Questions tagged [multidimensional-scaling]

Technique that renders observed or computed (dis)similarities among objects into distances in a low-dimensional space (usually Euclidean). It thus constructs dimensions for the data; the objects can be plotted and conceptualized in those dimensions

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11 views

Interpreting results from mMDS, PERMANOVA and SIMPER (PRIMER V7)

I am struggling with the interpretation of my mMDS, PERMANOVA and SIMPER analysis. Can someone help me explain in some more general terms, what exactly these results indicate? I ran a PERMANOVA to ...
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18 views

question about standardizing data

Ok so I'm confused about the whole concept of standardizing data. I get the concept of why we need to standardize data for, let's say multiple linear regression so the data points are similar, but ...
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outliers on multi-dimensional scaling plot?

I am in process of writing a grant where I am explaining my planned methylation analysis using R software "minfi". In the text of the grant I am mentioning looking for samples containing ...
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53 views

Is it sensible to do PCA on a distance matrix?

I have 10x10 distance matrix where the distance metrics is (1 - overlap coefficient). I want to represent the observations in this matrix in a low dimensional space to see how observations relate to ...
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Is there an MDS/embedding algorithm that is more suitable to the goal of clustering a graph

I am testing ideas on clustering a particular graph. After testing a set of graph clustering/community detection algorithms I thought about mapping the graph to a vector space and using vector space ...
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19 views

Does this shape one cluster? and why angles change every time i run the code?

I have data and tried to do clustering on it. every time I run the code with the below statements it changes the angle of the shape but still the same below shape ...
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Multi dimensional scaling with sparse data on test samples

Given the dissimilarity matrix of $k$ elements, I've computed the MDS projection of the points with reasonable results. I'm now facing the need to add new test samples to the projection, where I can ...
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30 views

Best technique for dimension reduction given binary and ordinal variables

I'm currently in the process of tagging a bunch of photos. I started off with some tags being binary variables (i.e. the tag in question was either present or absent) and some ordinal variables , ...
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32 views

Is it ok if I log/square root transform my variables and then scale them to perform a PCA? [duplicate]

My goal is to carry out an hierarchical cluster analysis using the principal components that explain most of the variance. None of my variables is normal and therefore I think I should transform them (...
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66 views

Gaussian Mixture Models and distance matrix

I have a (euclidean) distance matrix and I want to perform GMM clustering. I read in another post (gaussian mixture model - approximate a matrix) that I could apply MDS or PCA to this matrix and use ...
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29 views

Environmental Vector Fit to NMDS Data

I am new to doing NMDS in R, and I have a question about how the vectors that characterize the fit of environmental data. I am exploring how the concentrations of metals in sediment affect benthic ...
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What kind of graph shows the distance between any 2 points as a measure of similarity between them?

I would like to start by saying that I have looked across several sites on the StackExchange website, and have determined this would be the best to ask my question as it regards data-visualisation ...
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Multidimensional scaling/perceptual mapping validation question

Basically, I have this map that shows a collection of beer brands on a two dimensional map. One dimension represents how well-known the brand is and the other dimension represents the price. We have ...
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Conceptual difference between STRESS and SSTRESS

I am studying the difference between STRESS and SSTRESS optimization functions in the context of multidimensional scaling. I have encountered this definition of optimization criteria for the SSTRESS: $...
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Comparing 2D maps (Coordinates of configuration matrices)

I am experimenting with MDS and I wanted to compare Classical(Torgerson) and Metric algorithms, here is my code: ...
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60 views

What are the best methods for comparing Torgerson (Classical) Vs. Metric Vs. Non-Metric MDS results?

