# 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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### 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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### 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 ...
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### How to assess the significance of a single data point in Multidimensional scaling?

I'm looking for a way to determine a Stress-like value associated with the single data points of a Multidimensional scaling plot. The source of my data is a dissimilarity matrix from which I computed ...
1 vote
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### 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 find ...
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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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### Can I compare MDS space plots run for separate groups but with the same variables taken for each group?

I have run an ALSCAL procedure to assign 7 different variables into 2 dimensional space. Data derives from three different groups. I have run a combined analysis collapsing the groups properly to give ...
1 vote
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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 ...
1 vote
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### 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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### Is it ever acceptable to ignore the "leading minor of order 1 is not positive definite" error when plotting ellipses onto a NMDS?

I have a dataset that is evaluating the impacts of various factors on the composition of metabolites within trees. As part of this analysis I am running NMDS with metaMDS in vegan and plotting with ...
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### Using Principal Coordinates scores in subsequent analyses

If I do PCoA on a dataset, can I use these scores in subsequent analyses? My understanding is that Using PCA scores in subsequent regression is valid. However, it seems like this doesn't hold for NMDS ...
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### Is it okay to re-scale values that were standardized before some rows were excluded?

The data I was given is scaled to have mean = 0, sd = 1 (no, I do not have the original data, and no I cannot get it). After receiving the data I excluded half the rows, so obviously the resulting ...
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### 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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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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1 vote
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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