that was provided by NASA through a grant from the Space Telescope Science
Institute, which is operated by the Associations of Universities for Research
in Astronomy, Incorporated, under NASA contract NAS5- 26555. BLJ thanks
support from the European Space Agency (ESA). The CLASSY collaboration extends
special gratitude to the Lorentz Center for useful discussions during the
”Characterizing Galaxies with Spectroscopy with a view for JWST” 2017 workshop
that led to the formation of the CLASSY collaboration and survey.
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/.
SDSS-III is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS-III Collaboration including the
University of Arizona, the Brazilian Participation Group, Brookhaven National
Laboratory, Carnegie Mellon University, University of Florida, the French
Participation Group, the German Participation Group, Harvard University, the
Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA
Participation Group, Johns Hopkins University, Lawrence Berkeley National
Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for
Extraterrestrial Physics, New Mexico State University, New York University,
Ohio State University, Pennsylvania State University, University of
Portsmouth, Princeton University, the Spanish Participation Group, University
of Tokyo, University of Utah, Vanderbilt University, University of Virginia,
University of Washington, and Yale University.
This research has made use of the HSLA database, developed and maintained at
STScI, Baltimore, USA. We also thank the anonymous referee for the insightful
comments on the paper.

Table 5: Measured Outflow Parameters for Galaxies in the Combined Sample(1) Object | $V_{\text{out}}$ |  FWHM${}_{\text{out}}$ |  log(N(Si ii)) |  log(N(Si iii)) |  log(N(Si iv)) |  log($N_{\mathrm{\scriptstyle H}}$) |  log(N(H i)) | $\overline{C_{\text{f}}}$ | $\dot{M}_{\text{out}}$ |  log($\dot{p}_{\text{out}}$) |  log($\dot{p}_{\text{crit}}$) |  log($\dot{E}_{\text{out}}$)
---|---|---|---|---|---|---|---|---|---|---|---|---
|  km s-1 |  km s-1 |  cm-2 |  cm-2 |  cm-2 |  cm-2 |  cm-2 |  |  M$\odot$/yr | dynes | dynes | ergs/s
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
J0021+0052 |  231${}^{+77}_{-77}$ |  566${}^{+127}_{-127}$ |  14.39${}^{+0.06}_{-0.06}$ |  15.67${}^{+0.02}_{-0.02}$ |  15.12${}^{+0.06}_{-0.06}$ |  20.78${}^{+0.04}_{-0.05}$ |  17.50${}^{+0.02}_{-0.02}$ |  0.50${}^{+0.10}_{-0.10}$ |  16.5${}^{+7.1}_{-6.2}$ |  34.5${}^{+0.3}_{-0.4}$ |  33.3${}^{+0.1}_{-0.1}$ |  41.8${}^{+0.4}_{-0.5}$
J0036–3333 |  157${}^{+22}_{-22}$ |  413${}^{+117}_{-117}$ |  14.39${}^{+0.03}_{-0.03}$ |  15.50${}^{+0.02}_{-0.02}$ |  14.64${}^{+0.02}_{-0.02}$ |  20.49${}^{+0.02}_{-0.02}$ |  17.43${}^{+0.02}_{-0.02}$ |  0.76${}^{+0.04}_{-0.04}$ |  1.9${}^{+0.5}_{-0.4}$ |  33.5${}^{+0.1}_{-0.2}$ |  32.5${}^{+0.1}_{-0.1}$ |  40.8${}^{+0.2}_{-0.2}$
J0055–0021${}^{\text{(H15)}}$ |  197${}^{+63}_{-63}$ |  591${}^{+108}_{-108}$ |  15.33${}^{+0.04}_{-0.04}$ |  16.03${}^{+0.02}_{-0.02}$ |  14.88${}^{+0.06}_{-0.06}$ |  21.03${}^{+0.03}_{-0.03}$ |  18.40${}^{+0.03}_{-0.02}$ |  0.94${}^{+0.19}_{-0.19}$ |  36.5${}^{+14.9}_{-13.0}$ |  34.9${}^{+0.3}_{-0.3}$ |  34.0${}^{+0.1}_{-0.1}$ |  42.2${}^{+0.4}_{-0.5}$
J0127–0619 |  No Outflow∗ | … | … | … | … | … | … | … | … | … | …
J0144+0453 |  48${}^{+16}_{-16}$ |  182${}^{+61}_{-61}$ |  14.59${}^{+0.10}_{-0.10}$ |  15.39${}^{+0.02}_{-0.02}$ |  14.12${}^{+0.10}_{-0.10}$ |  20.97${}^{+0.03}_{-0.03}$ |  18.74${}^{+0.89}_{-0.24}$ |  0.36${}^{+0.07}_{-0.07}$ |  4.1${}^{+4.4}_{-1.9}$ |  33.3${}^{+0.4}_{-0.4}$ |  32.7${}^{+0.2}_{-0.1}$ |  40.0${}^{+0.5}_{-0.6}$
J0150+1308${}^{\text{(H15)}}$ |  212${}^{+28}_{-28}$ |  345${}^{+63}_{-63}$ |  14.86${}^{+0.04}_{-0.04}$ |  15.78${}^{+0.02}_{-0.02}$ |  14.83${}^{+0.08}_{-0.08}$ |  20.67${}^{+0.04}_{-0.04}$ |  17.80${}^{+0.02}_{-0.02}$ |  0.82${}^{+0.15}_{-0.15}$ |  17.3${}^{+4.8}_{-4.1}$ |  34.5${}^{+0.1}_{-0.2}$ |  33.8${}^{+0.1}_{-0.1}$ |  41.8${}^{+0.2}_{-0.2}$
J0337–0502 |  No Outflow∗ | … | … | … | … | … | … | … | … | … | …
J0405–3648 |  No Outflow∗ | … | … | … | … | … | … | … | … | … | …
J0808+3948 |  646${}^{+65}_{-65}$ |  382${}^{+127}_{-127}$ |  14.87${}^{+0.05}_{-0.05}$ |  15.47${}^{+0.02}_{-0.02}$ |  14.40${}^{+0.02}_{-0.02}$ |  19.99${}^{+0.01}_{-0.02}$ |  17.22${}^{+0.02}_{-0.02}$ |  0.70${}^{+0.07}_{-0.07}$ |  2.3${}^{+0.6}_{-0.5}$ |  34.0${}^{+0.1}_{-0.1}$ |  32.0${}^{+0.1}_{-0.1}$ |  41.5${}^{+0.1}_{-0.2}$
