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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Multidimensional scaling of random matrix

Suppose I have a random symmetric matrix W of size $n\times n$, with i.i.d. coefficients uniformly distributed in [0,1], and I set $W_{ii} = 0$. Then I apply a Multidimensional Scaling of dimension $...
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130 views

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 ...
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206 views

Temporal Multi Dimensional Scaling

Let's say I apply a multidimensional scaling(MDS) to a dynamic dataset of $n$ points (eg, time series). At each step I will obtain a projection (in 2/3D) of the $n$ points. If nothing meaningful ...
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129 views

Can we decomp a J x J x K array of correlation matrices with Tucker and/or Candecomp/Parafac?

Problem We have an array $\underline{X}$ of order $$items \times items \times people$$ (that is, $J \times J \times K$) where the cells are Pearson's correlation coefficients, each across some ...
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178 views

Can I rotate a (classical) MDS result with varimax etc.?

I have a matrix of (scaled) co-occurence counts which I would like to summarise using (classical, i.e. PCA-related) Multi-Dimensional Scaling (MDS), and then rotate (with ...
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142 views

How to perform multidimensional scaling where a subset of points are already fixed?

I have two sets of psychological variables. For simplicity, there is set A (10 variables) and Set B (10 variables). When you map Set A using two-dimensional multidimensional scaling (e.g., using <...
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1k views

How could a hyperparameter grid search be visualised?

Consider a hyperparameter grid search that looks at the training and testing scores of an estimator with respect to multiple parameters like training epochs, number of nodes in layer 1, number of ...
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2k views

non-metric multi-dimensional scaling in R: help with plotting and understanding Stress for isoMDS vs. metaMDS

I have a dataframe with 900 observations. There are 11 columns: 9 measured variables and 1 representing region. ...
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699 views

Using Non-Euclidean Distance Matrix in Multi-Dimensional Scaling

I'm trying to use a non-euclidean distance matrix in MDS. Specifically, I'm using cmdscale in R. The resulting eigen vector appears to have huge negative values. From what I've read it appears that ...
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566 views

Non-metric Stress in 3 way Multidimensional Scaling (INDSCAL): individuals vs. group

My data consists of 19 participants giving dissimilarity ratings for every possible pairwise comparisons of a set of 12 epistemic adverbs (so each participant gives 66 ratings). The goal is to ...
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258 views

When using Nonmetric Multidimensional Scaling, is there an explanatory metric similar to loadings in PCA?

As a beginner to MDS, here is my thought process: Given a data set of environmental factors that may effect a certain sites, when I run a PCA on each site I get a list of principal components. If I ...
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265 views

Quantifying differences in a discrete distribution across several populations

Suppose you have a discrete random variable, $Y$, with a large number (say, $300$) of discrete (which happen to be nominal) possible outcomes. The mass function, $p(y)=P(Y=y)$, is unknown but a sample ...
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317 views

MDS with city distances, some values missing

I have a matrix of distances between cities and I want to use [Multidimensional scaling] (MDS) to calculate the locations of the cities. What MDS algorithm is useful for this? Is it available in ...
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856 views

Contribution of variables on axis in PCoA

I am trying to analyze data using Principal Coordinates Analysis (Classical Multidimensional Scaling (CMDS)) in R. I've tried some different ways (i.e., pcoa {ape}, ...
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1answer
36 views

Quantifying relationship between items, given many groups of items

I'm having trouble researching this, or even writing this question, because I'm not sure what this is called and I'm not familiar with a lot of the terminology. The best I can do is an example. Let's ...
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871 views

Statistically correct to apply Multi-dimensional scaling or PCA to cosine similarity matrix?

Supposing I have a document-term matrix as scripted below: ...
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1answer
299 views

Unsupervised Learning on Multilevel/Multidimensional Data

I am working on a case-control study, where I for each individual have high dimensional data (like illustrated in the image). I would like to do both PCA analysis and Clustering on this data, but it ...
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839 views

Using similarity measures as distances

I have a matrix where each row corresponds to an observation with binary attributes, and I am interested in performing multidimensional scaling using cmdscale on ...
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54 views

Using the results of a non-metric multidimensional scaling to derive a measure of deviance

I'm working with a dataset containing the taxonomic compositions of floras all over the world and performed a non-metric multidimensional scaling (NMDS) based on the relative proportions of plant ...
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4k views

Multidimensional scaling using Python

I have 6,000 points for which I have all pairwise distances in a distance matrix. I want to get an idea whether these data were generated by a mixture of Gaussian distributions so I'm trying to get a ...
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2k views

Gower distance and MDS: How to determine which variables count?

I have morphological data from two different determined groups (It and Nd), where the variables are heterogeneous (continuous, ...
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1k views

Why does some model-based clustering fail to fit with a large number of dimensions?

