, ...
2
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0answers
16 views

Approximation of objective based on statistical distance

I am a computer science researcher (mostly theoretical) currently in midst of statistics and not able to figure out how to proceed. At an abstract level, I have a hypothesis for an unknown ...
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0answers
123 views

Comparing two vectors with the same numbers in different positions [closed]

I have two vectors of the same size representing one score for different sites (x and y coordinates) under distinct situations (each vector is one situation). At each vector the scores only change ...
0
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0answers
51 views

comparing probability histogram

I have two probability histogram samples. I know there are methods(i.e KS test etc) out there to compare histograms but I am trying to compare through simple sum of absolute difference between these ...
1
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1answer
170 views

If Manhattan distance always performs better on a dataset…what does it mean?

I'm analyzing my dataset using kNN. I experimented with various distance functions but Manhattan seems to perform better in terms of lowest RMSE over various values of k. I've read a bit about ...
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0answers
38 views

Distance metrics in “high” dimensions

Thanks in advance: this is a very nice site. This question has been made more specific in response to a comment. original question ----------------- Reading the various sources concerning distance ...
0
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2answers
123 views

Mahalanobis distance measure for clustering

Let's say I have a group of clusters. Would you recommend Mahalanobis distance measure for checking if new arrived data belongs to existing clusters or it is an outlier? Also, would you recommend ...
0
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1answer
58 views

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. ...
3
votes
1answer
42 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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0answers
121 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 ...
0
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0answers
11 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 ...
0
votes
1answer
25 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?
0
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1answer
44 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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1answer
127 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
92 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 ...
0
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1answer
15 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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0answers
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 ...
2
votes
1answer
196 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 ...
1
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1answer
40 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 ...
0
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1answer
51 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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0answers
21 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 ...
0
votes
1answer
76 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 ...
0
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0answers
111 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 ...
0
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0answers
88 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 ...
1
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0answers
15 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
112 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 ...
1
vote
1answer
99 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 ...
0
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1answer
458 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 ...
1
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1answer
281 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 ...
0
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1answer
260 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?
2
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1answer
224 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.
4
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1answer
298 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 ...