2k views

How does Principal Coordinate Analysis (PCoA) work, as compared to PCA? [duplicate]

I am familiar with PCA from Making sense of principal component analysis, eigenvectors & eigenvalues where you either normalize the data (to standard normal or ...
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647 views

When should you call it PCoA vs. PCA [duplicate]

I'm reviewing a paper. In it the authors use a genetic distance metric to created a distance matrix between subjects, then they run classic MDS on this distance matrix. Throughout the MS they call ...
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1 vote
57 views

Representing a distance matrix in the plane [duplicate]

I've worked with observations as vectors with both continuous and categorical variables. In both cases one can use dimensionality reduction techniques such as PCA (in the latter case through ...
20k views

How does Factor Analysis explain the covariance while PCA explains the variance?

Here is a quote from Bishop's "Pattern Recognition and Machine Learning" book, section 12.2.4 "Factor analysis": According to the highlighted part, factor analysis captures the covariance between ...
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16k views

Understanding distance correlation computations

As far as I understood, distance correlation is a robust and universal way to check if there is a relation between two numeric variables. For example, if we have a set of pairs of numbers: ...
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4k 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? ...
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19k views

PCA and exploratory Factor Analysis on the same dataset: differences and similarities; factor model vs PCA

I would like to know if it makes any logical sense to perform principal component analysis (PCA) and exploratory factor analysis (EFA) on the same data set. I have heard professionals expressly ...
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22k 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 ...
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7k 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 ...
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5k views

What is meant by PCA preserving only large pairwise distances?

I am currently reading up on t-SNE visualization technique and it was mentioned that one of the drawbacks of using principal component analysis (PCA) for visualizing high-dimensional data is that it ...
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10k views

Distances in PCA space [closed]

I'm working on a project involving PCA, and my knowledge up till now with this method is quite good. My work involves finding nearest neighbors (having the least Euclidean distance) to a particular ...
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7k views

Efficient way to compute distances between centroids from distance matrix

Let us have square symmetric matrix of squared euclidean distances $\bf D$ between $n$ points and vector lengthed $n$ indicating cluster or group membership ($k$ clusters) of the points; a cluster may ...
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4k views

Q-mode vs. R-mode PCA

I have some doubts on Q-mode and R-mode principal component analysis (PCA). I've read from different sources that: Q-mode PCA is equivalent to R-mode PCA of the transposed data matrix! Q-mode PCA (...
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2k views

What are shortcomings of PCA as a dimensionality reduction technique compared to t-SNE?

I have been reading and using tSNE which is able to preserve the neighbour around the a point in high dimension compared to PCA. For example I have these embeddings in 128 dimensional created by a ...
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