dlib C++ Library - lda_abstract.h

    // Copyright (C) 2014  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #undef DLIB_LDA_ABSTRACT_Hh_
    #ifdef DLIB_LDA_ABSTRACT_Hh_

    #include <map>
    #include "../matrix.h"
    #include <vector>

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        template <
            typename T
            >
        void compute_lda_transform (
            matrix<T>& X,
            matrix<T,0,1>& M,
            const std::vector<unsigned long>& row_labels,
            unsigned long lda_dims = 500,
            unsigned long extra_pca_dims = 200
        );
        /*!
            requires
                - X.size() != 0
                - row_labels.size() == X.nr()
                - The number of distinct values in row_labels > 1
                - lda_dims != 0
            ensures
                - We interpret X as a collection X.nr() of input vectors, where each row of X
                  is one of the vectors.
                - We interpret row_labels[i] as the label of the vector rowm(X,i).
                - This function performs the dimensionality reducing version of linear
                  discriminant analysis.  That is, you give it a set of labeled vectors and it
                  returns a linear transform that maps the input vectors into a new space that
                  is good for distinguishing between the different classes.  In particular,
                  this function finds matrices Z and M such that:
                    - Given an input vector x, Z*x-M, is the transformed version of x.  That is,
                      Z*x-M maps x into a space where x vectors that share the same class label
                      are near each other.
                    - Z*x-M results in the transformed vectors having zero expected mean.
                    - Z.nr() <= lda_dims
                      (it might be less than lda_dims if there are not enough distinct class
                      labels to support lda_dims dimensions).
                    - Z.nc() == X.nc()
                    - We overwrite the input matrix X and store Z in it.  Therefore, the
                      outputs of this function are in X and M.
                - In order to deal with very high dimensional inputs, we perform PCA internally
                  to map the input vectors into a space of at most lda_dims+extra_pca_dims
                  prior to performing LDA.
        !*/

    // ----------------------------------------------------------------------------------------

        std::pair<double,double> equal_error_rate (
            const std::vector<double>& low_vals,
            const std::vector<double>& high_vals
        );
        /*!
            ensures
                - This function finds a threshold T that best separates the elements of
                  low_vals from high_vals by selecting the threshold with equal error rate.  In
                  particular, we try to pick a threshold T such that:
                    - for all valid i:
                        - high_vals[i] >= T
                    - for all valid i:
                        - low_vals[i] < T
                  Where the best T is determined such that the fraction of low_vals >= T is the
                  same as the fraction of high_vals < T.
                - Let ERR == the equal error rate.  I.e. the fraction of times low_vals >= T
                  and high_vals < T.  Note that 0 <= ERR <= 1.
                - returns make_pair(ERR,T)
        !*/

    // ----------------------------------------------------------------------------------------

        struct roc_point
        {
            double true_positive_rate;
            double false_positive_rate;
            double detection_threshold;
        };

        std::vector<roc_point> compute_roc_curve (
            const std::vector<double>& true_detections,
            const std::vector<double>& false_detections
        );
        /*!
            requires
                - true_detections.size() != 0
                - false_detections.size() != 0
            ensures
                - This function computes the ROC curve (receiver operating characteristic)
                  curve of the given data.  Therefore, we interpret true_detections as
                  containing detection scores for a bunch of true detections and
                  false_detections as detection scores from a bunch of false detections.  A
                  perfect detector would always give higher scores to true detections than to
                  false detections, resulting in a true positive rate of 1 and a false positive
                  rate of 0, for some appropriate detection threshold.
                - Returns an array, ROC, such that:
                    - ROC.size() == true_detections.size()+false_detections.size()
                    - for all valid i:
                        - If you were to accept all detections with a score >= ROC[i].detection_threshold
                          then you would obtain a true positive rate of ROC[i].true_positive_rate and a
                          false positive rate of ROC[i].false_positive_rate.
                    - ROC is ordered such that low detection rates come first.  That is, the
                      curve is swept from a high detection threshold to a low threshold.
        !*/

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_LDA_ABSTRACT_Hh_