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Cosine Similarity: Word Embeddings
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Expression 9: "u" Subscript, 11 , Baseline equals 1
u
1
1
=
1
negative 10
−
1
0
10
1
0
9
Expression 10: "u" Subscript, 12 , Baseline equals 2
u
1
2
=
2
negative 10
−
1
0
10
1
0
10
Expression 11: "v" Subscript, 11 , Baseline equals negative 1
v
1
1
=
−
1
negative 10
−
1
0
10
1
0
11
Expression 12: "v" Subscript, 12 , Baseline equals 0.5
v
1
2
=
0
.
5
negative 10
−
1
0
10
1
0
12
Expression 13: "v" Subscript, 21 , Baseline equals 1
v
2
1
=
1
negative 10
−
1
0
10
1
0
13
Expression 14: "v" Subscript, 22 , Baseline equals 1
v
2
2
=
1
negative 10
−
1
0
10
1
0
14
Expression 15: left parenthesis, "t" "v" Subscript, 11 , Baseline , "t" "v" Subscript, 12 , Baseline , right parenthesis
t
v
1
1
,
t
v
1
2
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
1
1
domain t Maximum:
15
Expression 16: left parenthesis, "t" "v" Subscript, 21 , Baseline , "t" "v" Subscript, 22 , Baseline , right parenthesis
t
v
2
1
,
t
v
2
2
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
1
1
domain t Maximum:
16
Expression 17: left parenthesis, "t" "u" Subscript, 11 , Baseline , "t" "u" Subscript, 12 , Baseline , right parenthesis
t
u
1
1
,
t
u
1
2
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
1
1
domain t Maximum:
17
Expression 18:
18
19
powered by
powered by
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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