69,505 research outputs found
Enhancing Decision Tree based Interpretation of Deep Neural Networks through L1-Orthogonal Regularization
One obstacle that so far prevents the introduction of machine learning models
primarily in critical areas is the lack of explainability. In this work, a
practicable approach of gaining explainability of deep artificial neural
networks (NN) using an interpretable surrogate model based on decision trees is
presented. Simply fitting a decision tree to a trained NN usually leads to
unsatisfactory results in terms of accuracy and fidelity. Using L1-orthogonal
regularization during training, however, preserves the accuracy of the NN,
while it can be closely approximated by small decision trees. Tests with
different data sets confirm that L1-orthogonal regularization yields models of
lower complexity and at the same time higher fidelity compared to other
regularizers.Comment: 8 pages, 18th IEEE International Conference on Machine Learning and
Applications (ICMLA) 201
The Goldman-Rota identity and the Grassmann scheme
We inductively construct an explicit (common) orthogonal eigenbasis for the
elements of the Bose-Mesner algebra of the Grassmann scheme. The main step is a
constructive, linear algebraic interpretation of the Goldman-Rota recurrence
for the number of subspaces of a finite vector space. This interpretation shows
that the up operator on subspaces has an explicitly given recursive structure.
Using this we inductively construct an explicit orthogonal symmetric Jordan
basis with respect to the up operator and write down the singular values, i.e.,
the ratio of the lengths of the successive vectors in the Jordan chains. The
collection of all vectors in this basis of a fixed rank forms a (common)
orthogonal eigenbasis for the elements of the Bose-Mesner algebra of the
Grassmann scheme. We also pose a bijective proof problem on the spanning trees
of the Grassmann graphs.Comment: 19 Page
Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges
Let be an -node tree of maximum degree 4, and let be a set of
points in the plane with no two points on the same horizontal or vertical line.
It is an open question whether always has a planar drawing on such that
each edge is drawn as an orthogonal path with one bend (an "L-shaped" edge). By
giving new methods for drawing trees, we improve the bounds on the size of the
point set for which such drawings are possible to: for
maximum degree 4 trees; for maximum degree 3 (binary) trees; and
for perfect binary trees.
Drawing ordered trees with L-shaped edges is harder---we give an example that
cannot be done and a bound of points for L-shaped drawings of
ordered caterpillars, which contrasts with the known linear bound for unordered
caterpillars.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
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