Are single neocortical neurons as powerful as multi-layered networks? A recent compartmental modeling study has shown that voltage-dependent membrane nonlinearities present in a complex dendritic tree can provide a virtual layer of local nonlinear processing elements between synaptic in(cid:173) puts and the final output at the cell body, analogous to a hidden layer in a multi-layer network. In this paper, an abstract model neuron is in(cid:173) troduced, called a clusteron, which incorporates aspects of the dendritic "cluster-sensitivity" phenomenon seen in these detailed biophysical mod(cid:173) eling studies. It is shown, using a clusteron, that a Hebb-type learning rule can be used to extract higher-order statistics from a set of train(cid:173) ing patterns, by manipulating the spatial ordering of synaptic connections onto the dendritic tree. The potential neurobiological relevance of these higher-order statistics for nonlinear pattern discrimination is then studied within a full compartmental model of a neocortical pyramidal cell, using a training set of 1000 high-dimensional sparse random patterns.