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5
votes
2answers
61 views

Why are mixed data a problem for euclidean-based clustering algorithms?

Most classical clustering and dimensionality reduction algorithms (hierarchical clustering, principal component analysis, k-means, self-organizing maps...) are designed specifically for numeric data, ...
2
votes
1answer
43 views

How does the Gower distance calculate the difference between binary variables'?

I have 17 numeric and 5 binary (0-1) variables, with 73 samples in my dataset. I need to run a cluster analysis. I know that the Gower distance is a good metric for datasets with mixed variables. ...
1
vote
0answers
20 views

Unique matching for quantiles from one half of the density to a subset of the other half?

I am interested in finding the median absolute distance to quantiles. So, for $Q_\alpha$ the $0 \le \alpha \le 1$ quantile, I would like to find $Q_\gamma^*$ such that $Q_\gamma^*$ satisfies ...
0
votes
0answers
12 views

Want to findout satistical distance unsing another procedure except kullback liebler divergence

i want to find the distance between two pdf(pdf is calculated using kernel density estimator from two random data set of different size ) .Is there any alternative and efficent way to calculate ...
2
votes
1answer
50 views

Minimax space-filling design for 2 dimensions in practice

I think I understand the basic idea of a 2d minimax design. Given $n$ data points, choose locations for each point so that the maximum distance between anywhere in the input space and any of the $n$ ...
0
votes
0answers
27 views

Distance between two independent normal random variable

What is the PDF of $Z=\sqrt{(X-x_0)^2+(Y-y_0)^2}$ when X and y are i.i.d. zero mean normal random variable (i.e., $x\sim N(0,\sigma^2)$ and $x\sim N(0,\sigma^2)$)
3
votes
1answer
50 views

Euclidean distance with sparse and high dimension data

I have texts for a bunch of objects. From each text, I removed the stop words, and took each word as an attribute of the object. I then gave each word a rating based on sentiment analysis, so that the ...
1
vote
0answers
29 views

Average within-cluster distance using divisive clustering

I have to prove that the average within-cluster distance for 10 data points cannot increase when going from 1 cluster to 2 clusters (divisive clustering). Intuitively, it seems obvious that this is ...
0
votes
0answers
28 views

What is the relationship between naive Bayes and Mahalanobis distance

Recently, I found a code project which uses the Mahalanobis distance to compute Bayes value, but I don't know why you can do that. Second, as I know naive Bayes is based on the Bayes rule, and how ...
1
vote
0answers
27 views

How to compare the distances or divergence between two groups of datasets

If I have two groups of data sets. Each group has two arrays of empirical data. In the first group each array has, say, 50,000 data points, and in the second group each array has 3,000 data points. ...
0
votes
0answers
16 views

How to test differences in multiple pairwise distances? With mixed model?

I want to compare two set of variables: X1 = All the pairwise distances between individuals from group A and group ref R X2 = ALL the pairwise distances between individuals from group B and group ...
1
vote
0answers
26 views

Occupancy octree metrics (Kullback-Leibler)

As I'm currently working on scan matching for outdoor environments I was wondering about the best metric to compare two occupancy octrees (one resulted from the scan matching and one ground truth ...
1
vote
0answers
11 views

Partial correlations among three distance matrices

I am trying to test the hypothesis that related species should deviate more in niche space the more they overlap in geographic space. In other words, related species either forage similarly and don't ...
1
vote
1answer
40 views

Metric to compute structural similarity between two directed graphs

I'm working on a small project in which I try to compare directed a-cyclic graphs. Say I have (directed) three graphs: 1) ...
1
vote
1answer
19 views

Distribution of distances to an observation from the normal and the median of these distances

Given $x\sim \mathcal{N}(\mu=0, \sigma^2=1)$, the squared distances of the $x$ values to $\mu$ are distributed $\chi^2_1$. I am interested in the distribution of the squared distances to an arbitrary ...
0
votes
1answer
88 views

Mahalanobis distance in a hierarchical cluster analysis in SPSS

I am conducting a hierarchical cluster analysis in SPSS on my database with several neuropsychological and psychiatric variables. In my database, some of my variables (that is: two pairs of variables) ...
0
votes
1answer
29 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
votes
2answers
75 views

Dynamic Time Warping for irregular time series

I have been reading a lot about Dynamic Time Warping (DTW) lately. I am very surprised that there is no literature at all on the application of DTW to irregular time series, or at least I could not ...
0
votes
0answers
83 views

R. function hclust, euclidean distances and cosines

My data is a table of cosines and I want to analyze it with hclust, which works on squared Euclidean distances. shall I do: d <- dist(mydata, method = "euclidean") fit <- hclust(d, ...
0
votes
0answers
17 views

Weighing a variable based on distance to a known date

In a bankruptcy model, you want to assign a higher weight to a variable as a big event date approaches (such as a company's quarterly earnings announcement date) and you reverse this weighing as you ...
2
votes
2answers
126 views

How to visualize the comparison of 3 different types of distances among objects

I need to calculate the difference between six time series in three ways: Time Series are: Kamel, Dumper, Graben, Traktor, Generator Methods are: Euclidean distance, Manhattan distance and maximum ...
1
vote
0answers
26 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 ...
1
vote
1answer
53 views

Extract (ultrametric) distances from hclust or dendrogram

How can the matrix of (ultrametric) distances be extracted from the result of hclust (or a dendrogram in general) in R? The ...
0
votes
0answers
90 views

Computing a distance matrix between multiple multivariate time series

This question has also been asked on stackoverflow.com. Yet my aim is to ask for efficiency gains on the aforementioned platform. My aim here is the correctness of my approach. I am trying to cluster ...
0
votes
0answers
38 views

Dissimilar to multiple points

I have a few points in multiple dimensions. I am able to compute similarity between those items (using, say Cosine distance). For example, ...
1
vote
1answer
29 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. ...
0
votes
0answers
37 views

How to test the significance of clusters?

