Questions tagged [distance-functions]
Distance functions refer to functions used for quantifying the notion of distance between members of a set, or between objects.
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determine suitable values for the parameters of the distance function for this graph
Hi I've been learning data mining and came across this question. I couldn't seem to figure it out myself.
So we have a large single undirected graph(without attributes) G = (V,E) and want to detect ...
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71 views
Jaccard Index for Binary Data in R using dist function
I have a presence/absence table of 0s and 1s and I would like to cluster this data. I want to create a pairwise matrix using R's dist function which has a binary ...
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1answer
13 views
Finding the effect of nodes on a density heatmap
Let's say I have a geo-tagged dataset of all payment transactions for businesses in a city. I know whether each payment is made by cash or card, and have made a heatmap of where in the city the ...
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33 views
Relationship between KL divergence, JS divergence, and MMD?
What kind of relationship is there between the KL (Kullback-Leibler) divergence, JS (Jensen-Shannon) divergence, and MMD (maximum mean discrepancy)?
I know that they all share a global minimum at $P=...
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1answer
130 views
Is one-hot encoding and standardization of data equivalent to Gower's distance?
For clustering and other techniques for mixed data (numerical and categorical), Gower's distance is usually more preferred than Euclidean distance because the former computes distance differently for ...
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26 views
Similarity measure before and after dimensionality reduction or clustering
I have a dataset with 500 000 samples, each sample contains 30 features.
The values of the features are in the range 0.0 to 1.0.
...
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17 views
Mahalanobis: Covariance or correlation? [duplicate]
Is the Mahalanobis distance using correlations or covariances (among two vectors) to determine the similarity? I know that both are quite the same and differ only by a division of a standard deviation ...
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32 views
Distance between two distributions
I am analyzing time-series data, and I would like to detect a significant change in data distribution. I already know about Bhattacharyya distance, but that requires histograms of equal-sized bins. ...
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How to measure the “variability” across a set of many (>>2) probability distributions?
Given a set of many of discrete probability distributions, is there a way I can efficiently calculate a metric that quantifies how different the entire set of these probability distributions are to ...
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8 views
Calculate association trends
I have time series dataset for 10 consecutive periods (i.e. T, T+1, T+2, ..., T+9). Moreover, I also have 100 term triplets in each time period. Each triplet contains 3 objects namely x, y and z.
I ...
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1answer
93 views
Calculation of relative distance
I have 100 term triplets as shown in the below mentioned figure. Each triplet contains 3 objects namely x, y and z. I want to rank the triplets according to the following two properties.
y should be ...
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1answer
94 views
The violation of triangle inequality in KNN
If the 0<p<1 in the distance metrics, then the triangle inequality is violated.
The question as follows
Does the violation of this inequality affect the ...
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Distance metrics [closed]
I read about different distance metrics, such as Euclidean distance and so on.
What are the machine learning algorithms that use distance metrics in their calculations?
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1answer
172 views
How can I order kmeans clusters?
I have a kmeans cluster object and I would like to order the clusters. Not the observations within the clusters, rather the clusters in order of each other.
Is there a way of doing this? I found ...
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40 views
Fuzzy String Matching and Word Length
I'm attempting to calculate how likely it is that two words are the "same", but misspelled. I've narrowed it down to a few algorithms that will give me a similarity metric, but the problem is that ...
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12 views
How is the matching distance used in the Jaro similarity index?
I read the codes in this link to have a better understanding of the Jaro similarity index. According to wikipedia, one part of the algorithm requires comparing if there are common characters using a ...
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($L_2$) distance for noisy data
I'm given a subspace $V$ and a set of $n$ corrupted observations $\tilde{x}_1 = x_1 +\epsilon_1,...,\tilde{x}_n = x_n + \epsilon_n \in \mathbb{R}^D$. Assume $D$ is large and that $\epsilon_i \sim N(0, ...
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1answer
142 views
Cleaning Up the Data with Mahalanobis Distance [duplicate]
I have a data set and I want to cleaning up my data set from the ouliers, so I decide to use the Mahalanobis distance to find the outliers. But I have a problem here since my covariance matrix isn't ...
