# 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 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
24 views

### 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 ...
17 views

### What's the difference between metric multidimensional scaling and non-metric dimensional scaling? And how to deal with categorical variables?

So, I need to do some exploratory data analysis and I picked MDS to figure up if there were trends in the data. The structure of my data looks like this: ...
29 views

### 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)...
42 views

### Kruskal's non-metric multidimensional scaling

I have been reading Kruskal's 1964 "Nonmetric multidimensional scaling: A numerical method" and I am slightly confused by some details, this is probably due to my lack of knowledge of ...
63 views

### Proof that PCA is equivalent to MDS when using Euclidean distances

As I was watching a video explaining how MDS works, the narrator mentioned that PCA is equivalent to MDS when Euclidean distances are used. I got confused as to how that's the case. My guess is that ...
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 ...
112 views

### 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 ...
65 views

### 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 ...
38 views

### Stress value cut-off for best fit on MDS for metric data

I am drawing a multi-dimensional scaling plot using SPSS to interpret the clustering of metric data based on genetic distances. Upon using ALSCAL, I get a stress value of 0.11 for 2 dimensions and 0....
1 vote
43 views

### 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
20 views

### 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
59 views

### 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 ...
167 views

### 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 ...
126 views

### 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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### What to do with non-linear environmental correlates in NMDS variance analyses?

This is in response to @GavinSimpson's answer to NMDS and variance explained by vector fitting. From this post, Gavin shares the following: ...the vector fitting approach is inherently linear and we ...
1 vote
107 views

### 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'...
69 views

### 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 (...
1 vote
749 views

### 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 ...
1 vote
293 views

### 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'...
32 views

### 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
57 views

### 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 ...
1 vote
16 views

### 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 ...
1 vote
838 views

### 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
420 views

### 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: ...
155 views

### 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 ...
190 views

### 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 ...
1 vote
350 views

### 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 ...
349 views

### 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 ...
208 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 ...
2k views

### 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 ...
1 vote
512 views

### 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 ... 244 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, ...
115 views

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
961 views

### 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....
34 views

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 ...
282 views

### 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 ...
1 vote
938 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 ...
111 views

### 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 ...
1 vote
36 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 ...
547 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 (...
101 views

### 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 ...
208 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 ...
1 vote
102 views

### 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 ...
49 views