I am attempting to cluster data using Mclust. The data is originally from a dissimilarity matrix, transformed via multidimensional scaling in R (MASS::isoMDS). As I ...
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40 views

How to enhance the performance of naive CMDS?

I'm performing Classical MDS on the distance over columns of binary matrix. The result is like this: The points lies on two lines vertical to each other. I don't think useful information is shown in ...
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121 views

Sequential or dynamic multidimensional scaling

I am looking for a way to conduct sequential (dynamic) MDS based on several variables coded for a sequence of stimuli. Could anyone direct me to software for this purpose (especially R packages / code)...
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31 views

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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28 views

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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25 views

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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1answer
24 views

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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96 views

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 ...
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37 views

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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1answer
427 views

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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1answer
136 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 ...
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626 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 ...
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341 views

When the distance metric is not Euclidean, the metric Multidimensional Scaling (MDS) is nonlinear?

As it is commonly known, classic metric MDS (under Euclidean distance metric) is a linear dimension reduction method (equivalent to PCA), and it is also known to us that non-metric MDS is nonlinear, ...
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776 views

Pros and Cons of MinMax Normalization vs. Standardization

I have a large dataset with 800 columns and 6,000,000 rows with many dummy variables (70%+). I want to Normalize it. Given that so many variables are binary, taking values 0 or 1, I am tending ...
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261 views

NMDS anomaly - data does not support point placement

My data: Tracking forest communities (via species abundances) in various forest plots across time. My approach: Non-metric Multidimensional Scaling ordination I performed NMDS (using ...
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36 views

Analyzing jagged multidimensional data

I've been looking into this for a while now, but I don't think I know enough of the terminology to phrase this well enough for Google (my apologies). So essentially I'm looking at motion capture data ...
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53 views

How to create a line of best fit and identification of the variables on and MDS plot in R?

I am trying to run non-metric MDS on a dataset that has 28 rows (object = burials) and 27 columns (variables). I have coded it as binomial because my data is both qualitative and quantitative. I am ...
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163 views

Which MDS to use for interactions frequency distance matrix

I have kind of 'distance matrix', every element of which is represented by number of interactions (contacts) between pair of positions on single path-like(curve) object. It is stated, that number of ...
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379 views

Classification for multidimensional data

I have a dataset of timestamped measurements for various features. Each data point d is a Matrix MxN of M measurements (say time 1...M) for N different features. You can think of these as measurements ...
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55 views

How can I scale the $k$-th moment of a time series to a different time frequency?

I have a time series, let's say N daily log-returns. I want to study the moments (possibly the distribution) of the weekly returns. I have two ways: 1) Using the time-additivity property of ...
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46 views

Does it makes sense to perform MDS when $n<p$?

According to the reference quoted below, when performing a classical MDS on a dataset, I have to compute a centered matrix $B$ based on the dissimilarity matrix and then to compute the eigen-...
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52 views

What's right/wrong with using multi-dimensional scaling to analyze voting patterns of for members of an 11-member city council?

I'm trying to analyze voting patterns of an 11-member city council over a period of five years. Description of data file: each row (vector) is labeled as a councilmember; each column records ...
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1answer
155 views

Clustering before or after ordination

Can someone explain the implications of performing clustering either before or after performing NMDS? I have some ecological data and I am performing a clustering analysis to identify communities of ...
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378 views

Apply trained MDS model to new data

I have both a distance matrix and the original vectors, and am using MDS (Multidimensional Scaling) with R to generate vectors in more dimensions for the data. With dimensionality reduction (for ...
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777 views

Goodness of fit for multi dimensional scaling

What is considered to be an acceptable value for goodness-of-fit in multi-dimensional scaling (MDS). I tried to run an MDS analysis on my data with four dimensions in R. The goodness of fit comes ...
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895 views

nMDS in vegan for soil data

I am working with abiotic soil data such as bulk density, moisture levels and soil chemistry as response data (some quantitative some as percentages) and a mix of abiotic and biotic data as ...
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117 views

Suitable plot for 5 dimensional feature vectors?

I have a list of personality scores obtained from 100 people, based on the Big-Five personality test. Each person has one score for each of the five assessed traits. I put these scores into a 5 ...
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362 views

Is it correct to combine PCA and NMDS axes in a multiple regression?

I am considering to do a multiple regression in which some of the predictive variables are PCA (principal components) axes whereas others are NMDS (nonmetric muliple dimension scaling) axes. I would ...
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94 views

Multidimensional scaling of variables with multiple sub-features?

Let's say I have a year's worth of magazine issues (January, February, March, etc), and I want to visualize the differences among them. The classic example of multidimensional scaling (MDS) would have ...