Relational Data - Functions - Distance Functions

From FojiSoft Docs

L1Norm

Calculates the sum of absolute values of a vector.

Syntax 

L1Norm(vector)

Alias: normL1.

Arguments

Returned value

Examples

Query: 

SELECT L1Norm((1, 2));

Result: 

┌─L1Norm((1, 2))─┐
│              3 │
└────────────────┘

L2Norm

Calculates the square root of the sum of the squares of the vector values.

Syntax 

L2Norm(vector)

Alias: normL2.

Arguments

Returned value

Example

Query: 

SELECT L2Norm((1, 2));

Result: 

┌───L2Norm((1, 2))─┐
│ 2.23606797749979 │
└──────────────────┘

L2SquaredNorm

Calculates the square root of the sum of the squares of the vector values (the L2Norm) squared.

Syntax 

L2SquaredNorm(vector)

Alias: normL2Squared.

  • Arguments

Returned value

Example

Query: 

SELECT L2SquaredNorm((1, 2));

Result: 

┌─L2SquaredNorm((1, 2))─┐
│                     5 │
└───────────────────────┘

LinfNorm

Calculates the maximum of absolute values of a vector.

Syntax 

LinfNorm(vector)

Alias: normLinf.

Arguments

Returned value

  • Linf-norm or the maximum absolute value. Float.

Example

Query: 

SELECT LinfNorm((1, -2));

Result: 

┌─LinfNorm((1, -2))─┐
│                 2 │
└───────────────────┘

LpNorm

Calculates the root of p-th power of the sum of the absolute values of a vector in the power of p.

Syntax 

LpNorm(vector, p)

Alias: normLp.

Arguments

  • vector — Tuple or Array.
  • p — The power. Possible values: real number in [1; inf). UInt or Float.

Returned value

Example

Query: 

SELECT LpNorm((1, -2), 2);

Result: 

┌─LpNorm((1, -2), 2)─┐
│   2.23606797749979 │
└────────────────────┘

L1Distance

Calculates the distance between two points (the values of the vectors are the coordinates) in L1 space (1-norm (taxicab geometry distance)).

Syntax 

L1Distance(vector1, vector2)

Alias: distanceL1.

Arguments

Returned value

Example

Query: 

SELECT L1Distance((1, 2), (2, 3));

Result: 

┌─L1Distance((1, 2), (2, 3))─┐
│                          2 │
└────────────────────────────┘

L2Distance

Calculates the distance between two points (the values of the vectors are the coordinates) in Euclidean space (Euclidean distance).

Syntax 

L2Distance(vector1, vector2)

Alias: distanceL2.

Arguments

Returned value

Example

Query: 

SELECT L2Distance((1, 2), (2, 3));

Result: 

┌─L2Distance((1, 2), (2, 3))─┐
│         1.4142135623730951 │
└────────────────────────────┘

L2SquaredDistance

Calculates the sum of the squares of the difference between the corresponding elements of two vectors.

Syntax 

L2SquaredDistance(vector1, vector2)

Alias: distanceL2Squared.

Arguments

Returned value

  • Sum of the squares of the difference between the corresponding elements of two vectors. Float.

Example

Query: 

SELECT L2SquaredDistance([1, 2, 3], [0, 0, 0])

Result: 

┌─L2SquaredDistance([1, 2, 3], [0, 0, 0])─┐
│                                      14 │
└─────────────────────────────────────────┘

LinfDistance

Calculates the distance between two points (the values of the vectors are the coordinates) in L_{inf} space (maximum norm).

Syntax 

LinfDistance(vector1, vector2)

Alias: distanceLinf.

Arguments

Returned value

  • Infinity-norm distance. Float.

Example

Query: 

SELECT LinfDistance((1, 2), (2, 3));

Result: 

┌─LinfDistance((1, 2), (2, 3))─┐
│                            1 │
└──────────────────────────────┘

LpDistance

Calculates the distance between two points (the values of the vectors are the coordinates) in Lp space (p-norm distance).

Syntax 

LpDistance(vector1, vector2, p)

Alias: distanceLp.

Arguments

  • vector1 — First vector. Tuple or Array.
  • vector2 — Second vector. Tuple or Array.
  • p — The power. Possible values: real number from [1; inf). UInt or Float.

Returned value

Example

Query: 

SELECT LpDistance((1, 2), (2, 3), 3);

Result: 

┌─LpDistance((1, 2), (2, 3), 3)─┐
│            1.2599210498948732 │
└───────────────────────────────┘

L1Normalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in L1 space (taxicab geometry).

Syntax 

L1Normalize(tuple)

Alias: normalizeL1.

Arguments

Returned value

Example

Query: 

SELECT L1Normalize((1, 2));

Result: 

┌─L1Normalize((1, 2))─────────────────────┐
│ (0.3333333333333333,0.6666666666666666) │
└─────────────────────────────────────────┘

L2Normalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in Euclidean space (using Euclidean distance).

Syntax 

L2Normalize(tuple)

Alias: normalizeL1.

Arguments

Returned value

Example

Query: 

SELECT L2Normalize((3, 4));

Result: 

┌─L2Normalize((3, 4))─┐
│ (0.6,0.8)           │
└─────────────────────┘

LinfNormalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in L_{inf} space (using maximum norm).

Syntax 

LinfNormalize(tuple)

Alias: normalizeLinf.

Arguments

Returned value

Example

Query: 

SELECT LinfNormalize((3, 4));

Result: 

┌─LinfNormalize((3, 4))─┐
│ (0.75,1)              │
└───────────────────────┘

LpNormalize

Calculates the unit vector of a given vector (the values of the tuple are the coordinates) in Lp space (using p-norm).

Syntax 

LpNormalize(tuple, p)

Alias: normalizeLp.

Arguments

  • tuple — Tuple.
  • p — The power. Possible values: any number from [1;inf). UInt or Float.

Returned value

Example

Query: 

SELECT LpNormalize((3, 4),5);

Result: 

┌─LpNormalize((3, 4), 5)──────────────────┐
│ (0.7187302630182624,0.9583070173576831) │
└─────────────────────────────────────────┘

cosineDistance

Calculates the cosine distance between two vectors (the values of the tuples are the coordinates). The smaller the returned value is, the more similar are the vectors.

Syntax 

cosineDistance(vector1, vector2)

Arguments

Returned value

  • Cosine of the angle between two vectors subtracted from one. Float.

Examples

Query: 

SELECT cosineDistance((1, 2), (2, 3));

Result: 

┌─cosineDistance((1, 2), (2, 3))─┐
│           0.007722123286332261 │
└────────────────────────────────┘
Retrieved from "https://docs.foji.io/index.php?title=Relational_Data_-_Functions_-_Distance_Functions&oldid=2240"