# K-Means distribuído sobre dados binários comprimidos

2017 Feb 05
E quem disse que o K-Means estava morto hein?

**Distributed K-means over Compressed Binary Data**

**Abstract**—We consider a network of binary-valued sensors with a fusion center. The fusion center has to perform K-means clustering on the binary data transmitted by the sensors. In order to reduce the amount of data transmitted within the network, the sensors compress their data with a source coding scheme based on LDPC codes. We propose to apply the K-means algorithm directly over the compressed data without reconstructing the original sensors measurements, in order to avoid potentially complex decoding operations. We provide approximated expressions of the error probabilities of the K-means steps in the compressed domain. From these expressions, we show that applying the Kmeans algorithm in the compressed domain enables to recover the clusters of the original domain. Monte Carlo simulations illustrate the accuracy of the obtained approximated error probabilities, and show that the coding rate needed to perform K-means clustering in the compressed domain is lower than the rate needed to reconstruct all the measurements.

**Conclusion**: In this paper, we considered a network of sensors which transmit their compressed binary measurements to a fusion center. We proposed to apply the K-means algorithm directly over the compressed data, without reconstructing the sensor measurements. From a theoretical analysis and Monte Carlo simulations, we showed the efficiency of applying K-means in the compressed domain. We also showed that the rate needed to perform K-means on the compressed vectors is lower than the rate needed to reconstruct all the measurements.