I am trying to contrast results of various MDS approaches applied on the same dataset and understand their comparative interpretation. I calculate the goodness of fit for the various models with the ...
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Finding a Projection Plane in Dimensionality Reduction (e.g., Multidimensional Scaling)

I have a set of data points in high-dimensional space that I wish to map onto a lower dimension (3D or 2D). Question : How do I obtain the Projection (Hyper)Plane (e.g., its normal vector or its set ...
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Specific proof related to MDS distance matrix

Given a symmetric, positive semidefinite matrix A, and matrix D, where $D_{ij}=A_{ii}-2A_{ij}+A_{jj}$, prove that there exist n vectors {$\vec{v_1},...,\vec{v_n}$} such that $D_{ij}=||\vec{v_i}-\vec{...
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58 views

classic multi dimensional scaling example

I am reading this note. http://fourier.eng.hmc.edu/e176/lectures/MultidimensionScaling.pdf P.17 it has a Distance matrix, ...
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plotting the clustered data point based on Euclidean Distance Matrices

suppose I have two clusters, each of them have 5 points. I know the Euclidean Distance Matrix [ 10 x 10]. Is it possible to draw the points in a N-D space? how to do so?
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How to get coordinates when only pairwise distances are known? [duplicate]

I have $n$ points with pairwise distances known, $d_{i,j}: 0<i,j<n$. Their coordinates, $\vec{x}_i \in \mathbb{R}^k: 0 <i<n$, are unknown. I can set up $n^2 - n$ equations to solve for ...
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What is embedding? (in the context of dimensionality reduction)

In the context of dimensionality reduction one often uses word embedding, which seems to me a rather technical mathematical term, which rather stands out compared to the rest of the discussion, which ...
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Clustering common words for objects

I am currently running experiments aiming to simulate information transfer between agents. Without going into too much irrelevant detail, following the conclusion of a simulation I am left with a csv ...
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100 views

calling scores “changing” NMDS values from envfit() and R2 and P values

I have been following the excellent guide: NMDS ordination in R I wish to use the envfit function to see which of my environmental parameters correlate with community data dissimilarity. When I run ...
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151 views

Does feature scaling always make mean zero?

I came across a dataset which scaled the data and gave mean, closer to zero, not exactly zero. Any insights how does scaling work ? I read that it gives mean zero and variance 1. I tried using sklearn....
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Should you standardize and exclude correlated environmental variables prior to fitting them onto an ordination using envfit()?

I plan to fit a suite of environmental variables to a NMDS using envfit(). Should I first exclude those environmental variables that are correlated? Should I then ...
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Clustering algorithm for multiple feature types

I'm attempting to conduct a clustering analysis to identify groups of objects that are related to each other. I have to versions of the same data I'm working with. The first consists of the subjects ...
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484 views

How to analyse community composition in relation to environmental variables with nMDS?

I have a big data set (over 1000 observations) with abundances of over 60 species at 15 different sites over two years. Each site was divided into 30 sampling points and these were each sampled four ...
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113 views

Jaccard/binary (dis)similarity calculation to multidimensional scaling analysis

I have n N x n dataset of features (n) and subjects (N) in which I am attempting to cluster into a lower-dimensional space via multi-dimensional scaling. I'm confused about which MDS setup I need to ...
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545 views

Kruskal's Stress for MDS: How to compute this in R?

I am performing classical MDS on a dataset (Gower matrix returned by R cluster package function daisy). In my field, a measure ...
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Is it meaningful to perform statistical methods after multidimensional scaling?

Suppose I have data which I want to cluster, for example. I am not sure that the data are Euclidean i.e. they are really points in a Euclidean space with Euclidean metric. So I can try to first ...
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In Multidimensional Scaling (MDS), is it safe to assume that the optimal embedding dimension grows with the growth of sample size?

