  Operating with ignorance is an important concern of the Machine Learning
research, especially when the objective is to discover knowledge from the
imperfect data. Data mining (driven by appropriate knowledge discovery tools)
is about processing available (observed, known and understood) samples of data
aiming to build a model (e.g., a classifier) to handle data samples, which are
not yet observed, known or understood. These tools traditionally take samples
of the available data (known facts) as an input for learning. We want to
challenge the indispensability of this approach and we suggest considering the
things the other way around. What if the task would be as follows: how to learn
a model based on our ignorance, i.e. by processing the shape of 'voids' within
the available data space? Can we improve traditional classification by modeling
also the ignorance? In this paper, we provide some algorithms for the discovery
and visualizing of the ignorance zones in two-dimensional data spaces and
design two ignorance-aware smart prototype selection techniques (incremental
and adversarial) to improve the performance of the nearest neighbor
classifiers. We present experiments with artificial and real datasets to test
the concept of the usefulness of ignorance discovery in machine learning.
