Cosine Distance Matrix¶

Given \(n\) feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots x_n = (x_{n1}, \ldots, x_{np})\) of dimension Lmath:p, the problem is to compute the symmetric \(n \times n\) matrix \(D_{\text{cos}} = (d_{ij})\) of distances between feature vectors, where

\[d_{ij} = 1 - \frac {\sum_{k=1}^{p} x_{ik} x_{jk}} {\sqrt{ \sum_{k=1}^{p} x_{ik}^2 } \sqrt{ \sum_{k=1}^{p} x_{jk}^2 }}\]

\[i = \overline{1, n}\]

\[j = \overline{1, n}\]

Batch Processing¶

Algorithm Input¶

The cosine distance matrix algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Algorithm Input for Cosine Distance Matrix (Batch Processing)¶
Input ID	Input
`data`	Pointer to the \(n \times p\) numeric table for which the distance is computed. The input can be an object of any class derived from `NumericTable`.

Algorithm Parameters¶

The cosine distance matrix algorithm has the following parameters:

Algorithm Parameters for Cosine Distance Matrix (Batch Processing)¶
Parameter	Default Value	Description
`algorithmFPType`	`float`	The floating-point type that the algorithm uses for intermediate computations. Can be `float` or `double`.
`method`	`defaultDense`	Performance-oriented computation method, the only method supported by the algorithm.

Algorithm Output¶

The cosine distance matrix algorithm calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Algorithm Output for Cosine Distance Matrix (Batch Processing)¶
Result ID	Result
`cosineDistance`	Pointer to the numeric table that represents the \(n \times n\) symmetric distance matrix \(D_\text{cos}\). By default, the result is an object of the `PackedSymmetricMatrix` class with the `lowerPackedSymmetricMatrix` layout. However, you can define the result as an object of any class derived from `NumericTable` except `PackedTriangularMatrix` and `CSRNumericTable`.

Examples¶

Batch Processing:

cos_dist_dense_batch.cpp

Performance Considerations¶

To get the best overall performance when computing the cosine distance matrix:

If input data is homogeneous, provide the input data and store results in homogeneous numeric tables of the same type as specified in the algorithmFPType class template parameter.
If input data is non-homogeneous, use AOS layout rather than SOA layout.

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

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