Privacy-Preserving Clustering on Time-Series Data Using Fourier Magnitudes
Hea-Suk Kim, Yang‐Sae Moon · 2008
In this paper we propose Fourier magnitudes based privacy preserving clustering on time-series data. The previous privacy-preserving method, called DFT coefficient method, has a critical problem in privacy-preservation itself since the original time-series data may be reconstructed from privacy-preserved data. In contrast, the proposed DFT magnitude method has an excellent characteristic that reconstructing the original data is almost impossible since it uses only DFT magnitudes except DFT phases. In this paper, we first explain why the reconstruction is easy in the DFT coefficient method, and why it is difficult in the DFT magnitude method. We then propose a notion of distance-order preservation which can be used both in estimating clustering accuracy and in selecting DFT magnitudes. Degree of distance-order preservation means how many time-series preserve their relative distance orders before and after privacy-preserving. Using this degree of distance-order preservation we present greedy strategies for selecting magnitudes in the DFT magnitude method. That is, those greedy strategies select DFT magnitudes to maximize the degree of distance-order preservation, and eventually we can achieve the relatively high clustering accuracy in the DFT magnitude method. Finally, we empirically show that the degree of distance-order preservation is an excellent measure that well reflects the clustering accuracy. In addition, experimental results show that our greedy strategies of the DFT magnitude method are comparable with the DFT coefficient method in the clustering accuracy. These results indicate that, compared with the DFT coefficient method, our DFT magnitude method provides the excellent degree of privacy-preservation as well as the comparable clustering accuracy.