# What is the relationship of the cosine measure to correlation?

Table of Contents

- 1 What is the relationship of the cosine measure to correlation?
- 2 What is the relationship between Pearson correlation and cosine similarity?
- 3 Are sine and cosine correlated?
- 4 What is the difference between cosine similarity and cosine distance?
- 5 How do you find cross-correlation between two signals?
- 6 How does Matlab calculate cross-correlation?
- 7 Why use cosine similarity instead of Euclidean distance?
- 8 Is cosine similarity symmetric?
- 9 How does the cosine similarity function work?
- 10 What is the difference between correlation and dependence in statistics?

## What is the relationship of the cosine measure to correlation?

Cosine similarity has an interpretation as the cosine of the angle between the two vectors; you can illustrate this for vectors in R2 (e.g. here). Correlation is the cosine similarity between centered versions of x and y, again bounded between -1 and 1.

### What is the relationship between Pearson correlation and cosine similarity?

The two quantities represent two different physical entities. The cosine similarity computes the similarity between two samples, whereas the Pearson correlation coefficient computes the correlation between two jointly distributed random variables.

Correlation of two sine waves For functions known at discrete points this would be a sum rather than an integral, but in this case we have continuous signals so we integrate. So our correlation is simply cos φ: the correlation of two out-of-phase sine waves is the cosine of their phase difference.

**What is the relationship between two correlated variables?**

Complete correlation between two variables is expressed by either + 1 or -1. When one variable increases as the other increases the correlation is positive; when one decreases as the other increases it is negative. Complete absence of correlation is represented by 0.

**Why is cosine similarity?**

Cosine similarity is a metric used to measure how similar the documents are irrespective of their size. The cosine similarity is advantageous because even if the two similar documents are far apart by the Euclidean distance (due to the size of the document), chances are they may still be oriented closer together.

## What is the difference between cosine similarity and cosine distance?

Usually, people use the cosine similarity as a similarity metric between vectors. Now, the distance can be defined as 1-cos_similarity. The intuition behind this is that if 2 vectors are perfectly the same then similarity is 1 (angle=0) and thus, distance is 0 (1-1=0).

### How do you find cross-correlation between two signals?

To detect a level of correlation between two signals we use cross-correlation. It is calculated simply by multiplying and summing two-time series together. In the following example, graphs A and B are cross-correlated but graph C is not correlated to either.

#### How does Matlab calculate cross-correlation?

r = xcorr( x , y ) returns the cross-correlation of two discrete-time sequences. Cross-correlation measures the similarity between a vector x and shifted (lagged) copies of a vector y as a function of the lag.

**Does correlation and dependence mean the same thing?**

In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence.

**Does correlation always signify causal relationship between two variables?**

A correlation only shows if there is a relationship between variables. Correlation does not always prove causation as a third variable may be involved.

## Why use cosine similarity instead of Euclidean distance?

### Is cosine similarity symmetric?

A simple enough similarity measure is the cosine similarity measure. It is used often in Information Retrieval and it works well. It is also quite simple: cos(v,w)=. Clearly, it is reflexive (cos(v,v)=1) and symmetric (cos(v,w)=cos(w,v)).

#### How does the cosine similarity function work?

The function measures how similar two vectors are and from vector geometry it turns out that where is the angle between and hence the term cosine similarity. Thus cosine similarity works because it basically is just a form of squared Euclidean dissimilarity (distance) function applied to normalized vectors.

**How do you find a correlation between two variables?**

A correlation exists between two variables when one of them is related to the other in some way. A scatterplot is the best place to start. A scatterplot (or scatter diagram) is a graph of the paired (x, y) sample data with a horizontal x-axis and a vertical y-axis.

**What does it mean when there is no correlation?**

This means the two variables moved either up or down in the same direction together. Negative correlation: A negative correlation is -1. This means the two variables moved in opposite directions. Zero or no correlation: A correlation of zero means there is no relationship between the two variables.

## What is the difference between correlation and dependence in statistics?

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though it commonly refers to the degree to which a pair of variables are linearly related.