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What happens with Mahalanobis-Distance, when the assumption of equal Covariance-Matrices breaks down
Assume that we want to compare the forecast quality of various forecasters $f$ on $n$ values such as stock-market prices or whatever. We could then define a "Mahalanobis-Distance" (MD) (or rather ...
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What distance measure (e.g. Jaccard) to use when there are correlated observations?
I would like to use a simple distance measure (e.g. Jaccard) on a rather sparse set of 0/1 variables or probability densities, for which some of the observations are similar; this is due to repeated ...
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1answer
160 views
Is Earth Mover Distance has maximum bound?
I have two probability distributions which each distribution has sum up to 1.
I want to compute the distance between those two probability distributions. I want to use Earth Mover Distance to ...
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2answers
214 views
Is the maximum bound of Euclidean distance between two probability distributions equal to $\sqrt{2}$?
I used Euclidean distance to compute the distance between two probability distribution. The example of computation shown in the Figure below.
As my understanding, the maximum distance occur while $...
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Recovering a distance matrix from nonnegative sparse correlation matrix?
After doing extensive literature research in all sorts of science I am completely puzzled. I am trying to find out what the state-of-the-art techniques would be to recover a (let's say euclidean) ...
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202 views
Best way to compare CNN outputs vectors
I was training a CNN (which contains only convolutional an pooling layers) to extract features of a given image. Output vector size is ...
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1answer
103 views
When does the Wasserstein metric attain inequality WLOG?
I’m reading a classic paper [1] that describes a version of the Wasserstein metric (aka Mallows metric), defined as follows. Let $F$ and $G$ be probabilities in $\mathbb{R} ^B$, and let $U \sim F$ and ...
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2answers
108 views
Distance calculation on variables that cannot be represented in the Euclidean space
Given a variable such as number of events attended together, which is more of a multi-dimensional data how can you calculate a sort of distance between people (i.e. ...
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Name of divergence $D(p||q) = \max_x {p(x) - q(x)}$
$D(p||q) = \max_x {p(x) - q(x)}$ is thought of as a very simple divergence for two continuous probability distributions.
This satisfies minimum requirements of divergence, $D(p||q)\ge0$ and $D(p||q)=...
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1answer
188 views
K-means clustering on a large matrix using kendall's tau as a distance measure
I'm trying to use kmeans clustering on a relatively large matrix (4000x4000) using the amap::Kmeans function but R seems to be freezed even after more than half an hour. I have to restart R after this....
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2answers
169 views
Distance metric for source code
I'm trying to compare source code from multiple github projects, and in particular I'm looking for projects that include large chunks of code from other repositories, or large chunks with small ...
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1answer
35 views
How to compare hundreds of one-dimensional functions
I have hundreds (2002 in today's case) of functions of the distance between two objects: $f_1(x)$, $f_2(x)$, ..., $f_{2002}(x)$. They are correlation functions. They all converge to 0 when $x$ is ...
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6 views
Modifying input feature set to incorporate neighboring weekdays effect
I'm using k-NN regression for one of my problems where one of the feature of my input feature set contains the type of weekday (0 for Monday $\ldots$ 6 for Sunday). This has been used to account for ...
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21 views
How to calculate the similarity/distance between multiple measures for a single individual
I have what may be a relatively simple query, but I'm unsure of the best way to do it. I would like to calculate the similarity between multiple measures for a single individual. I have a data matrix ...
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2answers
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calculating distance to 1 (positive and negative numbers)
I have what I assume is a very simple question.
I have a range of numbers from 81 to -6, that corresponds to racios pop. growth/urban construction of cities. The ideal ratio would be = 1. I need, ...
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2answers
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Is there a version of the Mahalanobis distance for matrices?
I'm working on a computer vision problem and I want to use the Mahalanobis distance to cluster image patches (2D matrices having the same dimensions). I haven't been able to find any generalisation up ...