J0823+2806 |  136${}^{+45}_{-45}$ |  393${}^{+131}_{-131}$ |  14.27${}^{+0.04}_{-0.04}$ |  15.55${}^{+0.02}_{-0.02}$ |  14.92${}^{+0.03}_{-0.03}$ |  20.56${}^{+0.02}_{-0.02}$ |  17.43${}^{+0.02}_{-0.02}$ |  0.85${}^{+0.15}_{-0.15}$ |  3.3${}^{+1.4}_{-1.2}$ |  33.6${}^{+0.3}_{-0.4}$ |  33.0${}^{+0.1}_{-0.1}$ |  40.6${}^{+0.4}_{-0.5}$
J0926+4427 |  353${}^{+52}_{-52}$ |  402${}^{+130}_{-130}$ |  15.00${}^{+0.13}_{-0.13}$ |  15.71${}^{+0.02}_{-0.02}$ |  14.67${}^{+0.05}_{-0.05}$ |  20.90${}^{+0.08}_{-0.09}$ |  18.33${}^{+0.05}_{-0.05}$ |  0.50${}^{+0.10}_{-0.10}$ |  45.8${}^{+15.5}_{-13.1}$ |  35.0${}^{+0.2}_{-0.2}$ |  33.4${}^{+0.1}_{-0.1}$ |  42.3${}^{+0.2}_{-0.2}$
J0934+5514 |  112${}^{+37}_{-37}$ |  178${}^{+59}_{-59}$ |  14.16${}^{+0.10}_{-0.10}$ | … |  13.91${}^{+0.05}_{-0.05}$ | … | … | … | … | … | … | …
J0938+5428 |  215${}^{+72}_{-72}$ |  272${}^{+91}_{-91}$ |  15.12${}^{+0.14}_{-0.14}$ |  15.74${}^{+0.02}_{-0.02}$ |  14.57${}^{+0.04}_{-0.04}$ |  20.86${}^{+0.06}_{-0.06}$ |  18.50${}^{+0.13}_{-0.06}$ |  0.36${}^{+0.07}_{-0.07}$ |  12.2${}^{+5.4}_{-4.7}$ |  34.1${}^{+0.3}_{-0.4}$ |  33.5${}^{+0.1}_{-0.1}$ |  41.1${}^{+0.4}_{-0.5}$
J0940+2935 |  102${}^{+34}_{-34}$ |  168${}^{+56}_{-56}$ |  14.13${}^{+0.21}_{-0.21}$ |  14.68${}^{+0.02}_{-0.02}$ |  14.01${}^{+0.13}_{-0.13}$ |  19.99${}^{+0.08}_{-0.10}$ |  16.89${}^{+0.02}_{-0.02}$ |  0.50${}^{+0.10}_{-0.10}$ |  0.3${}^{+0.1}_{-0.1}$ |  32.4${}^{+0.3}_{-0.4}$ |  30.8${}^{+0.1}_{-0.1}$ |  39.2${}^{+0.4}_{-0.5}$
J0942+3547 |  97${}^{+26}_{-26}$ |  272${}^{+91}_{-91}$ |  13.77${}^{+0.05}_{-0.05}$ |  15.03${}^{+0.02}_{-0.02}$ |  14.35${}^{+0.03}_{-0.03}$ |  20.23${}^{+0.02}_{-0.02}$ |  17.19${}^{+0.02}_{-0.02}$ |  0.70${}^{+0.04}_{-0.04}$ |  0.4${}^{+0.1}_{-0.1}$ |  32.5${}^{+0.2}_{-0.3}$ |  31.3${}^{+0.1}_{-0.1}$ |  39.4${}^{+0.3}_{-0.4}$
J0944+3424 |  No Outflow∗ | … | … | … | … | … | … | … | … | … | …
J0944–0038 |  64${}^{+21}_{-21}$ |  163${}^{+54}_{-54}$ |  14.57${}^{+0.12}_{-0.12}$ |  15.46${}^{+0.03}_{-0.03}$ |  14.29${}^{+0.11}_{-0.11}$ |  20.95${}^{+0.05}_{-0.06}$ |  18.97${}^{+0.49}_{-0.55}$ |  0.55${}^{+0.11}_{-0.11}$ |  3.3${}^{+1.2}_{-1.1}$ |  33.4${}^{+0.3}_{-0.4}$ |  32.0${}^{+0.1}_{-0.1}$ |  40.3${}^{+0.4}_{-0.5}$
J1016+3754 |  116${}^{+31}_{-31}$ |  128${}^{+37}_{-37}$ |  13.64${}^{+0.11}_{-0.11}$ |  15.00${}^{+0.02}_{-0.03}$ |  14.55${}^{+0.03}_{-0.03}$ |  20.74${}^{+0.06}_{-0.07}$ |  17.74${}^{+0.02}_{-0.02}$ |  0.42${}^{+0.08}_{-0.08}$ |  2.2${}^{+0.7}_{-0.7}$ |  33.3${}^{+0.2}_{-0.3}$ |  31.5${}^{+0.1}_{-0.1}$ |  40.1${}^{+0.3}_{-0.4}$
J1024+0524 |  94${}^{+12}_{-12}$ |  286${}^{+54}_{-54}$ |  14.58${}^{+0.03}_{-0.03}$ |  15.54${}^{+0.02}_{-0.02}$ |  14.43${}^{+0.05}_{-0.05}$ |  21.00${}^{+0.02}_{-0.02}$ |  18.41${}^{+0.05}_{-0.03}$ |  0.65${}^{+0.05}_{-0.05}$ |  7.2${}^{+1.9}_{-1.6}$ |  33.9${}^{+0.1}_{-0.2}$ |  32.6${}^{+0.1}_{-0.1}$ |  40.9${}^{+0.2}_{-0.2}$
J1025+3622 |  155${}^{+24}_{-24}$ |  409${}^{+76}_{-76}$ |  14.79${}^{+0.04}_{-0.04}$ |  15.67${}^{+0.02}_{-0.02}$ |  14.62${}^{+0.03}_{-0.03}$ |  20.84${}^{+0.03}_{-0.03}$ |  18.15${}^{+0.02}_{-0.02}$ |  0.81${}^{+0.12}_{-0.12}$ |  25.2${}^{+7.1}_{-6.1}$ |  34.6${}^{+0.2}_{-0.2}$ |  33.5${}^{+0.1}_{-0.1}$ |  41.8${}^{+0.2}_{-0.2}$
J1044+0353 |  52${}^{+12}_{-12}$ |  123${}^{+24}_{-24}$ |  14.84${}^{+0.06}_{-0.06}$ | … |  13.43${}^{+0.17}_{-0.17}$ | … | … | … | … | … | … | …
J1105+4444 |  115${}^{+23}_{-23}$ |  247${}^{+60}_{-60}$ |  15.01${}^{+0.02}_{-0.02}$ |  15.75${}^{+0.02}_{-0.02}$ |  14.46${}^{+0.02}_{-0.02}$ |  20.84${}^{+0.01}_{-0.01}$ |  18.19${}^{+0.03}_{-0.02}$ |  0.84${}^{+0.04}_{-0.04}$ |  31.5${}^{+6.5}_{-6.4}$ |  34.5${}^{+0.2}_{-0.2}$ |  33.9${}^{+0.1}_{-0.1}$ |  41.5${}^{+0.2}_{-0.3}$
J1112+5503 |  349${}^{+107}_{-107}$ |  841${}^{+230}_{-230}$ |  14.93${}^{+0.05}_{-0.05}$ |  15.82${}^{+0.02}_{-0.02}$ |  14.83${}^{+0.03}_{-0.03}$ |  20.63${}^{+0.03}_{-0.03}$ |  17.81${}^{+0.01}_{-0.01}$ |  0.80${}^{+0.16}_{-0.16}$ |  25.2${}^{+10.0}_{-8.8}$ |  35.0${}^{+0.2}_{-0.3}$ |  33.5${}^{+0.1}_{-0.1}$ |  42.6${}^{+0.4}_{-0.5}$
J1113+2930${}^{\text{(H15)}}$ |  889${}^{+74}_{-74}$ |  237${}^{+79}_{-79}$ |  15.39${}^{+0.14}_{-0.14}$ | … |  12.85${}^{+0.23}_{-0.23}$ | … | … | … | … | … | … | …
J1119+5130 |  65${}^{+22}_{-22}$ |  200${}^{+54}_{-54}$ |  14.36${}^{+0.06}_{-0.06}$ |  15.00${}^{+0.03}_{-0.03}$ |  13.68${}^{+0.10}_{-0.10}$ |  20.71${}^{+0.03}_{-0.04}$ |  18.66${}^{+0.20}_{-0.13}$ |  0.32${}^{+0.06}_{-0.06}$ |  1.1${}^{+0.4}_{-0.4}$ |  32.9${}^{+0.3}_{-0.4}$ |  31.4${}^{+0.1}_{-0.1}$ |  39.9${}^{+0.4}_{-0.5}$
