
A lopes
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Papers by A lopes
of a wide variety of complex high-dimensional data. However, projection mappings obtained from different
techniques vary considerably, and users exploring the mappings or selecting between projection techniques
still have limited assistance in their task. Current methods to assess projection quality fail to capture
properties that are paramount to user interpretation, such as the capability of conveying class information,
or the preservation of groups and neighborhoods from the original space. In this paper we propose a
unifying framework to derive objective measures of the
local behavior of projection mappings that support
interpreting the mappings and comparing solutions regarding several properties. A quality value is
computed for each data point, from which a single global value may be also assigned to the projection.
Measures are computed from a recently introduced data graph model known as Extended Minimum Spanning Tree
(EMST). Measurements of the topology of EMST
graphs, built relative to the original and projected data representations, are scale independent and afford evaluation of multiple properties. We introduce measures of visual properties and of preservation of properties from the original space. They are targeted at (i) depicting class segregation capability; (ii) quantifying neighborhood purity regarding classes; (iii) evaluating neighborhood preservation; and
finally (iv) evaluating group preservation. We introduce the
measures and illustrate how they can inform users about the local and global behavior of projection
techniques considering multiple mappings of artificial and real data sets.
of a wide variety of complex high-dimensional data. However, projection mappings obtained from different
techniques vary considerably, and users exploring the mappings or selecting between projection techniques
still have limited assistance in their task. Current methods to assess projection quality fail to capture
properties that are paramount to user interpretation, such as the capability of conveying class information,
or the preservation of groups and neighborhoods from the original space. In this paper we propose a
unifying framework to derive objective measures of the
local behavior of projection mappings that support
interpreting the mappings and comparing solutions regarding several properties. A quality value is
computed for each data point, from which a single global value may be also assigned to the projection.
Measures are computed from a recently introduced data graph model known as Extended Minimum Spanning Tree
(EMST). Measurements of the topology of EMST
graphs, built relative to the original and projected data representations, are scale independent and afford evaluation of multiple properties. We introduce measures of visual properties and of preservation of properties from the original space. They are targeted at (i) depicting class segregation capability; (ii) quantifying neighborhood purity regarding classes; (iii) evaluating neighborhood preservation; and
finally (iv) evaluating group preservation. We introduce the
measures and illustrate how they can inform users about the local and global behavior of projection
techniques considering multiple mappings of artificial and real data sets.