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3answers
1k views
Can I use Manhattan distance on binary data for hierarchical clustering?
I understand that classically Jaccard and Hamming work best with binary data, but is there anything specifically wrong with using a Manhattan distance instead with the complete linkage function?
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357 views
Distance Matrix for Big Data
I have been struggling to create a distance matrix for some Big Data (800,000x20). I have tried R (dist function), Matlab (pdist function), and cloud computing (to increase RAM).
Ultimately, the ...
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427 views
Clustering in high dimensions: distance metrics, binary vs continuous, statistical tests for number of clusters / noise points [closed]
I’ve got several thousand observations in approximately 300-dimensional space, in a relatively sparse matrix (typically 30 non-zero dimensions per observation). I'm using a clustering algorithm (so ...
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Levenshtein distance “proper” range for fuzzy matching
I am hoping to use Levenshtein distance concept for fuzzy matching in SQL joins between two tables on t1.first_name||last_name = t2.first_name||last_name.
Is ...
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74 views
Finding optimal parameters for Mahalanobis distance's covariance matrix [closed]
I have to correctly classify a data set (~1000 instances) for 2 classes, either 0 or 1.
I have a training set of the same size. My first thought is to use a $k$-NN classification. However, instances ...
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1answer
2k views
Can KL-Divergence ever be greater than 1?
I've been working on building some test statistics based on the KL-Divergence,
\begin{equation}
D_{KL}(p \| q) = \sum_i p(i) \log\left(\frac{p(i)}{q(i)}\right),
\end{equation}
And I ended up with a ...
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2answers
49 views
Clustering with Self Organizing Maps including time, date and month as attributes
I am about to start up a project on pattern recognition in a highdimensional dataset holding information on transactional salesdata for a company. In that manner I have decided to use the method of ...
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1answer
131 views
Analysis or Comparison of Euclidean Distance matrix
Related: Average distance in distance matrix
I'm looking for some way to compare euclidean distance matrices. The matrices I need to compare will have constant number of rows but varying number of ...
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1answer
75 views
Mahalanobis distance invariant against further elements/individuals?
Assume following: There are ten individuals and each is represented by two properties (Size and Gender).
Now I measure the distance between two individuals A and B via the Mahalanobis distance:
$$
d(...
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114 views
covariance matrix of individuals or of the pool?
At first: I have individuals represented by vectors with four entries/properties:
...
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607 views
Distribution of the Mahalanobis distance between two samples from a Gaussian distribution
Let $\mathbf{X}=(X_1,\dots,X_p)\sim\mathcal{N}(\mu,\Sigma)$ be a Gaussian random vector. We all know that
$$d^2(\mathbf{X},\mu) = (\mathbf{X}-\mu)^T\Sigma^{-1}(\mathbf{X}-\mu) $$
has a $\chi^2_p-$...
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1answer
90 views
square root missing in code?
I'm using Pairwise Mahalanobis distance in R as code to calculate the Mahalanobis distance:
...
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1answer
797 views
Normalizing edit distance on strings
I am going to run a clustering algorithm on strings (sequences of characters). I would like to use the edit distance, but it seems to be misleading as I perceive ...
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417 views
Is the relative contrast theorem from Beyer et al. paper: “On the Surprising Behavior of Distance Metrics in High Dimensional Space” misleading?
This is cited very often when mentioning the curse of dimensionality and goes
(righthand formula called relative contrast)
$$ \lim_{d\rightarrow \infty} \text{var} \left(\frac{||X_d||_k}{E[||X_d||_k]...
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426 views
can I use manhattan distance function on hartigan wong kmeans clustering
I would like to perform Hartigan Wong clustering on high dimensional data. As I understand, Manhattan distance works better than the Euclidean distance in higher dimensions.
I have been using the K-...
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332 views
Euclidean vs Manhattan distance behaviour in high dimension - curse of dimensionality
I have compared different distance functions by computing the average tf/idf distance between documents. My results show a range between $10-15$ for the Manhattan and a range between $1-1.5$ for the ...