J1129+2034 |  51${}^{+17}_{-17}$ |  144${}^{+15}_{-15}$ |  14.30${}^{+0.08}_{-0.08}$ |  15.55${}^{+0.03}_{-0.03}$ |  14.39${}^{+0.09}_{-0.09}$ |  20.55${}^{+0.10}_{-0.12}$ |  18.01${}^{+0.04}_{-0.03}$ |  0.46${}^{+0.09}_{-0.09}$ |  0.3${}^{+0.1}_{-0.1}$ |  32.3${}^{+0.3}_{-0.4}$ |  31.5${}^{+0.1}_{-0.2}$ |  39.3${}^{+0.4}_{-0.6}$
J1132+1411 |  60${}^{+10}_{-10}$ |  215${}^{+69}_{-69}$ |  15.14${}^{+0.03}_{-0.03}$ |  15.82${}^{+0.02}_{-0.02}$ |  14.56${}^{+0.07}_{-0.07}$ |  20.82${}^{+0.03}_{-0.03}$ |  18.14${}^{+0.05}_{-0.05}$ |  0.76${}^{+0.08}_{-0.08}$ |  35.3${}^{+6.9}_{-6.6}$ |  34.4${}^{+0.1}_{-0.2}$ |  34.0${}^{+0.1}_{-0.1}$ |  41.3${}^{+0.2}_{-0.2}$
J1132+5722 |  No Outflow∗ | … | … | … | … | … | … | … | … | … | …
J1144+4012 |  246${}^{+33}_{-33}$ |  449${}^{+86}_{-86}$ |  15.17${}^{+0.04}_{-0.04}$ |  15.79${}^{+0.02}_{-0.02}$ |  14.55${}^{+0.07}_{-0.07}$ |  20.71${}^{+0.03}_{-0.03}$ |  18.12${}^{+0.03}_{-0.02}$ |  0.83${}^{+0.15}_{-0.15}$ |  24.9${}^{+6.7}_{-5.8}$ |  34.6${}^{+0.1}_{-0.2}$ |  34.0${}^{+0.1}_{-0.1}$ |  41.8${}^{+0.2}_{-0.2}$
J1148+2546 |  95${}^{+19}_{-19}$ |  239${}^{+52}_{-52}$ |  15.27${}^{+0.20}_{-0.20}$ |  15.62${}^{+0.02}_{-0.03}$ |  14.34${}^{+0.12}_{-0.12}$ |  21.06${}^{+0.06}_{-0.07}$ |  20.01${}^{+0.21}_{-0.20}$ |  0.67${}^{+0.10}_{-0.10}$ |  25.7${}^{+7.0}_{-6.4}$ |  34.3${}^{+0.2}_{-0.2}$ |  33.5${}^{+0.1}_{-0.1}$ |  41.2${}^{+0.2}_{-0.3}$
J1150+1501 |  67${}^{+22}_{-22}$ |  181${}^{+25}_{-25}$ |  14.58${}^{+0.03}_{-0.03}$ |  15.62${}^{+0.02}_{-0.02}$ |  14.71${}^{+0.06}_{-0.06}$ |  20.71${}^{+0.03}_{-0.03}$ |  17.90${}^{+0.02}_{-0.02}$ |  0.64${}^{+0.06}_{-0.06}$ |  1.1${}^{+0.4}_{-0.4}$ |  33.1${}^{+0.3}_{-0.4}$ |  31.3${}^{+0.1}_{-0.1}$ |  40.2${}^{+0.4}_{-0.5}$
J1157+3220 |  238${}^{+49}_{-49}$ |  277${}^{+84}_{-84}$ |  14.46${}^{+0.03}_{-0.03}$ |  15.49${}^{+0.02}_{-0.02}$ |  14.36${}^{+0.02}_{-0.02}$ |  20.29${}^{+0.01}_{-0.01}$ |  17.46${}^{+0.01}_{-0.01}$ |  0.78${}^{+0.06}_{-0.06}$ |  7.1${}^{+1.5}_{-1.5}$ |  34.1${}^{+0.2}_{-0.2}$ |  33.0${}^{+0.1}_{-0.1}$ |  41.4${}^{+0.2}_{-0.3}$
J1200+1343 |  192${}^{+13}_{-13}$ |  306${}^{+62}_{-62}$ |  14.90${}^{+0.08}_{-0.08}$ |  15.86${}^{+0.02}_{-0.02}$ |  14.82${}^{+0.03}_{-0.03}$ |  20.85${}^{+0.05}_{-0.06}$ |  18.07${}^{+0.02}_{-0.02}$ |  0.87${}^{+0.06}_{-0.06}$ |  10.0${}^{+2.6}_{-2.3}$ |  34.3${}^{+0.1}_{-0.1}$ |  32.5${}^{+0.1}_{-0.2}$ |  41.5${}^{+0.1}_{-0.1}$
J1225+6109 |  51${}^{+17}_{-17}$ |  198${}^{+33}_{-33}$ |  14.52${}^{+0.15}_{-0.15}$ |  15.41${}^{+0.02}_{-0.02}$ |  14.51${}^{+0.05}_{-0.05}$ |  20.70${}^{+0.09}_{-0.12}$ |  18.15${}^{+0.02}_{-0.02}$ |  0.64${}^{+0.13}_{-0.13}$ |  2.8${}^{+1.2}_{-1.1}$ |  33.5${}^{+0.3}_{-0.4}$ |  31.8${}^{+0.1}_{-0.2}$ |  40.5${}^{+0.4}_{-0.5}$
J1253–0312 |  113${}^{+38}_{-38}$ |  245${}^{+82}_{-82}$ |  14.61${}^{+0.10}_{-0.10}$ |  15.69${}^{+0.02}_{-0.02}$ |  14.56${}^{+0.09}_{-0.09}$ |  21.00${}^{+0.03}_{-0.03}$ |  17.90${}^{+0.15}_{-0.17}$ |  0.92${}^{+0.18}_{-0.18}$ |  7.7${}^{+2.7}_{-2.6}$ |  33.9${}^{+0.3}_{-0.4}$ |  32.7${}^{+0.1}_{-0.2}$ |  41.0${}^{+0.4}_{-0.5}$
J1314+3452 |  62${}^{+21}_{-21}$ |  187${}^{+54}_{-54}$ |  15.31${}^{+0.17}_{-0.17}$ |  15.73${}^{+0.03}_{-0.03}$ |  14.35${}^{+0.04}_{-0.04}$ |  20.84${}^{+0.03}_{-0.03}$ |  19.87${}^{+0.39}_{-0.36}$ |  0.80${}^{+0.02}_{-0.02}$ |  0.3${}^{+0.1}_{-0.1}$ |  32.5${}^{+0.3}_{-0.4}$ |  31.3${}^{+0.1}_{-0.1}$ |  39.6${}^{+0.4}_{-0.5}$
J1323–0132 |  No Outflow∗ | … | … | … | … | … | … | … | … | … | …
J1359+5726 |  161${}^{+23}_{-23}$ |  359${}^{+70}_{-70}$ |  14.99${}^{+0.02}_{-0.02}$ |  15.77${}^{+0.02}_{-0.02}$ |  14.60${}^{+0.03}_{-0.03}$ |  21.05${}^{+0.01}_{-0.01}$ |  18.54${}^{+0.03}_{-0.03}$ |  0.74${}^{+0.04}_{-0.04}$ |  29.5${}^{+4.5}_{-4.4}$ |  34.6${}^{+0.1}_{-0.1}$ |  33.4${}^{+0.1}_{-0.1}$ |  41.7${}^{+0.2}_{-0.2}$
J1414+0540${}^{\text{(H15)}}$ |  155${}^{+52}_{-52}$ |  273${}^{+87}_{-87}$ |  14.05${}^{+0.06}_{-0.06}$ |  15.48${}^{+0.02}_{-0.02}$ |  14.83${}^{+0.05}_{-0.05}$ |  20.53${}^{+0.01}_{-0.02}$ |  17.95${}^{+0.033}_{-0.033}$ |  0.81${}^{+0.16}_{-0.16}$ |  6.5${}^{+11.1}_{-5.6}$ |  34.1${}^{+0.5}_{-0.9}$ |  33.3${}^{+0.2}_{-0.4}$ |  41.3${}^{+0.6}_{-1.0}$
J1416+1223 |  398${}^{+68}_{-68}$ |  649${}^{+216}_{-216}$ |  14.24${}^{+0.06}_{-0.06}$ |  15.47${}^{+0.02}_{-0.02}$ |  14.65${}^{+0.03}_{-0.03}$ |  20.27${}^{+0.02}_{-0.02}$ |  17.24${}^{+0.02}_{-0.02}$ |  0.79${}^{+0.13}_{-0.13}$ |  2.8${}^{+0.8}_{-0.7}$ |  33.7${}^{+0.2}_{-0.2}$ |  32.9${}^{+0.1}_{-0.1}$ |  40.9${}^{+0.2}_{-0.3}$

