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A. H. Knn and . Density-implementation,

?. , if the normalized matrix with the data ?? alpha: float, is the density of the neighborhood ?? distances: list of p lists of N lists of N floats, is the distances for each data, for each variable ?? neighbors: list of p lists of N lists of N integers, is the neighborhood for each data, for each variable ?? densities: list of N lists of p integers, is the densities of data for each variable ?? sumDensities: list of N integers, is the sum of densities for each data ?? max: integer, is the number of the denser data, i.e. the selected sample ?? variableNeighbors: list of N lists of p integers, is the neighborhood for each variable of the selected data ?? inter: list of integers, integer, is the number of data in the matrix ?? p: integer, is the number of variables in the matrix ?? inputData: list of N lists of p floats

?. ?-euclidean, Algorithm 10, returning the densities of data for each variable ?? sumDensity: function, Algorithm 11, returning the sum of densities for each data ?? maximum: integer, function, Algorithm 12, returning the number of the denser data, i.e. the selected sample ?? variableNeighborhood: function, Algorithm 13, returning the neighborhood for each variable of the selected data ?? intersection: function, Algorithm 14, returning the intersection of the neighborhood of the selected data ?? num: function, returns the number of the data ?? append: function, is a function appending an integer to a list distances ? euclidean(N, p, inputData) neighbors ? neighborhood(N, p, distances, alpha) densities ? density(N, p, neighbors) sumDensities ? sumDensity(N, p, densities) max ? maximum(N, sumDensities) variableNeighbors ? variableNeighborhood(N, p, max, neighbors) inter ? intersection(N, p, variableNeighbors) rpz.sample ? num, function, Algorithm 8, returning the distances for each data, for each variable ?? neighborhood: function, Algorithm 9, returning the neighborhood for each data, for each variable ?? density: function

, is the distances for each data, for each variable ?? neighbors: list of p lists of N lists of N integers, is the neighborhood for each data, for each variable ?? densities: list of N lists of p integers, is the densities of data for each variable ?? sumDensities: list of N integers, is the sum of densities for each data ?? max: integer, is the maximum value of the sums ?? i_max: integer, is the number of the denser data, i.e. the selected sample ?? variableNeighbors: list of N lists of p integers, is the neighborhood for each variable of the selected data ?? inter: list of integers, is the intersection of the neighborhood of the selected data ?? rpz: Sample_t structure, is the selected sample with its neighborhood ?? varChunk: integer, is the number of variables computed by the thread ?? dataChunk: integer, Require: threadNumber: integer, the number (starting by 0) of the thread executing the algorithm ?? N: integer, is the number of data in the matrix ?? p: integer, is the number of variables in the matrix ?? inputData: list of N lists of p floats, if the normalized matrix with the data ?? alpha: float, is the density of the neighborhood ?? distances: list of p lists of N lists of N floats