Ordered clustering: A way to simplify analysis of multichannel signals

Abstract

We describe here new possibilities offered by a clustering method routinely used by many petroleum companies and which could be used in other applications where analysis of multichannel signals has a significant role to play. In hydrocarbon exploration, the method is an efficient tool to condense a large number of logs (measurements performed on rocks, at a regular sampling rate, by running sensors along the borehole wall) into a single signal (rock facies) whose variation is geologically meaningful. The method is comprised of a clustering (MRGC) process and an autoordering (CFSOM) process, both of which are fully non-parametric. In the first step, the data structure is broken into clusters. In the second step, a ID chain of neurons is forced to fit the shortest path through the kernels of all clusters and passing only once through each kernel. Finally, each cluster is assigned an index whose value increases from one end of the chain to the other. As a result of ordering, the output signal is devoid of any "noise" due to the indexation of clusters which is performed arbitrarily or randomly by other methods and its variations truly reflect natural variations of all input signals taken jointly, and hence it can be subjected to signal analysis and processing techniques. The path through the kernels of clusters can be likened to the principal non-linear axis of the data structure.