Explaining a Result to the End-User: A Geometric Approach for
It gives global indicators about the easiness to maintain viability. It gives information about the resilience r(u) of trajectories. Green trajectories are more resilient.
Explaining a Result to the End-User: A Geometric Approach for Classification Problems I.Alvarez & S.Martin Geometric information identifies in classification trees the most relevant tests to describe the situation (Alvarez, 04)
Geometric approach gives information about the robustness of the decision considering change in the input case
Decision tree for next year course applicants H1: Mark in mathematics is less than 50/100 yes
no
robustness r of case x r = d(x, Γ)
H2: Mean is less than 50/100
Repeat the year Andrew Math: 40/100 Mean: 30/100
yes
Repeat the year
Pass
Andrew’s trace of classification: mark in math < 50
Pass
B
50
p(Andrew) Andrew
H2
Fig. 1: The trace of Andrew’s classification doesn’t describe the situation (case B is still in the same class area), contrary to the tests defining case p(Andrew)
50
oligotrophic lake
eutrophic lake
The state of the lake is defined by the amount of phosphorus and by phosphorus inputs from agriculture (Carpenter et al, 99)
mean
Geometric information presents a complementary viewpoint to probabilistic information. Distant points from the decision
B(x,r)
Application to a deterministic classifier for the eutrophication lake problem
loss P q (t ) recycling from dP (t ) = − b.P(t ) + L(t ) + r. q m + P q (t ) sediments dt
Regulation law is a constraint on dL/dt. The viability model gives the set of states where it is possible to maintain the oligotrophic state and agriculture (Martin, 05) 100
boundary with low probability
1.4
Class membership probability 1.0
4
B
σ1
3 σ2
Γ
1.0
0.8
A
2
V2
1.2
0.8
p(A)
0.6
p(B)
1
P
math
Math: 51/100 Mean: Andrew’s mean
decision boundary Γ
x
no
Green trajectories are more resilient
0
u1
0.6
u2
Fig. 3:The distance to the viability decision boundary Γ gives infirmation about the robustness of viable states. It gives global indicators about the easiness to maintain viability. It gives information about the resilience r(u) of trajectories.
p(A )
0
0.4
A
rh (u ) = min t ≤ h {d (u (t ), Γ )}
0.4
-1
B
0.2
p(B)
M’
0.2
-2 M
0.0 -2
-1
0
1
2
3
4
V1
Fig. 2: Points with the same class membership probability can have a very different geometric situation. A is close to the decision boundary, a small change in its attribute values can change the decision.
0.0
-100 0.0
0.2
0.4
0.6 L
0.8
Algebraic Distance (%max)
Large areas inside the viability set are good indicator for viability control
Limits: Geometric approach applies to metric space x − min i only. Basic metrics: min − max y = i i
Computation costs can be exponential (Meijster et al, 00). standard
the study of the trace of reasoning, to answer to how and why questions (see ... the result given to the end-user, using part of the information encompassed in ... Fig. 2. Class membership probability from a SVM classifier (R package kernlab [13].
attractor near the boundary of a basin of attraction; This is also the case for decision ... When the decision boundary is described by an analytical formula, or by a.
remain problematic, e.g. the detection of overlapping speech and effective .... Since we have not implemented a music detector we assume that the few music ... TV show data is edited; shot selection is performed by a TV director who gen- ..... [9] P.
PAPER Special Section on Discrete Mathematics and Its Applications. A Combinatorial Approach to ..... Operations Research from Cornell Uni- versity in 1992.
PAPER Special Section on Discrete Mathematics and Its Applications. A Combinatorial Approach to ..... Operations Research from Cornell Uni- versity in 1992.
structure, consisting of main free flow canals and pressurized distribution networks, is ... kind and the existing management constraints. The Aix-Nord ... variation of energy prices, let us simply say that this price varies according to the period i
calibration datasets have subsequently been completed andааare included in standard production operations. The MISR instrument, (Diner et al., 1998), with its ...
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ranked according to their speaker discriminability according to the method used in [12]. This analysis .... v2.pdf, 2009. ... O'Reilly Media, 2008. [11] G. Jaffr and P.
there is a need to examine the social context where science writing takes place. ... craft. b) That the language of science is determined by scientific conventions ...
reference angular value. Indeed, the robustness of the low- level control of each link allows to make the hypothesis that static forces are exactly counterbalanced ...
All the methods including the block-structured approach for grid generation have their ... blocks and different grid refinement strategies for different blocks. ...... Melton, J.E., and Berger, M.J., Adaptation and surface modeling for Cartesian mesh
due to the lack of the automated techniques for block decomposition. All the methods ... suitable assembly of grid blocks. This approach is ... would enable any grid generation system to simply and efficiently construct both a block topology and.
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MD, 20742. Cynthia F. ... Systems Research, University of Maryland, College Park, MD, 20742. Jonathan Z. ...... Science, 300(5618), 498â502. Clifton, R. K. ...
some original proposals implicating Topic Detection, Lexical Tuning and Intelligent ... service systems, Information Extraction, Human-computer interaction.
email: {ichir,[email protected]}, web: {mahieddine.ichir,djafari}.free.fr. ABSTRACT. In this paper we address the problem of Bayesian blind source separation ...
Mono and Bistatic SAR Imaging geometries and the Fourier domain data. ..... which gives the possibility of jointly segmenting and reconstruction [18, 19, 20, 21].
Statistical Sense Disambiguation with Relatively Small Corpora using. Dictionary Definitions. Proceedings of the 33rd Annual Meeting of the ACL. MUC-5 (1993) ...
Development of a substructuring approach to model the vibroacoustic behavior of submerged stiffened cylindrical shells coupled to non-axisymmetric internal ...
to who actually won the election. .... adjacent regions also exert area forces upon shared vertices, resulting in a tug of war, with the .... Cellular Automata Machine.