Table 5: Continued Object | $V_{\text{out}}$ |  FWHM${}_{\text{out}}$ |  log(N(Si ii)) |  log(N(Si iii)) |  log(N(Si iv)) |  log($N_{\mathrm{\scriptstyle H}}$) |  log(N(H i)) | $\overline{C_{\text{f}}}$ | $\dot{M}_{\text{out}}$ |  log($\dot{p}_{\text{out}}$) |  log($\dot{p}_{\text{crit}}$) |  log($\dot{E}_{\text{out}}$)
---|---|---|---|---|---|---|---|---|---|---|---|---
|  km s-1 |  km s-1 |  cm-2 |  cm-2 |  cm-2 |  cm-2 |  cm-2 |  |  M$\odot$/yr | dynes | dynes | ergs/s
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
J1418+2102 |  51${}^{+7}_{-7}$ |  112${}^{+27}_{-27}$ |  15.23${}^{+0.20}_{-0.20}$ |  15.34${}^{+0.05}_{-0.06}$ |  13.98${}^{+0.13}_{-0.13}$ |  21.12${}^{+0.08}_{-0.10}$ |  20.54${}^{+0.07}_{-0.13}$ |  0.30${}^{+0.06}_{-0.06}$ |  1.0${}^{+0.3}_{-0.3}$ |  32.8${}^{+0.2}_{-0.2}$ |  31.3${}^{+0.1}_{-0.2}$ |  39.5${}^{+0.2}_{-0.2}$
J1428+1653 |  140${}^{+25}_{-25}$ |  325${}^{+108}_{-108}$ |  14.64${}^{+0.07}_{-0.07}$ |  15.72${}^{+0.02}_{-0.02}$ |  14.87${}^{+0.05}_{-0.05}$ |  20.70${}^{+0.04}_{-0.05}$ |  17.69${}^{+0.03}_{-0.02}$ |  0.75${}^{+0.13}_{-0.13}$ |  20.1${}^{+6.2}_{-5.3}$ |  34.4${}^{+0.2}_{-0.2}$ |  33.9${}^{+0.1}_{-0.1}$ |  41.5${}^{+0.2}_{-0.3}$
J1429+0643 |  230${}^{+51}_{-51}$ |  461${}^{+152}_{-152}$ |  14.83${}^{+0.06}_{-0.06}$ |  15.83${}^{+0.02}_{-0.02}$ |  15.00${}^{+0.06}_{-0.06}$ |  20.81${}^{+0.04}_{-0.05}$ |  17.80${}^{+0.02}_{-0.02}$ |  0.73${}^{+0.15}_{-0.15}$ |  22.1${}^{+7.6}_{-6.5}$ |  34.7${}^{+0.2}_{-0.2}$ |  33.2${}^{+0.1}_{-0.1}$ |  42.0${}^{+0.3}_{-0.3}$
J1444+4237 |  54${}^{+18}_{-18}$ |  112${}^{+37}_{-37}$ |  14.07${}^{+0.08}_{-0.08}$ |  14.99${}^{+0.02}_{-0.02}$ |  14.06${}^{+0.06}_{-0.06}$ |  20.68${}^{+0.03}_{-0.03}$ |  18.25${}^{+0.15}_{-0.13}$ |  0.40${}^{+0.06}_{-0.06}$ |  44.4${}^{+15.3}_{-15.0}$ |  34.4${}^{+0.3}_{-0.4}$ |  32.9${}^{+0.1}_{-0.1}$ |  41.1${}^{+0.4}_{-0.5}$
J1448–0110 |  145${}^{+43}_{-43}$ |  220${}^{+73}_{-73}$ |  14.03${}^{+0.06}_{-0.06}$ |  15.27${}^{+0.02}_{-0.02}$ |  14.66${}^{+0.07}_{-0.07}$ |  20.50${}^{+0.03}_{-0.03}$ |  17.57${}^{+0.02}_{-0.02}$ |  0.85${}^{+0.15}_{-0.15}$ |  1.2${}^{+0.5}_{-0.4}$ |  33.1${}^{+0.2}_{-0.3}$ |  31.6${}^{+0.1}_{-0.1}$ |  40.1${}^{+0.4}_{-0.5}$
J1521+0759 |  161${}^{+54}_{-54}$ |  398${}^{+133}_{-133}$ |  14.48${}^{+0.05}_{-0.05}$ |  15.49${}^{+0.02}_{-0.02}$ |  14.68${}^{+0.04}_{-0.04}$ |  20.48${}^{+0.03}_{-0.03}$ |  17.49${}^{+0.03}_{-0.02}$ |  0.54${}^{+0.11}_{-0.11}$ |  3.6${}^{+1.5}_{-1.3}$ |  33.5${}^{+0.3}_{-0.4}$ |  33.0${}^{+0.1}_{-0.1}$ |  40.3${}^{+0.4}_{-0.5}$
J1525+0757 |  408${}^{+28}_{-28}$ |  495${}^{+59}_{-59}$ |  15.21${}^{+0.14}_{-0.14}$ |  15.93${}^{+0.02}_{-0.02}$ |  14.82${}^{+0.04}_{-0.04}$ |  20.92${}^{+0.06}_{-0.06}$ |  18.21${}^{+0.04}_{-0.02}$ |  0.87${}^{+0.15}_{-0.15}$ |  20.6${}^{+5.6}_{-4.8}$ |  34.7${}^{+0.1}_{-0.1}$ |  33.9${}^{+0.1}_{-0.1}$ |  42.1${}^{+0.1}_{-0.1}$
J1545+0858 |  113${}^{+33}_{-33}$ |  203${}^{+51}_{-51}$ |  15.16${}^{+0.15}_{-0.15}$ |  15.77${}^{+0.03}_{-0.03}$ |  14.62${}^{+0.06}_{-0.06}$ |  21.38${}^{+0.05}_{-0.06}$ |  20.19${}^{+0.27}_{-0.36}$ |  0.61${}^{+0.06}_{-0.06}$ |  14.4${}^{+5.8}_{-5.0}$ |  34.1${}^{+0.2}_{-0.3}$ |  32.8${}^{+0.1}_{-0.1}$ |  40.9${}^{+0.3}_{-0.5}$
J1612+0817 |  459${}^{+63}_{-63}$ |  732${}^{+158}_{-158}$ |  15.43${}^{+0.11}_{-0.11}$ | … | … | … | … | … | … | … | … | …
J2103–0728${}^{\text{(H15)}}$ |  208${}^{+21}_{-21}$ |  290${}^{+97}_{-97}$ |  15.18${}^{+0.12}_{-0.12}$ |  15.83${}^{+0.02}_{-0.02}$ |  14.64${}^{+0.07}_{-0.07}$ |  20.47${}^{+0.04}_{-0.04}$ |  17.82${}^{+0.01}_{-0.02}$ |  0.79${}^{+0.10}_{-0.10}$ |  4.2${}^{+1.1}_{-0.9}$ |  33.9${}^{+0.1}_{-0.1}$ |  33.4${}^{+0.1}_{-0.1}$ |  41.2${}^{+0.2}_{-0.2}$
Notes: (1) Measured outflow information for 45 galaxies from the CLASSY sample
and 5 galaxies from Heckman et al. (2015). The latter is marked as (H15).
Descriptions for each column: (2) and (3) Measured outflow velocity (the
absolute value) and FWHM, respectively (Section 4.2); (4) and (6) Measured
column density of outflows from Si ii and Si iv lines (Section 5.1); (5), (7),
(8) CLOUDY models predicted column density for Si iii, total hydrogen, and H
i, respectively (Section 5.3); (9) The average covering fraction of outflows
(Section 5.1); (10), (11), and (13): The mass, momentum, energy rate of
outflows, respectively (Section 5.4.4 and 5.4.5); (12) the critical momentum
flux to drive the outflows discussed in Section 6.2. * These objects are
marked as “No Outflow” because less than half of their observed absorption
troughs show blue-shifted outflow component. Note that the rest ($<$ half) of
their absorption troughs may still show outflow features. See discussion in
Section 4.2.

