# Questions tagged [biplot]

Biplot or dual plot is an exploratory graph to present - as points or vectors - both the observations (sample) and the variables of the data. The axes are typically latent principal dimensions. Biplot is often used to depict principal component analysis, correspondence analysis, and other multivariate methods.

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13k views

### PCA and Correspondence analysis in their relation to Biplot

Biplot is often used to display results of principal component analysis (and of related techniques). It is a dual or overlay scatterplot showing component loadings and component scores simultaneously. ...
11k views

### Visualizing a million, PCA edition

Is it possible to visualize the output of Principal Component Analysis in ways that give more insight than just summary tables? Is it possible to do it when the number of observations is large, say ~...
78k views

### Interpretation of biplots in principal components analysis

I came across this nice tutorial: A Handbook of Statistical Analyses Using R. Chapter 13. Principal Component Analysis: The Olympic Heptathlon on how to do PCA in R language. I don't understand the ...
15k views

### Interpreting 2D correspondence analysis plots

I've been searching the internet far and wide... I have yet to find a really good overview of how to interpret 2D correspondence analysis plots. Could someone offer some advice on interpreting the ...
9k views

### Positioning the arrows on a PCA biplot

I am looking to implement a biplot for principal component analysis (PCA) in JavaScript. My question is, how do I determine the coordinates of the arrows from the $U,V,D$ output of the singular vector ...
13k views

### What are the four axes on PCA biplot?

When you construct a biplot for a PCA analysis, you have principal component PC1 scores on the x-axis and PC2 scores on the y-axis. But what are the other two axes to the right and the top of the ...
14k views

### What is the proper association measure of a variable with a PCA component (on a biplot / loading plot)?

I am using FactoMineR to reduce my data set of measurements to the latent variables. The variable map above is clear for me to interpret, but I am confused when ...
19k views

### What do the arrows in a PCA biplot mean?

Consider the following PCA biplot: ...
9k views

### Arrows of underlying variables in PCA biplot in R

At the risk of making the question software-specific, and with the excuse of its ubiquity and idiosyncrasies, I want to ask about the function biplot() in R, and, ...
21k views

One common thing to do when doing Principal Component Analysis (PCA) is to plot two loadings against each other to investigate the relationships between the variables. In the paper accompanying the ...
4k views

### How to interpret this PCA biplot coming from a survey of what areas people are interested in?

Background: I asked hundreds of participants in my survey how much they are interested in selected areas (by five point Likert scales with 1 indicating "not interested" and 5 indicating "interested"). ...
4k views

### Data space, variable space, observation space, model space (e.g. in linear regression)

Suppose we have the data matrix $\mathbf{X}$, which is $n$-by-$p$, and the label vector $Y$, which is $n$-by-one. Here, each row of the matrix is an observation, and each column corresponds to a ...
19k views

### Can the scaling values in a linear discriminant analysis (LDA) be used to plot explanatory variables on the linear discriminants?

Using a biplot of values obtained through principal component analysis, it is possible to explore the explanatory variables that make up each principle component. Is this also possible with Linear ...
1k views

### Variable ordering using PCA

I've downloaded a script to draw a correlation matrix using colored circles. This script allows to order variables using PCA, but I'm not sure how it works. The code responsible for ordering is below: ...
1k views

### Interpreting 2D correspondence analysis plots (Part II)

I'd like to ensure that I understand the process correctly. This is a follow-up question to Interpreting 2D correspondence analysis plots ...
389 views

### What, if any, dissimilarity is preserved in partial least squares (PLS)?

When we perform a principal components analysis (PCA) on a multivariate data set we are interested in finding orthogonal components that explain maximal variance in the data set. We can form a biplot ...
900 views

### Interpreting overlapping arrows on a PCA biplot: does it mean that the variables are redundant?

I'm new in principal component analysis (PCA) and I don't really understand the biplot representation of its results, so I would really appreciate some guidance. Having the example of the illustration ...
2k views

### Interpretation of biplot in PCA

Blue points all appear in the lower right-hand quadrant in the plane formed by the first two principal components. Is it a good interpretation of the biplot (right panel) to say that blue points are ...
7k views

### What are the units in this PCA biplot? [duplicate]

This is a plot of my data These are the values: ...
7k views

### Interpretation of PCA biplot?

I just ran my first ever PCA, so please excuse any naivety on my part. As input, I used five years worth of the following: S&P/ASX 200 A-REIT S&P/ASX 200 Consumer Discretionary S&P/ASX ...
1k views

### When to use distance biplot vs. correlation biplot in PCA

I wonder what could be good examples of using scaling 1 and 2 for a principal component analysis biplot. By examples, I mean ecological examples or applied examples of the PCA scaling so that one can ...
456 views

