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ATTENTION. The project has been renamed and moved. Checkout Hera under https://bitbucket.org/grey_narn/hera The HEAD of this repository will be empty. The history is still available. Sorry for the inconvenience. This is a program for computing Wasserstein distances between persistence diagrams using the geometric version of auction algorithm. Accompanying paper: M. Kerber, D. Morozov, A. Nigmetov. Geometry Helps To Compare Persistence Diagrams (ALENEX 2016, http://www.geometrie.tugraz.at/nigmetov/geom_dist.pdf) Bug reports can be sent to "nigmetov EMAIL SIGN tugraz DOT at". Wasserstein distance $W_{q, p}(X, Y)$ between two persistent diagrams is the minimum over all perfect matchings between $X$ and $Y$ ( $y(x)$ is the point of $Y$ matched to $x \in X$ ) of the following expression: $ ( \sum \| x - y(x) \|_p ^ { q } ) ^ { 1 / q} $ # Dependencies Requires boost 1.58 or higher. Your compiler must support C++11. # Usage: To use a standalone command-line utility wasserstein_dist: wasserstein_dist file1 file2 [wasserstein degree] [relative error] [internal norm]. Parameter wasserstein degree corresponds to $q$, when it tends to infinity, Wasserstein distance tends to the bottleneck distance. Parameter internal_p corresponds to p. Default values: wasserstein_degree = 1.0, relative_error = 0.01, internal_p = infinity. Valid values: wasserstein_degree must be in $[1.0, \infinity)$, relative_error must be positive, internal_p must be in $[1.0, \infinity]$ (to explicitly set internal_p to $\infinity$, supply inf).By default wasserstein degree is 1.0, relative error is 0.01, internal norm is l_infinity. file1 and file2 must contain persistence diagrams in plain text format (one point per line, empty lines are ignored, comments can be made with #): # this is how your input can look like x_1 y_1 # two real numbers per line ... # empty lines or comments are ignored x_n y_n To use from your code: #include "wasserstein.h" // All classes and functions are in geom_ws namespace std::vector<std::pair<double, double>> diagram1, diagram2; // any container class that supports range-for loops will do. // A pair represents a single point, // first component = x-coordinate, // second component = y-coordinate. // ... // load your diagrams into diagram1, diagram2 (off-diagonal points). // You can use function readDiagramPointSet: geom_ws::readDiagramPointSet("diagram1.txt", diagram1); geom_ws::readDiagramPointSet("diagram2.txt", diagram1); // ... // to get the distance: double wsDist = geom_ws::wassersteinDist(diagram1, diagram2, q, delta, p); // q is wasserstein degree, delta is relative error, // p is the internal norm in Wasserstein distance, defaults to infinity Necessary projections (diagonal points) will be added in the wassersteinDist function. See also code in wasserstein/example/wasserstein_dist.cpp. # License See wasserstein/license.txt # Building CMakeLists.txt in the root directory can be used to make the library (contained in wasserstein/src/ directory) and the command-line utility (in wasserstein/example/ directory) to compute the distance between two diagrams in txt files. On Linux/Mac: mkdir build cd build cmake .. make On Windows (checked with Visual Studio 2015, Community version) use cmake-gui to create the solution in build directory and build it with VS.