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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1answer
46 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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4k views

Visualizing multi-dimensional data (LSI) in 2D

I'm using latent semantic indexing to find similarities between documents (thanks, JMS!) After dimension reduction, I've tried k-means clustering to group the documents into clusters, which works ...
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126 views

Multidimensional Scaling terminology question

The picture below concerns Multidimensional Scaling (MDS), in which there are two terms " Matrix of distance "(δ) and "euclidean distance"(d). I don't understand the difference between them. Can you ...
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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
209 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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81 views

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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719 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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1answer
197 views

Finding optimal correspondences between objects given two square distance matrices

I would like to find the optimal correspondences between two systems of objects based on the distances between objects WITHIN the two systems. So, the input to the algorithm would be two square ...
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1answer
274 views

Methods of “Two-Way” Multidimensional Scaling (MDS)?

I just want to ask about the MDS. Below is the subcategory of the Multidimensional Scaling topic. Multidimensional Scaling Metric and Non-Metric Models Methods of "Two-Way" Multidimensional Scaling (...
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134 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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1answer
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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7k views

t-SNE versus MDS

Been reading some questions about t-SNE (t-Distributed Stochastic Neighbor Embedding) lately, and also visited some questions about MDS (Multidimensional Scaling). They are often used analogously, ...
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188 views

Scalable dimension reduction

Considering the number of features constant, Barnes-Hut t-SNE has a complexity of $O(n\log n)$, random projections and PCA have a complexity of $O(n)$ making them "affordable" for very large data sets....
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MDS on large dataset (R or Python)

I have a large 400000 $\times$ 400000 dataset (dissimilarity matrix) and I want to do multi-dimensional scaling on it. However, after looking at the generic cmdscale() function in R, it only takes ...
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325 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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1answer
333 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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57 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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351 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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1answer
886 views

NMDS: why is the r-squared for a factor variable so low

I am doing an NMDS ordination. The data come from a number of sites scattered around two lakes. In the plots, I coloured the samples from the two lakes blue and green. There seems to be some pretty ...
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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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1answer
482 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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138 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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5k views

Multiple regression - how to calculate the predicted value after feature normalization?

I'm currently doing the Andrew Ng machine learning course on coursera, and in Week2 he discusses feature scaling. I have seen the lecture and read many posts; I understand the reasoning behind ...
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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 ...
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810 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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874 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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Interpret multidimensional scaling plot

I have data with 4 observations and 24 variables. To understand the underlying relationship I performed Multi-Dimensional Scaling (MDS), and got a plot like this: Now the issue is with the correct ...
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439 views

Alternative to MDS plot for random forest visualisation

I'm using R and 'randomForest' package for binary classification. I can MDS plot (from the same package) the initial (more or less) class separation based on training set. However, this doesn't allow ...
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464 views

Multidimensional graph representation

I would like to know how to plot the following 30 observations on a graph, with 1 color for each country, using Kmeans or other methods on R. Each of the 40 independent variables can take value from 0 ...
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Is the Normalized Information Distance (NID) a euclidean distance?

I'm trying to determine if I can plot my dissimilarity matrix (which is a Normalized Information Distance / the "Universal Distance Metric" dissimilarity matrix), in a lower-dimensional space using ...
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5answers
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Are there any versions of t-SNE for streaming data?

My understanding of t-SNE and the Barnes-Hut approximation is that all data points are required so that all force interactions can be calculated at the same time and each point can be adjusted in the ...
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1answer
304 views

Is normalization required in Sammon mapping

I have a data set of 480 samples with 7-dimensions and I want to implement a Sammon mapping into 3-dimensions. In Principal Component Analysis to my understanding we need to normalize the data in ...
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1k views

Convert Pearson correlation matrix into dissimilarity matrix [duplicate]

I would like to execute multidimensional scaling (MDS) based on a matrix of Pearson correlation coefficients. The sklearn.manifold.MDS function takes a dissimilarity matrix as an input and I therefore ...
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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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48 views

Drawing a graph and grouping based on characteristics

Let's say that I have a list of my friends and each of them are tagged with some of their characteristics. That is, ...
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335 views

non-metric multidimensional scaling in R - smacof: why minimum stress model is so different from torgerson model?

Trying to understand how nMDS is applied with smacof package in R. From smacof vignette I understand that one can attempt to ...
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1answer
3k views

Scaling/Normalization not need for tree based models

I could not find a good answer/reference that can explain why rf/decision trees/gbm are not susceptible to the scale of values of numerical variables. My sense is that since boosting methods ...
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1answer
48 views

MDS methods - Pooling replicated seasonal trap data?

I've sampled 2 sites for wasps. At each site, I used 20 traps to catch wasps. I sampled each site once a month for 3 months: Site 1 = 20 samples + 20 samples + 20 samples Site 2 = 20 samples + 20 ...
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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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381 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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165 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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1answer
556 views

Distance preservation measure for Random Projection evaluation

Recently I have applied the Random Projection technique to several datasets. As you might know this method has the nice propoerty that pairwise distances between data points are approximatelly ...
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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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569 views

How to reduce the dimensionality of a similarity matrix (of categorical co-occurence counts)?

Our example person Azra has assigned (open-ended categories of her own choosing) to a fixed set of 35 items, recorded as logical values (...
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182 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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5answers
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What's the difference between principal component analysis and multidimensional scaling?

How are PCA and classical MDS different? How about MDS versus nonmetric MDS? Is there a time when you would prefer one over the other? How do the interpretations differ?
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329 views

Constructing N-dimensional vectors out of point distances

I was wondering if anyone had any insight or information on how one might go about determining point coordinates in an n-dimensional space from point pair distances. For example, say I start with a ...
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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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930 views

Normalizing data before applying MDS with strain criterion

The features of my dataset are like below: • BI-RADS assessment: 1 to 5 (ordinal) • Age: patient's age in years (integer) ...
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1answer
517 views

Learning vector embeddings from distances

So... I have a set of entities $\mathcal{E} = \{e_i \mid i \in [1,n]\}$, and I have a proper distance metric defined over $\mathcal{E}\times\mathcal{E}$, call it $d$, so the distance between $e_i$ ...