### Biplots: Adding supplementry points to a biplot which only use a subset of the variables

I have a matrix X where the rows denote the cases and the columns the variables. I use a standard row-metric preserving biplot in order to represent the cases in a subspace. If I wanted to add a ...
84 views

### How to analyze this biplot of PCA?

I have dones a PCA analysis about measurement of a fish morphometric between female and male. After the PCA result came out with biplot graph, I was a little bit confused to interpret this data. It ...
3k views

### How to interpret ggbiplot() visualization of PCA in R? [duplicate]

To apply and visualize PCA in R often ggbiplot() is used. What is the meaning of this plot ? Why it is useful for PCA ? We can consider this example: https://tgmstat.wordpress.com/2013/11/28/...
3k views

### Difference beween supplementary and active variables in PCA - Interpretation on obsevations?

I would like to introduce two supplementary variables into a PCA I'm conducting on a set of data measuring concentration in different material phases. However I'm unclear as to how to interpret the ...
848 views

### Linear Discriminant Analysis biplot [closed]

I am not sure about plotting a biplot for LDA. Suppose I have a 3 feature data set with 3 classes. Then, I perform LDA to reduce the dimensionality to 2. How can I create a biplot for the LDA? My ...
77 views

### When doing PCA, is it possible or correct to find the correlation between variables and the first two components combined?

So I saw a correlation matrix between variables and components like below: ...
14k views

### How to interpret this PCA biplot?

I am approaching PCA analysis for the first time, and have difficulties on interpreting the results. This is my biplot (produced by Matlab's functions pca and ...
2k views

### Varying lengths of eigenvectors on a PCA biplot [duplicate]

I'm conducting a PCA in Matlab on standardized variables. My goal is to interpret angles = loadings, correlations bw. variables and PC-axis directions = vectors point to the direction of the ...
220 views

### Understanding biplot for compositional data

Say in the biplot of some compositional data, I discovered that the links $\vec{AB}$ and $\vec{CD}$ intersect at roughly 90 degrees. So I can say that $\log {A\over B}$ and $\log{C\over D}$ are ...
333 views

### Interpreting a PCA Biplot of a time series?

I had a question in regards to PCA with times series data, and specifically how to possibly interpret it. Normally, PCA is used by other software that I use in relation to de-noising a data set by ...
439 views

### Interpreting negative coordinates and origin in 2D correspondence analysis plot [duplicate]

Why are there negative values in the range of the plot? How is the center of the plot (i.e., the $0.0$ point) found? How did the black-brown points end up in the third quadrant of the plot? Why ...
1k views

I am trying to make a reasonable looking PCA analysis, where not only data are projected in two axis, but also the loadings of the data are projected on top of the data. Similar to the following ...
523 views

I'm running a multiple correspondence analysis in R using the FactoMineR package: ...
177 views

### I want to run a same result of biplot in R

There is a software called Brandmap$^1$ which can return a biplot from a matrix. I am trying to run the same result in R but the coordinates are not the same. First I input a simple matrix into the ...
904 views

### Angles between variables on a PCA biplot and correlations between the variables

A friend or mine has performed a PCA and he asked me for help about interpretating a biplot. In that biplot I found that the vector representing a variable, say A, forms a very wide angle, perhaps ...
1k views

I was investigating the interpretation of a biplot and meaning of loadings/scores in PCA in this question: What are the principal components scores? According to the author of the first answer the ...
553 views

### PCA - more than 2 principal components for >80% variance

I have analyzed some datasets using prcomp and some of my data is nice and amenable to PCA. But the summary of one set is showing that at least 6 components are needed to cover 80% of the variance. I'...
265 views

### PCA figure formatting options in R

I've completed PCA analysis, in R with VEGAN package, of some ecological data on tree health. There are 80 trees total (so, 80 'sites') divided into four treatment categories. I've got the data ...
123 views

### Is a Biplot suitable ? Domestic Violence VS Non-Violence data

I have a small data set that consists solely of counts. I have several variables. For example State, for each state (Mexican States), for example, Tamauplipas I have the counts of domestic violence ...
20 views

In the context of PCA, is there any reason why the scores and loadings are put into a single plot, the biplot? Do they interact somehow or it is just a preference of just 1 plot over 2 plots?
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### How do I interpret this PCA plot made in R? [duplicate]

I am very new to PCA, and I understand that principal components 1 and 2 account for most of the variability in my data, but how can I make statements about my variables and their influence on each ...
198 views

### PCA and visualization using biplots on data with mixed types

I have a dataset of dimensions 1500x200 where the predictors are both quantitative (discrete and continuous), as well as qualitative (categorical and ordinal) and the dependent variable is continuous. ...
170 views

I am trying to do a Canonical correspondence analysis (CCA) using the community data and chemical data. I have my family level taxonomic data as community data. In chemical data I have 18 variables: ...