Table 6: Ancillary Parameters for Galaxies in the Combined Sample(1) Object | $z$ |  r50 |  r50 | $V_{\text{cir}}$ |  log SFR/M⋆ | log SFR/A
---|---|---|---|---|---|---
|  | (″) | (kpc) |  (km s-1) |  (yr-1) |  (M$\odot$/yr/kpc2)
| (2) | (3) | (4) | (5) | (6) | (7)
J0021+0052 | 0.09839 | 0.25 | 0.45 |  72.1${}^{+20.8}_{-8.0}$ |  -8.02${}^{+0.21}_{-0.40}$ |  0.98${}^{+0.14}_{-0.16}$
J0036–3333 | 0.02060 | 0.28 | 0.11 |  74.1${}^{+12.1}_{-11.7}$ |  -8.12${}^{+0.33}_{-0.30}$ |  2.09${}^{+0.23}_{-0.21}$
J0055–0021${}^{\text{(H15)}}$ | 0.16744 | 0.20 | 0.56 |  98.3${}^{+22.3}_{-9.6}$ |  -7.93${}^{+0.38}_{-0.35}$ |  1.34${}^{+0.36}_{-0.19}$
J0127–0619 | 0.00550 | 0.15 | 0.02 |  57.0${}^{+6.0}_{-6.3}$ |  -9.49${}^{+0.22}_{-0.21}$ |  1.88${}^{+0.16}_{-0.17}$
J0144+0453 | 0.00532 | 3.54 | 0.43 |  27.5${}^{+5.8}_{-4.1}$ |  -8.46${}^{+0.52}_{-0.41}$ |  -0.88${}^{+0.51}_{-0.41}$
J0150+1308${}^{\text{(H15)}}$ | 0.14668 | 0.25 | 0.63 |  115.3${}^{+21.6}_{-13.6}$ |  -8.29${}^{+0.39}_{-0.32}$ |  1.11${}^{+0.35}_{-0.20}$
J0337–0502 | 0.01346 | 1.62 | 0.46 |  18.5${}^{+2.7}_{-2.8}$ |  -7.37${}^{+0.26}_{-0.22}$ |  -0.44${}^{+0.43}_{-0.84}$
J0405–3648 | 0.00280 | 6.43 | 0.50 |  13.7${}^{+2.9}_{-2.3}$ |  -8.42${}^{+0.39}_{-0.42}$ |  -2.01${}^{+0.30}_{-0.34}$
J0808+3948 | 0.09123 | 0.08 | 0.13 |  73.1${}^{+8.8}_{-13.2}$ |  -7.85${}^{+0.39}_{-0.25}$ |  2.27${}^{+0.27}_{-0.20}$
J0823+2806 | 0.04730 | 0.28 | 0.25 |  87.2${}^{+11.6}_{-17.4}$ |  -7.90${}^{+0.46}_{-0.24}$ |  1.88${}^{+0.33}_{-0.17}$
J0926+4427 | 0.18030 | 0.23 | 0.66 |  57.8${}^{+10.9}_{-10.5}$ |  -7.73${}^{+0.33}_{-0.29}$ |  0.59${}^{+0.16}_{-0.14}$
J0934+5514 | 0.00264 | 1.53 | 0.11 |  10.9${}^{+1.6}_{-0.9}$ |  -7.79${}^{+0.14}_{-0.22}$ |  -0.42${}^{+0.07}_{-0.09}$
J0938+5428 | 0.10210 | 0.28 | 0.51 |  75.0${}^{+15.8}_{-8.3}$ |  -8.10${}^{+0.25}_{-0.35}$ |  0.84${}^{+0.20}_{-0.21}$
J0940+2935 | 0.00171 | 3.06 | 0.18 |  14.6${}^{+4.5}_{-2.1}$ |  -8.71${}^{+0.44}_{-0.58}$ |  -1.34${}^{+0.37}_{-0.42}$
J0942+3547 | 0.01483 | 0.33 | 0.10 |  25.8${}^{+5.6}_{-3.3}$ |  -8.31${}^{+0.24}_{-0.35}$ |  0.45${}^{+0.15}_{-0.21}$
J0944+3424 | 0.02005 | 3.74 | 1.52 |  39.5${}^{+6.4}_{-9.3}$ |  -8.20${}^{+0.77}_{-0.36}$ |  -1.17${}^{+0.65}_{-0.28}$
J0944–0038 | 0.00487 | 2.34 | 0.28 |  15.9${}^{+2.9}_{-3.9}$ |  -7.60${}^{+0.45}_{-0.31}$ |  -0.46${}^{+0.16}_{-0.19}$
J1016+3754 | 0.00391 | 1.52 | 0.15 |  14.8${}^{+2.3}_{-2.4}$ |  -7.89${}^{+0.32}_{-0.28}$ |  -0.34${}^{+0.18}_{-0.18}$
J1024+0524 | 0.03326 | 0.40 | 0.26 |  32.1${}^{+5.5}_{-7.0}$ |  -7.67${}^{+0.39}_{-0.28}$ |  0.57${}^{+0.15}_{-0.17}$
J1025+3622 | 0.12720 | 0.35 | 0.77 |  62.1${}^{+12.2}_{-9.5}$ |  -7.83${}^{+0.31}_{-0.30}$ |  0.46${}^{+0.20}_{-0.17}$
J1044+0353 | 0.01286 | 0.38 | 0.10 |  15.6${}^{+3.0}_{-3.7}$ |  -7.39${}^{+0.43}_{-0.28}$ |  0.60${}^{+0.17}_{-0.14}$
J1105+4444 | 0.02148 | 4.11 | 1.79 |  66.9${}^{+11.7}_{-11.8}$ |  -8.29${}^{+0.37}_{-0.37}$ |  -0.61${}^{+0.22}_{-0.28}$
J1112+5503 | 0.13153 | 0.20 | 0.46 |  100.5${}^{+13.9}_{-19.7}$ |  -7.99${}^{+0.41}_{-0.28}$ |  1.48${}^{+0.27}_{-0.22}$
J1113+2930${}^{\text{(H15)}}$ | 0.17514 | 0.37 | 1.07 |  92.3${}^{+16.5}_{-12.1}$ |  -8.60${}^{+0.28}_{-0.41}$ |  0.0${}^{+0.20}_{-0.34}$
J1119+5130 | 0.00444 | 2.18 | 0.13 |  15.3${}^{+3.0}_{-1.4}$ |  -8.35${}^{+0.18}_{-0.34}$ |  -0.62${}^{+0.11}_{-0.21}$
J1129+2034 | 0.00466 | 0.38 | 0.04 |  36.8${}^{+7.4}_{-8.1}$ |  -8.46${}^{+0.67}_{-0.47}$ |  1.56${}^{+0.56}_{-0.39}$
