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Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural
attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease
aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease
and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because
Gleason grading is done manually by a pathologist visually examining glass (or digital) slides, subtle morphologic
and architectural differences of histological attributes may result in grading errors and hence cause high
inter-observer variability. Recently some researchers have proposed computerized decision support systems to
automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as
well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between
intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate
a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving
nonlinear relationships between object instances. Classification can then be performed in the low dimensional
space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the
dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain
the low dimensional manifold to a specific range of possible manifold shapes, the range being determined
via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1)
identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM,
and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a manifold constrained by
the SSMM. We demonstrate these applications of the SSMM in the context of distinguishing between Gleason
patterns 3 and 4 using glandular morphologic features in a prostate histopathology dataset of 58 patient studies.
Identifying and eliminating noisy samples from the manifold via the SSMM results in a statistically significant
improvement in classification accuracy (CA), 93.0 ± 1.0% with removal of noisy samples compared to a CA of
90.9 ± 1.1% without removal of samples. The use of the SSMM for OSE of new independent test instances also
shows statistically significant improvement in CA, 87.1±0.8% with the SSMM compared to 85.6±0.1% without
the SSMM. Similar improvements were observed for the synthetic Swiss Roll and Helix datasets.
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