How can one test the significance of the clusters obtained after a clustering procedure? Are there separate tests for the distance/similarity/dissimilarity measure used to get the distance matrix and ...
6
votes
3answers
1k views

Calculate the Kullback-Leibler Divergence in practice?

I am using KL Divergence as a measure of dissimilarity between 2 $p.m.f.$ $P$ and $Q$. $$D_{KL}(P||Q) = \sum_{i=1}^N \ln \left( \frac{P_i}{Q_i} \right) P_i$$ $$=-\sum P(X_i)ln\left(Q(X_i)\right) + ...
3
votes
0answers
48 views

Using similarity matrix to measure diversity of a group

I wish to measure the "diversity" of a group of objects. Right now I'm using Euclidean distance to compute the similarity matrix between all the objects in the group. I'm searching for a measure of ...
1
vote
0answers
72 views

PDF for net displacement of bivariate normal X and Y

this is my first post on StackExchange so I hope I'm posting in the right place. I'm trying to derive the correct probability density function for the net displacement of random variables X and Y ...
2
votes
1answer
78 views

Distribution of distance from center of sample group

We have a bivariate normal process where $X, Y \sim N(0, \sigma)$, with no covariance. (For convenience we can assert that $\sigma = 1$, or that we have a good estimate for its value.) What is the ...
1
vote
1answer
87 views

Problem with estimating probability using the multivariate Gaussian

I'm working on a problem where I need to find the probability of a given data sample belonging to a give class using the Bayes Theorem for classification. From everything I've been able to find so ...
-1
votes
1answer
74 views

Cluster with distance threshold in R

I'd like to get clusters with a maximum inner distance threshold. Now I use hc <- hclust(d) and cutree(hc, numofclasses). ...
1
vote
0answers
46 views

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 ...
2
votes
1answer
110 views

Multidimensional Scaling “eurodist”

I have a question regarding Multidimensional Scaling. I used the dataset eurodist from the package datasets to generate a 2 ...
0
votes
0answers
9 views

Too Large Values with Assembled Distance Transform

I am trying to apply ADT as a distance between two images or their DCT coefficents. The ADT is given as (image taken from "Bidirectional PCA with assembled matrix distance metric for image recognition ...
0
votes
0answers
45 views

How genetic beta-diversity reflects traditional beta-diversity?

Im trying to figure out how betadisper {vegan, R}, and more specifically how the 'average distance to median' relates to betadiversity in a more traditional sense. betadisper calculates the variance ...
1
vote
1answer
193 views

Normalized cross correlation vs Euclidean distance in template matching

What is the difference between normalized cross-correlation and Euclidean distance in pattern recognition? -- especially if we want to do recognition with template matching. I understand about ...
0
votes
1answer
26 views

Distance Transform In Image?

I understand how to compute Distance Transform for BW image In BW image we can calculate the distance of the pixel with non zero pixel value using Eucledian Distance. But I dont undertand how to ...
0
votes
1answer
38 views

string clustering: similarity criterion

I have a set of strings of dimension $10,000$. I want to group similar strings together in one group, perform clustering. As string metric, I am using the ...
3
votes
1answer
215 views

Is there an intuitive characterization of distance correlation?

I've been staring at the wikipedia page for distance correlation where it seems to be characterized by how it can be calculated. While I could do the calculations I struggle to get what distance ...
3
votes
2answers
145 views

Confidence interval for distance from center

We have a bivariate normal process where $X \sim N(\mu_x, \sigma), \, Y \sim N(\mu_y, \sigma)$, with no covariance. $(\mu_x, \mu_y)$ are unknown. (For convenience we can assert that $\sigma = 1$, or ...
0
votes
0answers
43 views

Learning from distance matrices

I have a task to build multi-task classification model based on distance (similarity) matrix only. They are already precalculated and no changes here can be applied. Can you, please, recommend me ...
1
vote
0answers
35 views

Why it is better to use the cumulative distribution to compute distances?

In the comments of this question, it was pointed out that, when comparing two distributions, it is more natural and more general use the cumulative distribution (CDF) instead of the distribution ...
0
votes
0answers
49 views

Distance between nominal vectors: a review

I have a seemingly easy question which however is troubling me a bit. I have couples of vectors made up of nominal attributes. They can be of different length and sometimes some of the attributes in ...
1
vote
0answers
23 views

Computing a “concentration of event occurrence” index

I'm looking at the concentration of an event occurrences in a given interval of time. For example, we suppose that an event occurred 4 times in an interval of length 10. I can represent this as a ...
2
votes
0answers
81 views

Genetic distance over spatial scales

I have matrices of genetic distances for x number of individuals within a population and their corresponding point coordinates -one genetic distance matrix per point coordinates. I was imagining ...
1
vote
1answer
142 views

Jensen-Shannon divergence for finite samples

I have two finite samples $s_1$ and $s_2$ and two distributions $p_1(s_1)$ and $p_2(s_2)$ that are associated to these samples. I'm essentially interested to measure the distance or similarity between ...
0
votes
0answers
26 views

Distance from bivariate Gaussian mean in terms of variance

Not sure if my question is a valid one but I will just put it out here. Consider a bivariate data set $(x_i, y_i)$ $[i=1,...,n]$ to which a bivariate Gaussian Distribution is fitted. Now, consider ...
1
vote
1answer
97 views

Earth Mover's Distance (EMD) between two Gaussians

Is there a close formula (or some kind of bound) on the EMD between $x_1\sim N(\mu_1, \Sigma_1)$ and $x_2 \sim N(\mu_2, \Sigma_2)$?