J1132+1411 | 0.01763 | 8.86 | 3.19 |  54.8${}^{+7.5}_{-9.3}$ |  -8.25${}^{+0.39}_{-0.31}$ |  -1.37${}^{+0.27}_{-0.24}$
J1132+5722 | 0.00510 | 0.84 | 0.10 |  21.9${}^{+4.2}_{-3.1}$ |  -8.38${}^{+0.42}_{-0.38}$ |  0.11${}^{+0.35}_{-0.28}$
J1144+4012 | 0.12695 | 0.40 | 0.89 |  122.3${}^{+26.2}_{-13.9}$ |  -8.37${}^{+0.34}_{-0.35}$ |  0.82${}^{+0.31}_{-0.21}$
J1148+2546 | 0.04524 | 1.31 | 1.17 |  38.2${}^{+6.8}_{-7.8}$ |  -7.61${}^{+0.37}_{-0.30}$ |  -0.40${}^{+0.15}_{-0.17}$
J1150+1501 | 0.00250 | 1.29 | 0.09 |  16.0${}^{+3.5}_{-2.7}$ |  -8.17${}^{+0.36}_{-0.41}$ |  -0.08${}^{+0.23}_{-0.29}$
J1157+3220 | 0.01120 | 2.89 | 0.68 |  69.5${}^{+9.0}_{-13.3}$ |  -8.07${}^{+0.53}_{-0.28}$ |  0.51${}^{+0.42}_{-0.21}$
J1200+1343 | 0.06690 | 0.18 | 0.22 |  37.6${}^{+12.0}_{-10.1}$ |  -7.37${}^{+0.49}_{-0.46}$ |  1.27${}^{+0.18}_{-0.21}$
J1225+6109 | 0.00233 | 2.91 | 0.21 |  19.3${}^{+3.4}_{-3.9}$ |  -8.19${}^{+0.43}_{-0.36}$ |  -0.50${}^{+0.26}_{-0.26}$
J1253–0312 | 0.02267 | 0.85 | 0.39 |  27.4${}^{+4.5}_{-7.8}$ |  -7.09${}^{+0.53}_{-0.27}$ |  0.58${}^{+0.15}_{-0.15}$
J1314+3452 | 0.00285 | 0.30 | 0.03 |  25.9${}^{+4.0}_{-4.6}$ |  -8.24${}^{+0.63}_{-0.31}$ |  1.72${}^{+0.56}_{-0.24}$
J1323–0132 | 0.02246 | 0.23 | 0.10 |  11.2${}^{+0.8}_{-1.8}$ |  -7.03${}^{+0.28}_{-0.12}$ |  0.47${}^{+0.13}_{-0.11}$
J1359+5726 | 0.03390 | 1.10 | 0.74 |  45.5${}^{+8.6}_{-8.4}$ |  -7.98${}^{+0.33}_{-0.32}$ |  -0.11${}^{+0.14}_{-0.20}$
J1414+0540${}^{\text{(H15)}}$ | 0.08190 | 0.23 | 0.36 |  107.6${}^{+17.0}_{-19.7}$ |  -8.12${}^{+0.51}_{-0.32}$ |  1.67${}^{+0.91}_{-0.48}$
J1416+1223 | 0.12316 | 0.13 | 0.27 |  100.3${}^{+19.2}_{-19.5}$ |  -8.02${}^{+0.41}_{-0.34}$ |  1.91${}^{+0.27}_{-0.23}$
J1418+2102 | 0.00857 | 0.40 | 0.08 |  10.6${}^{+2.8}_{-2.9}$ |  -7.35${}^{+0.51}_{-0.38}$ |  0.31${}^{+0.19}_{-0.17}$
J1428+1653 | 0.18170 | 0.35 | 1.04 |  98.3${}^{+16.6}_{-9.5}$ |  -8.34${}^{+0.24}_{-0.35}$ |  0.39${}^{+0.21}_{-0.27}$
J1429+0643 | 0.17350 | 0.15 | 0.43 |  59.0${}^{+9.0}_{-12.3}$ |  -7.38${}^{+0.39}_{-0.24}$ |  1.35${}^{+0.19}_{-0.14}$
J1444+4237 | 0.00219 | 8.20 | 7.33 |  12.6${}^{+1.5}_{-1.3}$ |  -8.42${}^{+0.18}_{-0.20}$ |  -4.47${}^{+0.08}_{-0.11}$
J1448–0110 | 0.02738 | 0.23 | 0.12 |  26.7${}^{+4.6}_{-6.4}$ |  -7.22${}^{+0.44}_{-0.27}$ |  1.41${}^{+0.17}_{-0.16}$
J1521+0759 | 0.09426 | 0.28 | 0.47 |  67.7${}^{+15.0}_{-11.8}$ |  -8.05${}^{+0.34}_{-0.34}$ |  0.80${}^{+0.20}_{-0.18}$
J1525+0757 | 0.07579 | 0.25 | 0.35 |  137.3${}^{+44.6}_{-23.5}$ |  -9.06${}^{+0.37}_{-0.81}$ |  1.10${}^{+0.26}_{-0.70}$
J1545+0858 | 0.03772 | 0.33 | 0.24 |  25.1${}^{+4.8}_{-6.3}$ |  -7.15${}^{+0.47}_{-0.29}$ |  0.80${}^{+0.20}_{-0.16}$
J1612+0817 | 0.14914 | 0.20 | 0.51 |  113.7${}^{+21.3}_{-19.3}$ |  -8.20${}^{+0.37}_{-0.38}$ |  1.37${}^{+0.26}_{-0.29}$
J2103–0728${}^{\text{(H15)}}$ | 0.13689 | 0.10 | 0.24 |  159.5${}^{+48.4}_{-25.4}$ |  -9.00${}^{+0.44}_{-0.64}$ |  1.74${}^{+0.36}_{-0.51}$
Notes: (1) Ancillary parameters for 45 galaxies from the CLASSY sample and 5
galaxies from Heckman et al. (2015). The latter is marked as (H15). The
derivation of these parameters are discussed in Section 4.4. Descriptions for
each column: (2) Redshift of the galaxy derived from UV emission lines; (3)
and (4) Adopted half-light radius for each galaxy in units of ″ and kpc,
respectively, which are derived from either HST/COS or optical images; (5)
Measured galaxy circular velocity; (6) and (7) The log of specific star-
formation rate (SFR) and SFR per unit area, respectively, which are derived
from SED fittings.

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pnasresearcharticle Kadriu All authors contributed equally to this work. 1To
whom correspondence should be addressed. E-mail<EMAIL_ADDRESS>
# Extractive approach for text summarization using graphs

Kastriot Kadriu  University of Ljubljana, Faculty of Computer and Information
Science, Večna pot 113, SI-1000 Ljubljana, Slovenia  Milenko Obradovic
University of Ljubljana, Faculty of Computer and Information Science, Večna
pot 113, SI-1000 Ljubljana, Slovenia

###### Abstract

Natural language processing is an important discipline with the aim of
understanding text by its digital representation, that due to the diverse way
we write and speak, is often not accurate enough. Our paper explores different
graph related algorithms that can be used in solving the text summarization
problem using an extractive approach. We consider two metrics: sentence
overlap and edit distance for measuring sentence similiarity. Relevant
structures have been implemented and the code can be obtained in this link
(1).

###### doi:

Introduction to Network Analysis 2020/21

The manuscript was compiled on

While the quantity of information is growing exponentially, there’s a need to
compress the content in condensed versions. The summarization of information
is a problem that deals with presenting the main idea of the text without the
need to read all the content of the text. Such task is heavily relied on the
calculation of sentence similiarity, and in that regard, various methods have
been tried.
Two methods for automatic text summarization are considered: extractive and
abstractive. Extractive summarization is based on the identification of
important sections of the text and producing a subset of the sentences from
the original text, whereas abstractive summarization tries to reproduce the
important content in a new way after interpretation and examination of text
using more advenced techniques.
Supervised summarization models are built by treating the problem as a
classification task, and by classifying which features in a sentence are
relevant for summarization.
Those models aren’t very reliable because of the unpredictable nature of
language, from which it is not easy to generate a classification pattern. In
addition, such models require training data which worsen the data acquisition
problem which is already a challenge on its own.
Task summarization problem concerns itself with representing data in such way
that the importance of each sentence and their terms is properly considered.
Text should be represented in such ways that the inter-word and inter-sentence
dependency is kept.
The task is challenged by a sustainable data source for validation and
subsequently, an efficient metric for evaluating it and other text-
understanding tasks. The challenges are topics of Document Understanding
Conference, which later became Text Analaysis Conference. A domain-independent
evaluation is also complex to be achieved. For example, a model reporting a
high accuracy in summarizing news articles might not perform with the same
accuracy when summarizing, let’s say, Reddit posts.
Generally, best performing models are deep learning based. The construction of
such models is faced with challenges of its own mainly regarded with
computational resources. For that reason, it’s important to consider more
simpler approaches like the ones that are presented in this paper.
Our contribution includes a direct implementation of graph-based algorithms
for computing relevant data that could summarize the test documents the best.
The respective algorithms help us extract the most important sentences that
will constitute the summary. We test two different metrics for computing
sentence similiarity, and in one of them we employ a notion of graph
similiarity - edit distance - Figure 1.

Figure 1: Pipeline of our model

## Related work

Text summarization is an open problem. There hasn’t been report of an official
model who can achieve a decent data-independent accuracy. Current state-of-art
models achieve accuracy of around 50% percent. Those models are usually deep
learning models. (6) achieves state-of-the-art results on the CNN/Daily mail
dataset. The model presented there is the Reinforced Neural Extractive
Summarization (RNES) model. (5) presents a general overview of two ranking
algorithms - PageRank and HITS, and an agnostic overview of building a graph
representation of text to be used for summarization by extraction. In
addition, for smooth-er outputs, shortest path algorithm is suggested. This
paper lacks concrete results tested on some dataset.
(2, 15) dive deeper in the use of PageRank algorithm for text summarization,
whose use in such cases is referred to as TextRank. Sentences are extracted
using the respective algorithm in a weighted graph built with nodes
representing the sentences to be summarized, and weighted edges represent the
similarity those sentences have with each other. Similiarity between sentences
is calculated as their overlap which can be determined as the number of common
words between their lexical representation. The resulting model is an
unsupervised model that has achieved 47% accuracy, as evaluted by the ROGUE
metric, on 567 news articles provided by the Document Understanding
Evaluations (DUC) 2002. The paper also explores the use of TextRank in keyword
extraction. The paper introduces the respective algorithm very well but could
benefit by the computation of a larger batch of test data.

(8) implements the TextRank algorithm and expands on the pre and post-
processing part. The data (sentences) is encoded and different methods are
considered such as tf-idf and Word2vec. Moreover, the implementation is tested
on Malayaian content, demonstrating the domain independence of the algorithm.
Another extractive text summarization algorithm is LexRank, which is based on
computing the importance of a sentence by the concept of eigenvector
centrality presented in (10). The similiarity between sentences, also
represented as nodes, is calculated as the cosine similiarity between the
vector of their words mapped as their idf values.
Topic based approaches are seen on (11, 13, 14). They are based on the
distribution of words accross documents from which it is possible to derive
topics that later constitute summaries. (17) treats the problem of
summarization as a compression problem that could be integrated in both
extractive and abstractive summarization approaches, and (4) builds a small
world network to summarize biomedical articles.

## Results

Native structures have been implemented with the aim of supporting
experiments. Graphs have been created using NetworkX (23), whereas linguistic
processing has been done with nltk (22) and stanza (16).
The aim of our experiments was to test how well different centrality measures
are able to identify the most important parts of the text. For that reason, we
consider pagerank, hits, closeness, betweenness and degree measures. In
addition, when construction the edges of the graph, we use two different
metrics for measuring how similar two sentences are, thus determing the weight
of the link between those two nodes: word overlap and edit distance. The edge
candidates are then ranked based on their weight, and then, by a threshold
value, the edges with the top weights are created.
The model has been evaluated using 3500 documents from the CNN/Dailymail (18,
19) dataset - Table 1, which is a collection of news articles with their
highlights serving as our summarization tests.

Table 1: CNN/Dailymail dataset statistics. Number of test documents | 3500
---|---
Average document length | 33 sentences
Average summary length | 5 sentences
Average document-summary compression | 0.85

Various methods have been tested with two different metrics: sentences overlap
and sentences edit distance (TED). After employing strategies described in the
Methods section, top five sentences, number which is based on the average
summary length, are extracted that represent the generated summary with our
method(s). The summary is then compared with the ground truth summary provided
in the dataset using the ROGUE metric.
Edit distance for sentence similiarity is more time consuming because it adds
three extra steps in our pipeline: word dependency parsing, tree construction
and edit distance calculation.
We report on recall and F1 score values. We are using recall to evaluate how
much of the ’correct’ content is included in summaries, and F1 score to give a
balanced evaluation score that is not based on the attributes that recall
takes into account such as the summary length.

