If \(\sum_{i=0}^{ \vert \mathbf{x} \vert } x_{i}^{2} = 1\), what can you say about \(\mathbf{x}\)? - Unit 4.2: Count-based vectors - Use this assignment in your class!

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Unit 4.2: Count-based vectors

What is meant if the cosine of two words is 1?

What's the cosine similarity between [-3, 3, 4] and [2, -5, -1]?

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Gus Hahn-PowellAPR 12, 2021, 2:11:33 AM

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When does

cos (a, a) = a \cdot b

When does

cos (a, a) = a \cdot b

## Euclidean distance Implement Euclidean distance using `numpy`:

d_{2} (a, b) = \sqrt{\sum_{i = 0}^{| a |} (a_{i} - b_{i})^{2}}

where

d_{2}

represents the Euclidean distance of vectors

a

and

b

## Dot product Implement the function `dot_product` using `numpy`. Your function should take two `np.ndarray`s representing

x

and

y

and return a single number.

What is

[3, 9, 1] \cdot [0, 3, - 4]

## Dot product Implement the function `dot_product` using `numpy`. Your function should take two `np.ndarray`s representing

x

and

y

and return a single number.

Given

a = [7, 2]

, what vector has the same direction, but 3 times the magnitude of

a

\sum_{i = 0}^{| x |} x_{i}^{2} = 1

, what can you say about

x

\sum_{i = 0}^{| x |} x_{i}^{2} = 1

, what can you say about

x

Complete the code to calculate the frequency of words that co-occur within a symmetric window (

k = 1

) for the given word.

When

k = 2

, what will be target word and context words in the

k

-window for the sentence "The Spanish galleon disappeared into the night"?

Provide symmetric

k

-windows of size

k = 1

k = 2

k = 3

, and

k = 4

for *Shakespeare* in the following sentence: >the greatest Shakespeare play is Macbeth

\sum_{i = 0}^{| x |} x_{i}^{2} = 1

, what can you say about

x

[0.40269101, 0.01537547, 0.01537547]

[1, .5, 0]

[0.3137279, 0.12549116, 0.94118371]

[0.44022545, 0.17609018, 0.44022545]

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