ecdfRep.py

# Copyright (c) 2015, Nils Hammerla
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
#    list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright notice,
#    this list of conditions and the following disclaimer in the documentation
#    and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
# ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
# (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
from __future__ import print_function
import numpy as np

def ecdfRep(data, components):
    #
    #   rep = ecdfRep(data, components)
    #
    #   Estimate ecdf-representation according to 
    #     Hammerla, Nils Y., et al. "On preserving statistical characteristics of 
    #     accelerometry data using their empirical cumulative distribution." 
    #     ISWC. ACM, 2013.
    #
    #   Input: 
    #       data        Nxd     Input data (rows = samples).
    #       components  int     Number of components to extract per axis.
    #
    #   Output:
    #       rep         Mx1     Data representation with M = d*components+d
    #                           elements.
    #
    #   Nils Hammerla '15
    #
    m = data.mean(0)
    data = np.sort(data, axis=0)
    data = data[np.int32(np.around(np.linspace(0,data.shape[0]-1,num=components))),:]
    data = data.flatten(1)
    return np.hstack((data, m))

if __name__ == '__main__':
    a = np.random.randn(100,3)
    e1 = ecdfRep(a,5)
    print (e1)
    print ("all done")