My question is more of a theoretical nature, so it'd be great to have some references to papers, but it'd be also nice to see some experiments. Let $D:=[d_{ij}]$ be an $n \times n$ distance matrix, i....
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2k views

'Median scaling' and 'Normalization by median deviation'

Here I am providing a paragraph from a paper, "This “median” scaling is performed by subtracting the median of the variable’s distribution in the data sample and normalising by the median deviation."...
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Mean shift clustering and the curse of dimensionality

I've often come across resources that mention that mean shift based clustering doesn't work well in higher dimensions. The sources are as follows: Page 1 of https://www.ncbi.nlm.nih.gov/pmc/articles/...
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Connection between Stochastic Neighbor Embedding and MDS

In the original SNE paper the authors mention a connection between the SNE objective function and an MDS-like stress function in the regime $\sigma_i \rightarrow \infty$, as follows. When $\sigma_i^...
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Explaining MDS space

I have a set of dummy variables (~300) indicating a particular feature, and rows which represent an individual. I plot this data after using nMDS to visualize which individuals are more similar to ...
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289 views

Is multidimensional scaling (PCoA) a linear dimensionality reduction technique?

Classic MDS (cMDS or PCoA) preserves global distances, characteristic of linear techniques. However, metric MDS seeks to minimize a cost function (stress), while non-metric MDS (nMDS) preserves only ...
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Multidimensional scaling with censored and missing distances

I would like to apply MDS to a high-dimensional distance matrix but the difficulty is than the distance matrix contains many missing and censored values (i.e. distances like >8). Does anyone know of ...
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156 views

Hierarchical clustering on principle components for multidimensional scaling

Essentially I have a data set of distant objects in which I've loaded onto factors using a multidimensional scaling technique. From my understanding, the factor loadings only differ between MDS and ...
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489 views

k-means/k-nearest neighbours on multi-dimensional scaled data

I used the Python manifold library for multi-dimensional scaling on my distance matrix. Can I use k-means or k-nearest neighbours on ...
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637 views

How to visualize proximity score in Random Forests

For a Random Forest, we can construct a N x N (where N is the number of data points) proximity matrix ...
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173 views

Does a PCoA (or MDS) assume normality of the variables behind distances?

More precisely, if I conduct a cmdscale (classical multidimensional scaling) on an Euclidean distance matrix by considering $n$ observations of $p$ variables i.e. $D_{ij}=\sqrt{ \sum_p (x_{ip} - x_{...
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569 views

K means clustering of MDS data

I've recently run a very large data set through a multidimensional scaling analysis and am attempting to cluster the results into groups. I've read a few papers that utilize hierarchical clustering to ...
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Principle coordinates analysis - visualization and assigning text to graph in r [closed]

I've recently run a principle coordinates analysis in r with ~ 200 subjects and 17 binary variables. I've plotted my points successfully, the challenge I'm facing is that when I plot the text with the ...
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56 views

When is the result of multidimensional-scaling unique up to isometry?

What conditions on the ambient space and/or the given matrix of dissimilarities guarantee that all point configurations that minimise the error function of multidimensional scaling (MDS) are congruent,...
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223 views

How to localize points from an incomplete distance matrix in R?

Suppose you have 3 shops and 2 supply units, and you only know the 6 pairwise (Euclidean, assuming 2D) distances between each shop and each supply unit, but not the pairwise distances between the ...
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692 views

Project new point into MDS space

I am trying to project a new point A(x, y, z) into a predefined MDS space in R. This is what I have so far: ...
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2k views

Is it necessary to deal with the outliers if we perform Normalisation on the data?

I am wondering, if it is necessary to remove outliers from the dataset if we perform Normalisation on the data as after Normalisation, all the values will shrink to value between 0 and 1. So, is it ...
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189 views

One-hot encoding for SOM

I have a question regarding how I should convert categorical data to numerical data. I'm using this kdd99cup intrusion detection dataset, which has a 41 attributes and class label is the type of ...
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842 views

Negative eigenvalues when computing MultiDimensional Scaling given nonnegative distance matrix

I am using the Smile MDS https://github.com/haifengl/smile/blob/master/core/src/main/java/smile/mds/MDS.java and occasionally running into: ...

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