# 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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### 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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### 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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### 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 ...
14 views

### 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 ...
101 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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### 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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### 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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### Relationship between Principal Component Analysis and Multidimensional Scaling? [duplicate]

I understand the concept of MDS, but I am struggling to understand the similarities between the two.
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### Checking accuracy of classical Multidimensional Scaling - how to define metrics to measure accuracy?

Say I'm given a set of distances between the samples in a data set and a given dimension $p.$ I'm asked to embed the dataset in $\mathbb{R}^p$ using classical multidimensional scaling (MDS). To be ...
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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....
859 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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### Analyze dataset with multidimensional scaling

I am ask to analyze a dataset via multidimensional scaling. There are 9 variables in totals, with 1 of them being factor. I plan to make a Classical MDS plot, but there are 8 variables ( i drop the ...
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### Data transformation - pointwise or batch?

A data transformer performs a pre-preprocessing step ("transformation") before an estimator can fit or classify the data. The transformation step is a projection (any idempotent map: $T^2 = T$), ...
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### Fitting environmental variables to an ordination (artificially replicating data?)

I collected five samples of animal tissue from each of 3 different sampling sites (15 samples total). For each sample, I determined bacterial community composition, so I have a standard multivariate ...
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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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### 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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### 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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### 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 ...
499 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: ...
1k 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 ...
153 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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### 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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### How to embed in Euclidean space

I have what I think might be a standard machine learning problem but I can't find a clear solution. I have lots vectors of different dimensions. For each pair of vectors I can compute their ...
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### Book about ordination in ecology

I am looking for a book that would cover a lot of different ordinations techniques (indirect gradient analysis e.g. PCA, CA, DCA, MDS, nMDS but also direct gradient analysis e.g. CCA, CCorA, RDA) with ...
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### Method named 'BEST' in multivariate analysis - what is it?

I've read a few ecological papers where a 'BEST' procedure is used to assess effect of environmental parameters on biological community composition, after multivariate analysis like MDS. For instance ...
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### Feature scaling/normalization and prediction

I have a dataset which I have split into a training and a test set. I have thereafter applied normalization on the training set and saved the mean (U) and standard deviation (SD) estimated based on ...
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### Multidimensional scaling with periodic boundaries

For a specific application at hand, I need to visualise samples from a high dimensional space into 2D, while respecting their distances as much as possible. Normally, I would simply use ...
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### cmdscale in R returns difficult to explain results

PROBLEM DESCRIPTION: We have two very similar 8D datasets. The OLD has 107 records, the NEW has 111 record (107 from the OLD plus 4 additional record). The NEW dataset download The OLD dataset ...
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### Scaling unknown time series for prediction with RNN

I'm trying to build a RNN model to predict arterial blood pressure (ABP) time series based on two other time series, namely, ECG and PPG. It is available to me a set of multivariate time series of ...
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### Should I standardize my data or not?

I am currently working on a dataset concerning the color magnitude of astronomical point sources. There are 9 covariates, each representing a specific color of a point source. I used k-means, ...
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### Which dimensionality reduction technique preserves the k nearest neighbors (euclidean space)?

I'm looking for a lower dimensional projection of data such that the k nearest neighbors (in Euclidean space) in high dimensions remain the k nearest neighbors in low dimensions. I found that Isomap ...
164 views

### Are NMDS Axis the same calculated for one or more dimensions?

I used NMDS axes of an ecological community as proxys for the community similarity in the different samples. I would like to "quantify" the importance of the different NMDS axis according to the ...
806 views

### Convert distance matrix to coordinate(s)

I have a (SNP) distance matrix that I would like to convert to coordinates (ideally just one linear scale) in R. I am planning to use the transformed coordinates in principle component analysis along ...