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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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 of fit of the MDS is reported. Other researchers usually perform this ...
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15 views

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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32 views

Does MDS represent groupings? [closed]

How to Do Linguistics with R says: Multidimensional Scaling is a convenient tool for visual exploration of multivariate data. Its advantage in comparison with cluster analysis is that MDS can ...
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Relationship between Principal Component Analysis and Multidimensional Scaling? [duplicate]

I understand the concept of MDS, but I am struggling to understand the similarities between the two.
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Checking accuracy of classical Multidimensional Scaling - how to define metrics to measure accuracy?

Say I'm given a set of distances between the samples in a data set and a given dimension $p.$ I'm asked to embed the dataset in $\mathbb{R}^p$ using classical multidimensional scaling (MDS). To be ...
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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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141 views

'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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46 views

Analyze dataset with multidimensional scaling

I am ask to analyze a dataset via multidimensional scaling. There are 9 variables in totals, with 1 of them being factor. I plan to make a Classical MDS plot, but there are 8 variables ( i drop the ...
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Data transformation - pointwise or batch?

A data transformer performs a pre-preprocessing step ("transformation") before an estimator can fit or classify the data. The transformation step is a projection (any idempotent map: $T^2 = T$), ...
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32 views

Fitting environmental variables to an ordination (artificially replicating data?)

I collected five samples of animal tissue from each of 3 different sampling sites (15 samples total). For each sample, I determined bacterial community composition, so I have a standard multivariate ...
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56 views

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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54 views

Detrended Correspondence Analysis or Non-metric multidimensional scaling

For an ecology project I am analysing how and if the species composition of a habitat type (heathland for example) changes through time. This was done by measuring fixed plots within a habitat type ...
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78 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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285 views

Non-metric multidimensional scaling, no convergence

I'm using MetaMDS from the VEGAN package to run a non-metric multidimensional scaling analysis. My stress level for 3 dimensions is in the excellent range (i.e., stress<.05), however, the model ...
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43 views

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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Parallel analysis for principle components analysis and Multi-dimensional scaling

Does the same method for conducting a parallel analysis for principal component analyses apply to find the cut-off point for multidimensional scaling? Under the pretense that PCA and linear MDS are ...
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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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Setting the number of dimensions in an MDS

I have two distance matrixes. The distance matrixes are two topics of a Latent Dirichlet Allocation. The distance is computed based on the probability distribution of the 6 words with the highest ...
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123 views

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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304 views

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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360 views

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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25 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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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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404 views

Project new point into MDS space

I am trying to project a new point A(x, y, z) into a predefined MDS space in R. This is what I have so far: ...
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617 views

Is it necessary to deal with the outliers if we perform Normalisation on the data?

I am wondering, if it is necessary to remove outliers from the dataset if we perform Normalisation on the data as after Normalisation, all the values will shrink to value between 0 and 1. So, is it ...
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139 views

One-hot encoding for SOM

I have a question regarding how I should convert categorical data to numerical data. I'm using this kdd99cup intrusion detection dataset, which has a 41 attributes and class label is the type of ...
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497 views

Negative eigenvalues when computing MultiDimensional Scaling given nonnegative distance matrix

I am using the Smile MDS https://github.com/haifengl/smile/blob/master/core/src/main/java/smile/mds/MDS.java and occasionally running into: ...
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847 views

How to embed in Euclidean space

I have what I think might be a standard machine learning problem but I can't find a clear solution. I have lots vectors of different dimensions. For each pair of vectors I can compute their ...
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1answer
123 views

Book about ordination in ecology

I am looking for a book that would cover a lot of different ordinations techniques (indirect gradient analysis e.g. PCA, CA, DCA, MDS, nMDS but also direct gradient analysis e.g. CCA, CCorA, RDA) with ...
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52 views

Method named 'BEST' in multivariate analysis - what is it?

I've read a few ecological papers where a 'BEST' procedure is used to assess effect of environmental parameters on biological community composition, after multivariate analysis like MDS. For instance ...
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Feature scaling/normalization and prediction

I have a dataset which I have split into a training and a test set. I have thereafter applied normalization on the training set and saved the mean (U) and standard deviation (SD) estimated based on ...
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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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286 views

cmdscale in R returns difficult to explain results

PROBLEM DESCRIPTION: We have two very similar 8D datasets. The OLD has 107 records, the NEW has 111 record (107 from the OLD plus 4 additional record). The NEW dataset download The OLD dataset ...
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536 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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823 views

Should I standardize my data or not?

I am currently working on a dataset concerning the color magnitude of astronomical point sources. There are 9 covariates, each representing a specific color of a point source. I used k-means, ...
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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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157 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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751 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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417 views

Why normalize data after doing Multidimensional scaling?

I am running simulations from a paper on graphical clustering based on latent positions. Essentially, the first step is to do Multidimensional Scaling on the Adjacency matrix, after which the authors ...
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366 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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59 views

Feature scaling and when to use which

I am looking into running regression on a multivariate data set. I am looking into different ways to scale my data: standardization, L2 and L1 normalizations. In what case would you use which method? ...
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426 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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564 views

Can MDS coordinates be used as variables in further analyses?

I have calculated an NMDS from vegetation community data taken from two habitat types using the metaMDS() function in vegan. My ...
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163 views

How to normalize three variables into one ordinal scale?

I have three same scaled variables (Strategy 1: Stay, Strategy 2: Move, Strategy 3: Move far) which I want to compare in a heatmap for different locations. For each strategy an operator earns a ...
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2k views

Scaling on Categorical Variables for KNN Imputation

Problem: I am attempting to impute on a data set in R (6000+ rows, 55 columns) with high NA proportions in most variables (from 10 - 80% missing) and have found evidence to support the KNN approach to ...
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How do I scale/standardize one set of data that is non-linear (due to temp variations in a device) to that of a data set that is linear?

I have data from two instruments over time. One of the instruments does not show a linear trend due to an anomaly but I want to standardize that data against that of the second instrument because I ...