BallMapper              Create vertices and edges (with additional
                        properties) of a Ball Mapper graph
                        representation of the input data. Please be
                        aware that the program will not perform any
                        normalization on the data. As with cluster
                        analysis we recommend that you consider whether
                        to normalize the data prior to running the
                        function.
ColorIgraphPlot         Produce a static color visualization of the
                        Ball Mapper graph. It is based on the output
                        from BallMapper function.
GrayscaleIgraphPlot     Produce a static grayscale visualization of the
                        Ball Mapper graph. It is based on the output
                        from the BallMapper function.
colorByAllVariables     Produce a collection of png files with mapper
                        graphs colored by following coordinates (so
                        that the number of files is the same as the
                        number of coordinates).
colorByAverageValueOfOtherVariable
                        Produce a new coloring vector being an average
                        of values of given function at points covererd
                        by each vertex of Ball Mapper graph.
colorByStDevValueOfOtherVariable
                        Produce a new coloring vector being a standard
                        deviation of values of given function at points
                        covererd by each vertex of Ball Mapper graph.
color_by_distance_to_reference_points
                        This function will provide a new coloring which
                        is the minimal and average distance of points
                        in the point cloud to the referece points. The
                        output from this procedure can be used as an
                        alternative coloring in BallMapper.
coloredDynamicNetwork   This procedure produces a dynamic graph with
                        colors. It allows zoom-in operation and
                        displays information about vertices when they
                        are clicked upon.
coordinates_of_points_in_subcollection
                        This is an auxiliery function. It take the
                        coordinates of points, ids of subset of points,
                        and number of coordinate, and return a sorted
                        vector of the given coodrinate in the
                        considered points. For instance, given the
                        collection of points: 1 2 3 4 5 6 7 8 9 and
                        which_subset = 2,3 and number_of_coordinate = 2
                        the procedure below will return the vector
                        [2,5,8].
find_dominant_difference_using_averages
                        This procedure take two subset of points (that
                        come from the vertices of Ball Mapper) and
                        return the coordinates on which the averages of
                        those two collections differs most. To ballance
                        the effect of potentially different orders of
                        magnitude of data in column, we divide the
                        difference in means by the mean of the whole
                        column.
find_dominant_difference_using_averages_normalized_by_sd
                        This procedure take two subset of points (that
                        come from the vertices of Ball Mapper) and
                        return the coordinates on which the averages of
                        those two collections differs most. To ballance
                        the effect of potentially different orders of
                        magnitude of data in column, we divide the
                        difference in means by the standard deviation
                        of the whole column.
normalize_to_average_0_stdev_1
                        This function normalize each column (variable)
                        of the input dataset so that the the average of
                        the normalized column is 0 and its standard
                        deviation is 1.
normalize_to_min_0_max_1
                        This function normalize each column (variable)
                        of the input dataset so that the maximum is
                        mapped to one, minimum to zero, and the
                        intermediate values linearly to the appropriate
                        points in the interval (0,1).
pointToBallList         Produce a two column list. The first column
                        contain the number of point (possibly with
                        repetitions), the second one contains the
                        number of landmark points that cover it. For
                        example, let us assume that point 1 is covered
                        by landmark 1 and 2, and point 2 is covered by
                        the landmark 2. In this case the obtained list
                        is of a form: 1 1 1 2 2 2 This list can be used
                        for a further analysis of various parts of Ball
                        Mapper graph.
points_covered_by_landmarks
                        This function returns a list of points covered
                        by the given collection of landmarks.
readBallMapperGraphFromFile
                        This procedure read the BallMapper object from
                        file. The parameter of the file is filename. We
                        assume that files: filename_vertices
                        filename_edges filename_edges_strength
                        filename_points_covered_by_landmarks
                        filename_landmarks filename_coloring
simpleDynamicNetwork    This is a simple example of dynamic
                        visualization using networkD3 library. This
                        version do not implement coloring of vertices,
                        just give a general overview of the edges.
storeBallMapperGraphInFile
                        This procedure store the Ball Mapper graph in a
                        file in the following format:
