to Analyze Structure of

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8 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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Using Dynamic Quantum Clustering
to Analyze Structure of
Hierarchically Heterogeneous
Samples at the
Nanoscale

Allison Hume

Mentor: Marvin Weinstein

Problem: Interface of materials


Sample data: Roman
pottery


Red and Black colors
are from different
iron oxides


Similar problems:


Lithium
-
ion batteries


Catalyst breakdown

http://
touritaly.org/tours/capua/museum.htm

Data


X
-
ray Absorption Near Edge Structure (XANES) for each
pixel: 30nm resolution


Large field of view: half a million data points


Can DQC be used for this data?


Transmission image at 7050 eV


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Transmission image at 7250 eV


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Spectrum of a pixel


Florian

Meirer
, ProtoSig1_a1_Clustering_Analysis_report_v2

Singular

Value Decomposition

Original Curve

Singular

Value Decomposition

Curve Reconstructed from first N Components

N = 5

Singular

Value Decomposition

Curve Reconstructed from first N Components

N = 30

Singular

Value Decomposition

N = 70

Curve Reconstructed from first N Components

Singular

Value Decomposition

N = 146

Curve Reconstructed from first N Components

DQC: Modeling the Data


Each data point is a 5
-
dimensional Gaussian


Data set is sum of Gaussians:


M. Weinstein, D. Horn. Dynamic quantum clustering: a method for visual
exploration of structures in data.

Physical Review E 2009 (80) 066117.

DQC: a QM Problem


Composite function is
ground state of
Hamiltonian



Define potential
according to time
-
independent
Schrodinger
equation:


M. Weinstein, D. Horn. Dynamic quantum clustering: a method for visual
exploration of structures in data.

Physical Review E 2009 (80) 066117.

Clustering Process:

Clustering Process:

Data collapses
into clumps and
strands

Clustering Process:

Data collapses
into clumps and
strands

Clustering Process:

Some strands
collapse to
points, others
remain

Clustering Process:

Some strands
collapse to
points, others
remain

Clustering Process:

Separation
continues

Clustering Process:

Separation
continues

Clustering Process:

Separation
continues

Identifying Clusters

Recreate the Picture

F.
Meirer
, Y. Liu, A. Mehta. Mineralogy and morphology
at
nanoscale

in hierarchically heterogeneous materials.
June 24, 2011.

Spectra

Iron phases

Hercynite phases

Hematite

Importance of Sub
-
clustering

Sub
-
clusters of blue show big difference in shape


revealing the existence of Iron

Conclusion

Special Thanks to:

Marvin Weinstein

Apurva

Mehta

David Horn

Florian

Meirer

Yijin

Liu


DOE & SLAC

Steve Rock & SULI Program



DQC vs. Gradient Descent

D
.
Horn, A. Gottlieb. Algorithm for Data Clustering in Pattern Recognition Problems Based
on Quantum Mechanics. Physical Review Letters 2001 (88) 018702.