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Euclidean Distance
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The Euclidean distance for real valued features is the square root of the sum of squared disparity between the corresponding feature dimensions of two data points.

.. math::

    d({\bf x},{\bf x'})= \sqrt{\sum_{i=0}^{d}|{\bf x_i}-{\bf x'_i}|^2}

where :math:`\bf x` and :math:`\bf x'` are :math:`d` dimensional feature vectors.

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Example
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Imagine we have files with data. We create CDenseFeatures (here 64 bit floats aka RealFeatures) as

.. sgexample:: euclidean.sg:create_features

We create an instance of :sgclass:`CEuclideanDistance` by passing it :sgclass:`CDenseFeatures`.

.. sgexample:: euclidean.sg:create_instance

Distance matrix can be extracted as follows:

.. sgexample:: euclidean.sg:extract_distance

We can use the same instance with new :sgclass:`CDenseFeatures` to compute distance.

.. sgexample:: euclidean.sg:refresh_distance

If desired, squared distance can be extracted like:

.. sgexample:: euclidean.sg:extract_sq_distance

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References
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:wiki:`Euclidean_distance`

.. bibliography:: ../../references.bib
    :filter: docname in docnames