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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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133
votes
5answers
90k views

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?
21
votes
1answer
6k 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, ...
19
votes
5answers
6k views

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 ...
18
votes
3answers
3k views

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? ...
14
votes
1answer
13k views

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 ...
12
votes
4answers
12k views

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 ...
11
votes
3answers
4k 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 ...
11
votes
2answers
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 ...
9
votes
2answers
185 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....
7
votes
2answers
908 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 ...
6
votes
2answers
3k views

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 ...
6
votes
2answers
1k views

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 ...
6
votes
3answers
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 ...
6
votes
2answers
4k views

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 ...
6
votes
1answer
276 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 ...
6
votes
1answer
2k views

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 "...
6
votes
1answer
5k views

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 ...
6
votes
1answer
488 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 ...
5
votes
2answers
3k views

Multidimensional scaling pseudo-code

I am planning to write a program that performs MDS. Any pointers to where I can access the pseudo-code for MDS? Thanks!
5
votes
1answer
1k views

How to distance and to MDS-plot objects according their complex shape

Suppose I have four basal forms of signal (blue, purple, red, green). I also have created transition forms between each other. If you carefully look on the picture below, you can see that for example ...
5
votes
1answer
1k views

Help me understand nMDS algorithm

I have been reading Zuur, Ieno and Smith (2007) Analyzing ecological data, and on page 262, they try to explain how nMDS (non-metric multidimensional scaling) algorithm works. As my background is in ...
5
votes
1answer
195 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 ...
5
votes
2answers
675 views

Is it legit to run clustering on MDS result of a distance matrix?

I am new to the topic of clustering and face the following problem: I have multiple binary datasets with 10k to 40k entries and 135 features each: $$ \begin{matrix} \newcommand{\feat}{\text{feat}} \...
5
votes
1answer
7k 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 ...
5
votes
0answers
80 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 $...
4
votes
2answers
7k views

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 ...
4
votes
2answers
5k views

How to best display crosstab data?

I have a 10x10 matrix composed of two variables with 10 brands each. One variable is the brand purchased, the other is the brand considered. My matrix shows a crosstabulation between the two. I need ...
4
votes
1answer
2k views

The `Shepard` function in R package `MASS`

The function Shepard is listed in the help file for MASS::isoMDS, but nothing is said about it. What does this function do?
4
votes
2answers
490 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 ...
4
votes
2answers
550 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 (...
4
votes
1answer
919 views

MDS: Is Kruskal's Stress-1 affected by scale of the data, or the number of points?

In Multidimensional Scaling, Kruskal's Stress-1 is a commonly used measure of fit. It is defined as: $\sqrt{\frac{\sum (d_{ij}-\delta_{ij})^{2}}{\sum d_{ij}^{2}}}$ where $d_{ij}$ represents the ...
4
votes
1answer
424 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 ...
4
votes
1answer
124 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 ...
4
votes
1answer
921 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) ...
3
votes
1answer
4k views

NMDS and variance explained by vector fitting

I just ran a non metric multidimensional scaling model (nmds) which compared multiple locations based on benthic invertebrate species composition. After running the analysis, I used the vector fitting ...
3
votes
1answer
400 views

Using metric MDS with non-metric distances and assessing the fit quality

I'm going to perform MDS by means of cmdscale function of standard R library. I spent several hours googling it and finally have ...
3
votes
2answers
1k views

R - Multidimensional Scaling and Missing Values

I include MDS analysis in a customer survey and have about 10 brands I want to include in the perceptual map at the end. Meaning the customers would have to rate 45 comparisons and give a similarity ...
3
votes
1answer
5k views

Adding labels to points using mds and scatter3d package with R

I have a dataset forwhich i have performed an mds and visualized the results using scatterplot3d library. However i would like to see the names of the points on the 3d plot. How do i accomplish that? ...
3
votes
1answer
250 views

Using a distance matrix *with errors* to find the coordinates of points

(I asked this same question in stackoverflow, without getting any answer, but maybe this is a more appropriate forum.) I would like to find the coordinates of a set of points in 3D from a distance ...
3
votes
1answer
520 views

Individual differences scaling, additional investigations

I am learning individual differences scaling (AKA three-way multidimensional scaling) and I want to know what different ways there are to state that my results are reliable. I had to perform ...
3
votes
1answer
710 views

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 ...
3
votes
1answer
469 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 ...
3
votes
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 ...
3
votes
1answer
493 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 $e_i$ ...
3
votes
1answer
302 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 ...
3
votes
1answer
282 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: ...
3
votes
1answer
322 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 ...
3
votes
1answer
135 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 ...
3
votes
0answers
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 ...
3
votes
0answers
207 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 ...