# 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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### How can I assign households to coordinates in a social space consistent with pairwise distance measures?

How can I assign households to coordinates in a social space consistent with pairwise distance measures? I have a question which is somewhat ill-defined, about creating an interesting and useful ...
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### Transforming count data for NMDS?

I am looking at species count data. Due to large counts of certain species, I initially fourth root transformed the data. I am using Bray-Curtis distance measurement. However when using vegan::metaMDS,...
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### Should data be transformed for NMDS? [duplicate]

I am looking at species count data. Due to large counts of certain species, I initially fourth root transformed the data. However when using vegan::metaMDS-Bray Curtis distance, the stress value for ...
1 vote
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### Dimensionality reduction and precomputed distance matrix

I have a question about dimensionality reduction. I want to understand how methods like MDS and t-SNE work. In particular, I'd like to understand the difference when I precompute the distance matrix ...
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### Interpreting Multidimensional Scaling (MDS) Plot: Rotation and Axis Orientation

First post here, so let me know if I'm missing things. I'm working with a multidimensional scaling (MDS) plot generated in MATLAB using cmdscale(1-(corr(Betas))). Based on prior experiments, I suspect ...
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### NMDS with ecological data containing many zeros in R - data transformations

I am trying to perform NMDS metaMDs() on mixed taxonomic data in R. My taxa data is organized with rows as observations and columns as different taxa. These data ...
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1 vote
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### How is variance explained of a classical mds model calculated (in matlab)

I've tried to research this question but have had to rely on answers to only somewhat similar scenarios which have led me in different directions. For example, I've been advised to calculate variance ...
1 vote
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### Plotting PCA cordinates as composites of environmental parameters into NMDS ordination of species assemblages

I have conducted a PCA and identified that the principal components (PC) are not driven by a single environmental parameter but are affected by several for each PC. I was then advised to retrieve the ...
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### procrustes alternative

Im comparing two multidimensional MDS solutions, the solutions have the same number of dimensions. I don't think I can use the permutation version of procrustes analysis (commonly, PROTEST in R::vegan)...
1 vote
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### Given a psd matrix $Q$ and a kernel function $f(y_i, y_j)$, how do I find $Y \in \mathbb{R}^{n \times d}$ that best approximates $Q$? [duplicate]

The question is basically the title. I have a matrix $Q$ that I know is positive semi-definite. I now want to find the $Y$ that approximates this matrix under some kernel function $f(y_i, y_j)$. I ...
1 vote
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### Can I scale a dataset using different methods on different columns and why?

relatively new to this and this question has been plaguing me. Say I have a dataset with feature A, feature B, and feature C. I need to scale for my model. Based on their distributions, feature A is ...
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### Evaluate relative quality of covariance matrix relative to a set

My ultimate goal is a way to evaluate a group of "m" covariance matrices (all size n*n) so I can pick an arbitrary one and calculate "this one is tighter than the average covariance ...
1 vote
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### Detect variable leading to grouping in Non-Metric Multidimensional Scaling (NMDS)

I'm performing an NMDS analysis on a Jaccard distance matrix of 347 variables across 341 subjects. I'm using mMDS from the Vegan package in R, everything seems to run fine, I get convergence and a ...
1 vote
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### How do I interpret a multidimensional scaling with a linear curve?

For context, I have a input dataset of 156 images and I'm extracting the feature maps for each image at the last fully connected layer of the AlexNet model. I get 156 feature maps, each of size [1, ...
1 vote
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### Formal way to test if a non-linear approach is necessary to correlating environmental variables to NMDS ordination axes?

I've got a follow-up question to this post regarding correlating [non-]linear environmental variables to NMDS ordination axes. My original plan was to use function ...
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1 vote
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### How to [properly] correlate environmental variables to NMDS ordination axes?

Data + setup: I've constructed an NMDS ordination from a Bray-Curtis distance matrix calculated from relativized abundances (basal areas) of trees. Samples include ~40 forested plots that have been ...
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### Clustering on MDS Data

I have computed a matrix of MDS distances using R's dist() function and then reduced to two-dimensional coordinates using cmdscale() function. If I apply PAM or k-means clustering (the choice of ...
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1 vote
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### Interpreting NMDS environmental correlations in the context of spatial and temporal autocorrelation

Do I need to account for autocorrelation when assessing correlations of environmental variables on an NMDS (nonmetric multidimensional scaling) ordination of species data? If so, how? Data + setup: I'...
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### Preselect explanatory variables with PCA for a further multivariate analysis

I have dataset composed of samples (here corresponding to sites), species, environmental variables linked to the species (e.g.: species biomass, abundance and size) and explanatory variables (...
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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 ...
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### Need to scale environmental variables when correlating to NMDS axes?

