# Tag Info

Accepted

### Is cosine similarity identical to l2-normalized euclidean distance?

For $\ell^2$-normalized vectors $\mathbf{x}, \mathbf{y}$, $$||\mathbf{x}||_2 = ||\mathbf{y}||_2 = 1,$$ we have that the squared Euclidean distance is proportional to the cosine distance, \begin{align} ...
• 5,832

### How I can convert distance (Euclidean) to similarity score

If $d(p_1,p_2)$ represents the euclidean distance from point $p_1$ to point $p_2$, $$\frac{1}{1 + d(p_1, p_2)}$$ is commonly used.
• 7,524
Accepted

• 22.6k

### Definition of normalized Euclidean distance

The normalized squared euclidean distance gives the squared distance between two vectors where there lengths have been scaled to have unit norm. This is helpful when the direction of the vector is ...
• 3,115
Accepted

### What is the inverse square of a distance (Euclidean)?

Imagine that we want to classify as red or blue the unknown gray point in the data cloud. Your algorithm is set up to measure ...
• 24.6k
Accepted

### K-means: Why minimizing WCSS is maximizing Distance between clusters?

K-means is all about the analysis-of-variance paradigm. ANOVA - both uni- and multivariate - is based on the fact that the sum of squared deviations about the grand centroid is comprised of such ...
• 53.3k
Accepted

### Efficient way to compute distances between centroids from distance matrix

Let the points be indexed $x_1, x_2, \ldots, x_n$, all of them in $\mathbb{R}^d$. Let $\mathcal{I}$ be the indexes for one cluster and $\mathcal{J}$ the indexes for another cluster. The centroids ...
• 297k
Accepted

### Variance and asymptotic normality of $\frac{1}{n-1}\sum_{i=1}^{n-1}(x_{i+1}-x_i)^2$, where $X \sim \mathcal{N}(0,1)$

TLDR; $s(z)$ is asymptotically normal, and its variance is $\frac {12} {n-1}$ according to CLT for Markov chains. It can be shown that the distribution is a special case of generalized $\chi^2$ ...
• 57.1k

### My neural network can't even learn Euclidean distance

The output seems to strongly suggest that one or more of your neurons goes dead (or perhaps the hyperplane of weights for two of your neurons have merged). You can see that with 3 Relu's, you get 3 ...
• 13.4k

### Expected magnitude of a vector from a multivariate normal

The answer by user3697176 gives all the needed information, but nonetheless, here is a slightly different view of the problem. If $X_i \sim N(0,\sigma^2)$, then $Y = \sum_{i=1}^n X_i^2$ has a Gamma ...
• 42.6k