  Understanding black-box Machine Learning methods on multidimensional data is
a key challenge in Machine Learning. While many powerful Machine Learning
methods already exist, these methods are often unexplainable or perform poorly
on complex data. This paper proposes visual knowledge discovery approaches
based on several forms of lossless General Line Coordinates. These are an
expansion of the previously introduced General Line Coordinates Linear and
Dynamic Scaffolding Coordinates to produce, explain, and visualize non-linear
classifiers with explanation rules. To ensure these non-linear models and rules
are accurate, General Line Coordinates Linear also developed new interactive
visual knowledge discovery algorithms for finding worst-case validation splits.
These expansions are General Line Coordinates non-linear, interactive rules
linear, hyperblock rules linear, and worst-case linear. Experiments across
multiple benchmark datasets show that this visual knowledge discovery method
can compete with other visual and computational Machine Learning algorithms
while improving both interpretability and accuracy in linear and non-linear
classifications. Major benefits from these expansions consist of the ability to
build accurate and highly interpretable models and rules from hyperblocks, the
ability to analyze interpretability weaknesses in a model, and the input of
expert knowledge through interactive and human-guided visual knowledge
discovery methods.
