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 ...
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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 ...
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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 ...
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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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Identical loadings in a PCA

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 ...
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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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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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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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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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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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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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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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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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'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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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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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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