# Tag Info

Accepted

### Should data be centered+scaled before applying t-SNE?

Centering shouldn't matter since the algorithm only operates on distances between points, however rescaling is necessary if you want the different dimensions to be treated with equal importance, since ...
• 2,049
Accepted

### Curse of dimensionality- does cosine similarity work better and if so, why?

Contrary to various unproven claims, cosine cannot be significantly better. It is easy to see that Cosine is essentially the same as Euclidean on normalized data. The normalization takes away one ...
Accepted

### Mathematical demonstration of the distance concentration in high dimensions

There is a simple mathematical thought experiment that sheds light on this phenomenon, although it might not seem immediately applicable. I will therefore describe this experiment briefly and follow ...
• 327k
Accepted

### How do I know my k-means clustering algorithm is suffering from the curse of dimensionality?

It helps to think about what The Curse of Dimensionality is. There are several very good threads on CV that are worth reading. Here is a place to start: Explain “Curse of dimensionality” to a child....

• 127k
Accepted

### Why does the condition number of the covariance matrix explode as number of variables increases?

Explaining this in the comments was a little limiting, apologies: Assuming centered data matrix $X$, then your covariance matrix $M = X^T X$. This will have high condition number if the range of ...

### Does "curse of dimensionality" really exist in real data?

Curse of dimensionality in machine learning is more often the problem of exploding empty space between the few data points that you have. Low manifold data can make it even worse. Here is an example ...
• 2,071
Accepted

### Different definitions of "curse of dimensionality"

It is not a mathematical object like a derivative that needs to be defined formally without any ambiguity. It is an umbrella term for those two issues encountered when using high dimensional data. The ...
• 3,189
Accepted

### PCA too slow when both n,p are large: Alternatives?

Question 1: Let's say you have observed a data matrix $X \in \mathbb R^{n \times p}$. From this you can compute the eigendecomposition $X^T X = Q \Lambda Q^T$. The question now is: if we get new data ...
• 20.4k