BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//TUC//Events//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:Europe/Athens
TZNAME:EEST
DTSTART:19700329T030000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=3
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0300
TZNAME:EET
DTSTART:19701025T040000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=10
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CREATED:20210602T082154Z
LAST-MODIFIED:20210602T082154Z
DTSTAMP:20230127T202206Z
UID:1674843726@tuc.gr
SUMMARY:Ομιλία κ. Antonios Varvitsiotis " No
n-commutative Extension of Lee-Seung
's Algorithm for Positive Semidefini
te Factorizations"
LOCATION:Η ομιλία θα γίνει με τηλεδιάσκεψη
DESCRIPTION:https://www.ece.tuc.gr/index.php?id=
9269&L=928%27A%3D0&tx_tucevents2_tuc
eventsdisplay%5Bevent%5D=2439&tx_tuc
events2_tuceventsdisplay%5Baction%5D
=show&tx_tucevents2_tuceventsdisplay
%5Bcontroller%5D=Event\nAntonios Var
vitsiotis, Assistant Professor at th
e Singapore University of Technology
and Design\n\nTitle\n A Non-commuta
tive Extension of Lee-Seung's Algori
thm for Positive Semidefinite Factor
izations\n Abstract\n Given a data m
atrix $X\in \mathbb{R}_+^{m\times n}
$ with non-negative entries, a Posit
ive Semidefinite (PSD) factorization
of $X$ is a collection of $r \times
r$-dimensional PSD matrices $\{A_i\
}$ and $\{B_j\}$ satisfying the cond
ition $X_{ij}= \mathrm{tr}(A_i B_j)$
for all $\ i\in [m],\ j\in [n]$. P
SD factorizations are fundamentally
linked to understanding the expressi
veness of semidefinite programs as w
ell as the power and limitations of
quantum resources in information the
ory. The PSD factorization task gen
eralizes the Non-negative Matrix Fac
torization (NMF) problem in which we
seek a collection of $r$-dimensiona
l non-negative vectors $\{a_i\}$ and
$\{b_j\}$ satisfying $X_{ij}= a_i^T
b_j$, for all $i\in [m],\ j\in [n]
$ -- one can recover the latter prob
lem by choosing matrices in the PSD
factorization to be diagonal. The m
ost widely used algorithm for comput
ing NMFs of a matrix is the Multipli
cative Update algorithm developed by
Lee and Seung, in which non-negativ
ity of the updates is preserved by s
caling with positive diagonal matric
es. In this paper, we describe a no
n-commutative extension of Lee-Seung
's algorithm, which we call the Matr
ix Multiplicative Update (MMU) algor
ithm, for computing PSD factorizatio
ns. The MMU algorithm ensures that
updates remain PSD by congruence sca
ling with the matrix geometric mean
of appropriate PSD matrices, and it
retains the simplicity of implementa
tion that the multiplicative update
algorithm for NMF enjoys. Building
on the Majorization-Minimization fra
mework, we show that under our updat
e scheme the squared loss objective
is non-increasing and fixed points c
orrespond to critical points. The a
nalysis relies on Lieb's Concavity
Theorem. Beyond PSD factorizations,
we show that the MMU algorithm can
be also used as a primitive to calcu
late block-diagonal PSD factorizatio
ns and tensor PSD factorizations. W
e demonstrate the utility of our met
hod with experiments on real and syn
thetic data. \n Joint work with Yon
g Sheng Soh, National University of
Singapore. \n About the speaker\nhtt
ps://sites.google.com/site/antoniosv
arvitsiotis/ \n Assistant Professor
Varvitsiotis received a PhD in Mathe
matical Optimization from the Dutch
National Research Institute for Math
ematics and Computer Science (CWI).
Prior to joining the Singapore Unive
rsity of Technology and Design he he
ld Research Fellow positions at the
Centre for Quantum Technologies (Com
puter Science group) and the Nationa
l University of Singapore (Departmen
t of Electrical and Computer Enginee
ring and Department of Industrial an
d Systems Engineering). He also hold
s a MSc degree in Theoretical Comput
er Science and a BSc in Applied and
Theoretical Mathematics, both from t
he National University of Athens in
Greece. Dr. Varvitsiotis’ research i
s focused on fundamental aspects of
continuous and discrete optimisation
, motivated by real-life application
s in data science, engineering, and
quantum information.\n \n Meeting I
D: 923 5451 8920\n Password: 953377\
n
STATUS:CONFIRMED
ORGANIZER;RSVP=FALSE;CN=TUC;CUTYPE=TUC:mailto:webmaster@tuc.gr
DTSTART:20210602T130000
DTEND:20210602T140000
TRANSP:OPAQUE
CLASS:DEFAULT
END:VEVENT
END:VCALENDAR