# 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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### 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?
1answer
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### 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, ...
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 ...
3answers
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### What is the role of MDS in modern statistics?

I recently came across multidimensional scaling. I am trying to understand this tool better and its role in modern statistics. So here are a few guiding questions: Which questions does it answer? ...
1answer
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### RandomForest - MDS plot interpretation

I used randomForest to classify 6 animal behaviours (eg. Standing, Walking, Swimming etc.) based on 8 variables (different body postures and movement). The MDSplot in the randomForest package gives ...
4answers
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### Performing PCA with only a distance matrix

I want to cluster a massive dataset for which I have only the pairwise distances. I implemented a k-medoids algorithm, but it's taking too long to run so I would like to start by reducing the ...
3answers
5k views

### How to project high dimensional space into a two-dimensional plane?

I have a set of data points in a N-dimensional space. In addition, I also have a centroid in this same N-dimensional space. Are there any approaches that can allow me to project these data points into ...
2answers
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### 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 ...
2answers
246 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....
2answers
946 views

### Big-O Scaling of R's cmdscale()

I'm trying to run R's multidimensional scaling algorithm, cmdscale, on roughly 2,200 variables, i.e. a 2,200x2,200 distance matrix. It's taking forever (about a ...
3answers
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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 ...
2answers
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### In multidimensional scaling, how can one determine dimensionality of a solution given a stress value?

In multidimensional scaling, how can one determine dimensionality of a solution given a stress value? From what I understand, stress value is inversely related to the number of dimensions of a MDS ...
3answers
7k 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 ...
2answers
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### How to calculate the R-squared value and assess the model fit in multidimensional scaling?

I would like to do Multidimensional Scaling (MDS) using cmdscale() in R. I have read that it is useful to try out how many dimensions are suitable for the data by ...
2answers
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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 ...
1answer
295 views

### Reference for dimension reduction techniques

This is a follow-up question to Is PCA appropriate for comparing subsets of panel data?. It turns out that, yes, PCA is appropriate. But there are also many other ways to reduce n-dimensional data to ...
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### Interpretation of MDS factor plot

Suppose I run Multidimensional Scaling and I got the resulting plot. Can anybody suggest me how to interpret the plot. Please find one of my result below. Here I've 5 concepts which I run the MDS ...
1answer
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### MDS and PCA eigenvalues and eigenvectors

I understand that Multidimensional scaling (MDS) is same as doing Principal Components analysis (PCA) if Euclidean distance is used, this is known as Metric MDS. But I came across this in a book that "...
1answer
552 views

### Similarities and dissimilarities in classical multidimensional scaling

I am having trouble reconciling between several terms in MDS. According to [1], Section 14.8, Classical MDS takes similarities as inputs. In [2], also cited in Wikipedia, Classical MDS takes ...
1answer
8k views

### How to interpret variation explained by principal coordinates?

I have recently seen a couple of Principal Coordinates Analysis (PCoA) projection plots which show "percentage variation explained" by the respective principal coordinates. Given that the analysis is ...
0answers
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1answer
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### 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 ...
1answer
459 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 ...
1answer
186 views

### How to determine the number of random initializations to use in non-metric multidimensional scaling?

I'm trying to determine how many random initializations (restarts) I should use when performing an nMDS ordination. I understand I want to choose the solution that minimizes the stress, but how many ...