Questions tagged [hellinger]

The Hellinger distance measures a distance between two distributions that are absolutely continuous wrt the same dominating measure. It is bounded by one.

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Should I use Hellinger transformed species (abundance) data for NMDS if this is what I used for RDA ordination?

I am conducting both constrained and unconstrained analyses on the same species abundance data. For the constrained ordination, I ran the RDA (redundancy analysis) on log x+1 and hellinger transformed ...
2 votes
1 answer
36 views

Is this Hellinger Distance expression correct?

Further to my previous post on the Hellinger Distance, there was one comment raised about there being different expressions of the Hellinger Distance. This has intrigued me. In the Encyclopedia of ...
2 votes
1 answer
63 views

Equating different forms of Hellinger Distance

For a research report, I want to show that the standard expression of the Hellinger Distance between two discrete distributions, $$H(p,q)={\sqrt{\frac{1}{2} \sum_{x \in X} \left[\sqrt{p(x)}-\sqrt{q(x)}...
1 vote
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646 views

What is the difference between a PCA, RDA and CCA analysis?

I am trying to understand the difference between a PCA, RDA and CCA analysis. Here is an example of a CCA triplot. It seems that a PCA + RDA = CCA plot. Here it's a CCA triplot, which incorporates one ...
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77 views

Calculate a measure based on LDA topics and Hellinger distance

I am trying to calculate some sort of ambiguity/heterogeneity measure from text based topic probabilities from a Latent Dirichlet Allocation model and the Hellinger distance between the topic ...
1 vote
1 answer
115 views

What is the correct expression of the Hellinger Distance equation?

I am aware there are various ways to calculate the Hellinger Distance (H) depending on the context and data. One of these ways, as I understand, is via the Bhattacharyya coefficient (BC). For discrete ...
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Statistical significance of distance between difference of vectors (LDA)

I have an output from Latent Dirichlet Allocation (LDA) which sums up the corpus of about 2,000 documents into 50 topics. The 2,000 documents belong to a category each (in total there are 4 categories,...
1 vote
0 answers
78 views

How to perform PCA analysis on space-time data for few species in R? [closed]

The data-set I'm looking to analyze has 6 sites. Each site was sampled at five unique locations each month for a year. We could identify abundance of 4 species across the data set. Together, I have ...
1 vote
0 answers
47 views

Is there a closed form solution for the Hellinger Distance between two Wishart distributions?

Given two Wishart distributions $X_0 \sim W_{p_0}(V_0,n_0)$, $X_1 \sim W_{p_1}(V_1,n_1)$, what is the Hellinger Distance between them? Can it be obtained in closed form assuming $p_0 = p_1$? For ...
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3 votes
1 answer
2k views

Hellinger Distance between 2 vectors of data points using cumsum in R

I have numerous vectors of data points and I want to compute the hellinger distance between the probability distributions of every 2 vectors. I am using this version of the Hellinger distance equation:...
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Sample Hellinger Distance is Negative

The Hellinger distance between a true density $f$ and an estimate $\hat f$ is defined as $$H(f,\hat f) = \sqrt{1 - \int \sqrt{\frac{\hat f(x)}{f(x)}}f(x)\ \mathrm dx}.$$ I estimate the Hellinger ...
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2 votes
1 answer
239 views

Is Hellinger transformation suitable for repeated (in time) site-species abundance data?

I have fish survey data from four different years and several locations, where I would like to study the difference in abundance and biomass between sites and check whether time dependence influences ...
1 vote
1 answer
180 views

Hellinger distance for two shifted log-normal distributions

If I am not mistaken, Hellinger distance between P and Q is generally given by: $$ H^2(P, Q) = \frac12 \int \left( \sqrt{dP} - \sqrt{dQ} \right)^2 .$$ If P and Q, however, are two differently ...
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4 votes
1 answer
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Is Hellinger transformation suitable to access species abundance - environmental variable relationships?

While working with a multivariate dataset, I noticed that Hellinger transformation reveals relationships with the dataset I did not see otherwise. The fact that a transformation affects species ...
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Hellinger distance to find outliers. How to go from data to probability distribution?

One can find outliers in a data set if you fit that data in a probability distribution and see how well the data fits in the model (Normal data instances occur in high probability regions of a ...
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104 views

Lower bound for difference of probabilities of a same event under two different distributions

Say $P$ and $Q$ are two probabilities distributions on $[n]$. I can upper bound the difference of the probability of an event $A$ under $P$ and $Q$ by the total variation distance between $P$ and $Q$. ...
5 votes
1 answer
5k views

Distance between discrete histograms

I am on the search for a universal distance metric for comparison of two histograms. Consider the two figures below. Each of the figures contains a desired distribution (blue line) and a measured ...
21 votes
2 answers
2k views

Is there an unbiased estimator of the Hellinger distance between two distributions?

In a setting where one observes $X_1,\ldots,X_n$ distributed from a distribution with density $f$, I wonder if there is an unbiased estimator (based on the $X_i$'s) of the Hellinger distance to ...
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