Table 2: Recall values of the evaluation using the sentence overlap metric and t=0.5. Method | Rogue-1 | Rogue-2 | Rogue-L
---|---|---|---
Pagerank | 0.50 | 0.19 | 0.44
Hits | 0.48 | 0.19 | 0.42
Closeness | 0.50 | 0.20 | 0.45
Betweenness | 0.50 | 0.20 | 0.44
Degree | 0.50 | 20 | 0.45
Clusters | 0.47 | 0.18 | 0.42
Table 3: Recall values of the evaluation using TED metric and t=0.5. Method | Rogue-1 | Rogue-2 | Rogue-L
---|---|---|---
Pagerank | 0.48 | 0.17 | 0.426
Hits | 0.48 | 0.17 | 0.423
Closeness | 0.51 | 0.19 | 0.45
Betweenness | 0.51 | 0.19 | 0.45
Degree | 0.51 | 0.19 | 0.45
Clusters | 0.43 | 0.14 | 0.38
Table 4: F score values of the evaluation using the sentence overlap metric and t=0.5. Method | Rogue-1 | Rogue-2 | Rogue-L
---|---|---|---
Pagerank | 0.26 | 0.10 | 0.28
Hits | 0.26 | 0.10 | 0.28
Closeness | 0.28 | 0.12 | 0.30
Betweenness | 0.28 | 0.11 | 0.29
Degree | 0.28 | 0.11 | 0.29
Clusters | 0.27 | 0.10 | 0.27
Table 5: F score values of the evaluation using TED metric and t=0.5. Method | Rogue-1 | Rogue-2 | Rogue-L
---|---|---|---
Pagerank | 0.24 | 0.08 | 0.244
Hits | 0.24 | 0.08 | 0.246
Closeness | 0.24 | 0.09 | 0.25
Betweenness | 0.24 | 0.09 | 0.25
Degree | 0.24 | 0.09 | 0.25
Clusters | 0.25 | 0.08 | 0.25

The results from Table 2, 3, 4 and 5 might not have very seductive numbers but
they are standard numbers across summarization models and are actually
comparable with the state-of-the-art models, like the one in (6), although we
can not make direct comparisons because their model has been tested in a
greater batch of testing data than ours. Rogue-1 tells us the number of golden
tokens found in the summary. Rogue-2 tells us the number of bigrams that were
matched between test and ground truth summary but the values here aren’t
expected to be high as the ordering of the sentences (and words, although
since our approach is extractive, that’s not a big issue for our case)
matters. Rouge-L is an important value to consider as it measures the relation
of the two contents in a wider context.

## Discussion

The performance of closeness, betweenness and degree centrality measures is
approximate with each other. It is completely affected by the threshold value
that determines the number of edges to be created. Hypothetically, if the
threshold is 1, the output of the summary would be the first 5 lines of the
article. In addition, using those methods, there is a limitation on the
possibilities for fine tuning the results.
Pagerank and hits perform the most consistently, and that is based on the fact
that those algorithms take into account the weight of the edges. Those methods
aren’t affected by the number of generated edges, as long as the weights are
properly accounted for. Those methods are in the same spirit, they both
formalise link analysis as eigenvector problems. Pagerank reports higher
accuracy because it is able to operate in the complete graph, unlike Hits
which operates on a smaller subgraph. In addition, those methods work well
because they do not rely on the isolated information regarding the node but
instead, they take into account the entire graph and the relationships within.
The clustering method offers more room for tuning the results. The clustering
process is based on finding cliques which is a hard problem. It is more
computationally expensive compared to other algorithms. It performs best with
the tree edit distance as this measure is able to represent the similiarity of
sentences for clustering purposes. It is affected by the threshold parameter.
The lack of higher numbers in the results is not neccessarily because of the
actual quality of our summaries, rather than the limitation that ROGUE metric
has. ROGUE address content selection between the test and the grouth truth
content without accounting for other quality aspects such as coherence,
gramamaticality or fluency. The content selection is relied on lexical overlap
but a good summary isn’t always expressed with the same lexical links, and
this happens especially in abstractive summarization. It would have been nice
if there were more ground truth summaries to compare our generated summaries
with, as they could constitute a more leveled evaluation. The dataset we used,
however, provided only one summary per article.
Our paper offers an overview in using graphs to represent the relation that
sentences have, relevant algorithms for detecting the relationships within the
graph and presenting them but it could be improved in several ways. First, a
more natural way of picking the top relevant sentences for summary can be
integrated, instead of arbitrary picking top $N$ sentences. Then, to have
results tailored for specific purposes, the sentence similiarity metrics could
have been modified to report higher scores for the presence of certain
structures in the sentences, such as noun, verbs or adjectives.
The clustering method could be favorable as we can incorporate a hybrid
approach towards summarization by turning the problem into a graph compression
problem after finding the relevant clusters, where for each cluster we try to
compress it into a single sentence by linking the most important part of
sentences. Other than text summarization, the findings in this paper can also
be referenced as proposals for solving classification problems using graphs.
The work on text summarization problem needs to be supported by a standard
dataset that covers a more diverse textual content. Future work should also
approach new metrics for content evaluation that could overcome ROGUE
limitations. Such metrics should account for the relation that words have with
each other, preferrably through an embedding methodology and based on an
external corpus, although in the first sight this already looks
computationally heavy and that’s another issue that would need to be taken
care off.

## Methods

### Pre-processing

Sentences of a document have been tokenized, cleaned up and the next processes
have been executed depending on the metric. For the sentence similiarity, the
words in sentences are represented by their lemmas so that the context is not
missed even if words are in different forms. For the edit distance, we build
dependency parsed trees for each sentence using the stanford parser (stanza).

### Metrics

One metric used for measure sentence similiarity is by checking their
overlapping words (2). To avoid bias on long sentences, the number of
overlapping words is normalised by the lengths of both sentences.

$Sim(S_{i},S_{j})=\frac{|\\{w_{k}|w_{k}\in S_{i}\&w_{k}\in
S_{j}\\}|}{log(|S_{i}|+log(|S_{j}|))}$

The other metric used to measure how similar two sentences are is the edit
distance, in our case since the sentences are represented as tree, we work
with tree edit distance. The tree edit distance (TED) (21) is calculated using
the algorithm proposed by Zhang and Shasha in (20). TED is a more accurate
metric because it is able to account for the number of words in a sentence
needed to be changed to match the other sentence, as compared to string based
distance metrics that report on character changes, and such metric would be
totally incorrect when comparing sentences of different lengths. The
similarity of two sentences based on their distance is calculated as:

$Sim(i,j)=\frac{1}{1+d(T_{i},T_{j})}$

### Graph construction

After the document has been processed into sentences, we construct the
undirected graph by generating a node for each sentence. Then, similiarities
between each pair of sentences is calculated. Afterwards, the similiarities
are sorted from highest to lowest, and based on a user defined threshold $t$,
we pick the top $t$ percent of similiar pairs to serve as the edges of the
graph.

Figure 2: Sentence similiarity graphs generated using t=0.1 and t=0.5
respectively.

### Algorithms

The implementation of PageRank, Hits, Closeness, Betweenness and degree
measures is straight forward - after the scores for each node(sentence) have
been computed, they are ranked and top N sentences are picked where $N$ is a
user defined parameter symbolizing the desired summary length. Whereas, for
the clustering method, after the cliques in the graph have been found we
process them in the following way:

  * •

we ignore cliques with one item

  * •

for cliques with more than two items, we consider their closeness scores from
which we pick the one item with the highest scores

  * •

in case one item is found to be the highest scoring item in more than one
clique, we pick that as the representive for the cluster with the bigger
clique, and the selection moves onto the second highest scoring item in the
remaining clique

### Evaluation

Our extracted summaries are evaluated using the Recall-Oriented Understudy for
Gisting Evaluation - ROGUE metric. We have incorporated three types of ROGUE
evaluation metric. Rogue-1, the overlap of unigrams (each word) between
extracted summary and ground truth summary provided in the dataset, Rogue-2,
the overlap of bigrams in the respective relation, and Rogue-L which reports
on the longest common subsequence statistics. The authors would like to
acknowledge these works:

## References

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