I've created a Non-metric MultiDimensional Scaling (NMDS) ordination from a Bray-Curtis dissimilarity matrix. (Starting data were basal areas of various tree species across multiple research plots). I'...
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### Scaling outliers in a dataset and reverse scaling

I have a data set with lots of small integer values and occasional large integers. For instance 1,1,1,3,2,1,320,2,3,4. I would like to scale my outlier values such that I can perform regression on my ...
1 vote
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### Should I include numbers on my NMDS axes?

The actual values of NMDS axes are essentially arbitrary, as I understand them - there's no meaning to be gained from a value of 1 or 100 or 10,000. In keeping with good design principles should I ...
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1 vote
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### When visualizing multidimensional scaling, is it weird if Dimension 1 is the y axis?

Since Dimension 1 is longer than the Dimension 2, I want to make the plot vertically long rather than horizontally long so that it's easier to include it in my thesis. But is it acceptable to make ...
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### How to deal with stress over 0.2 in NMDS in large dataset [closed]

I am analysing a large dataset (2000 rows by 250 columns) of the presence of species in several locations over the last 20 years. I have conducted a NMDS in order to identify differences between the ...
1 vote
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### How to reconstruct a Euclidean distance matrix from grouped pairwise-distance means and standard deviations?

Coordinates and Labels Take the simple case of 3 distinct object classes and 5 instances of each class situated in 3D Euclidean space. The coordinates and labels might look like the following: ...
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### How does PC-ORD calculate the amount of variation captured by each axis in NMDS?

I've always been taught that a major downside of NMDS is that there's no way to calculate the amount of variance captured by each axis. Variance doesn't come into the calculation at all so this made ...
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### Sum of PCA principal components

Short I wonder is it possible to sum the principal components together to obtain a score? For example, PC1 + PC2. Details I got the below dataframe: admin_username sales sign book team_sales ...
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1 vote
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### Detecting outliers in a multiple time-series

I have some broker prices incoming in real-time for several products. Sometimes a broker makes a typo and sends a wrong price, or my parsing engine assigns the price to the wrong product - these are ...
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### statistical significance after NMDS in r

I have performed an Non-metric multidimensional scaling (NMDS) to see if my two stations were different in terms of plankton abundances, using the metaMDS function in r (before I have performed a sqrt ...
258 views

### What is the maximum number of dimensions in MDS?

If I have an arbitrary Euclidean distance matrix $D=(d_{ij}:i=1,\ldots, I; j=1,\ldots, I)$ and I want to reconstruct its elements (pairwise Euclidean distances) via classical Euclidean MDS. That is ...
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### If a data set appears to be normal after some transformation is applied, is it really normal?

Suppose you have a data set that doesn't appear to be normal when its distribution is first plotted (e.g., it's qqplot is curved). If after some kind of transformation is applied (e.g., log, square ...
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### What does an r-squared of 1 mean for stress plot of NMDS analysis?

I'm doing a non-metric multidimensional scaling analysis. The analysis results in two convergent solutions and the output all look good, but when I made a stress plot to check the data I am getting an ...
386 views

### What is the difference between symmetric and non-symmetric in Procrustes/Protest analysis?

I'm basing my question off of someone else's stackoverflow post. My questions are the following: 1. A widely used R package vegan has a function called procrustes, ...
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I have a data set in which two variables are collinear (r^2 ≈ 0.7). I decided to extract the principal components, and then include these in a regression analysis to see which of the two variables ...
1 vote
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### How to scale multidimensional time series data per group

I am dealing with panel data and want to scale it in order to use it for some ML models: id year A B C 1 2000 3,539,101 265.152 .0683649 1 2001 3,539.101 2,485.833 .0683649 1 2002 3,539.101 2,939....
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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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### 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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### 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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### 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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### 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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### 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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### 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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