120k 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?
21k views

### Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?

For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
56k views

### How do I test a nonlinear association?

For plot 1, I can test the association between x and y by doing a simple correlation. For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test the ...
35k views

### k-means implementation with custom distance matrix in input

Can anyone point me out a k-means implementation (it would be better if in matlab) that can take the distance matrix in input? The standard matlab implementation needs the observation matrix in input ...
19k views

### Converting similarity matrix to (euclidean) distance matrix

In Random forest algorithm, Breiman (author) constructs similarity matrix as follows: Send all learning examples down each tree in the forest If two examples land in the same leaf increment ...
2k views

### Is there an intuitive characterization of distance correlation?

I've been staring at the wikipedia page for distance correlation where it seems to be characterized by how it can be calculated. While I could do the calculations I struggle to get what distance ...
5k views

### Sums-of-Squares (total, between, within): how to compute them from a Distance Matrix?

I am having trouble understanding the concept of Sum of Squares in the context of distance matrices (Studer et al. 2010). The Sum of Squares I am familiar with is the classical $SS$ from ANOVA, ...
2k views

### Cosine-Similarity vs non-linear measures

In NLP, people often use cosine similarity to measure how close two vector spaces are to each other. However, we know that cosine-similarity is the same thing as Pearson correlation, for centered ...
623 views

### Why is distance covariance defined squared, while covariance is not?

I am dealing in a data science project with correlation analyses using pearson and distance correlation. While trying to understand the differences between them, I learned about the differences by ...
695 views

### Obtain within-group Gram matrix out of distance matrix

Gram matrix Let $\bf X$ be a n x p dataset with columns (variables) centered. Then p x p $\bf X'X$ is the total scatter matrix ...
276 views

### What is the distance correlation for Anscombe’s quartet?

Is the newer descriptive statistic (distance correlation) able to resolve these troubling four datasets (Anscombe’s quartet)?
In the setup of classical MultiDimensional Scaling (MDS), assume that $D:=[d_{ij}]$ be an $n \times n$ distance matrix, i.e. $d(i,i)=0, d(i,j)=d(j,i) > 0 \forall i, j = 1 \dots n.$ Assume that: ...