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histograms.tex

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102 | 102 | shows that the table requires no more space than the traditional one, and | |

103 | 103 | because it uses a graphical representation rather than a textual one, it is | |

104 | 104 | instantly readable. | |

105 | % | ||

106 | %The remainder of this article is organized as follows: | ||

107 | %Section~\ref{s:shortcomings} presents the shortcomings of current practices, | ||

108 | %Section~\ref{s:sparklines} describes the concept of sparkline histogram, | ||

109 | %Section~\ref{s:stats} discusses the difficulties of comparing optimization | ||

110 | %methods, Section~\ref{s:comparison} compares stacked focused histograms to | ||

111 | %other ways of presenting experimental data and Section~\ref{s:conc} concludes | ||

112 | %this paper. | ||

105 | 113 | %}}}1 | |

106 | 114 | ||

107 | 115 | \section{\uppercase{Shortcomings of current practices}}\label{s:shortcomings}%{{{1 | |

… | … | ||

141 | 141 | the time to read the numbers carefully and compare them. | |

142 | 142 | %}}}1 | |

143 | 143 | ||

144 | \section{\uppercase{The Sparkline histograms}} %{{{1 | ||

144 | \section{\uppercase{The Sparkline histograms}}\label{s:sparklines} %{{{1 | ||

145 | 145 | ||

146 | 146 | % Since the goal of an author is to describe a set of values and that we ruled | |

147 | 147 | % out the use of any estimator such as the average as not significant on samples | |

… | … | ||

333 | 333 | a full-size example of stacked, focused sparklines and is compared against the | |

334 | 334 | traditional table of average values (in Table~ \ref{tab:stdavg}; see | |

335 | 335 | Section~\ref{s:comparison} for a detailed description of those tables). | |

336 | |||

337 | Reading a sparkline histogram is a three step procedure. First the reader | ||

338 | needs to verify the range, which gives him a rough estimate of the scale of | ||

336 | Reading a sparkline histogram is a three step procedure: | ||

337 | \begin{enumerate} | ||

338 | \item Verify the range, which gives a rough estimate of the scale of | ||

339 | 339 | the values, serving the same function as the average value, or the y-axis of a | |

340 | 340 | convergence graph. If the range is outside of what the reader considers | |

341 | interesting, the rest of the graph can be discarded. The reader should focus | ||

342 | next on the dump bin. Those algorithms that are entirely, or almost entirely | ||

343 | dumped can be discarded as uninteresting. The remaining part is the one the | ||

344 | author of the graphic has deemed interesting. | ||

341 | interesting, the rest of the graph can be discarded. | ||

342 | \item Focus on the dump bin. Those algorithms that are entirely, or almost | ||

343 | entirely dumped can be discarded as uninteresting. | ||

344 | \item Draw conclusions from the remaining part, which is the one the author of | ||

345 | the graphic has deemed interesting. | ||

346 | \end{enumerate} | ||

345 | 347 | ||

346 | 348 | To create a stack of histograms as presented above, the following procedure | |

347 | 349 | has been applied. It must be noted that this procedure assumes that | |

… | … | ||

393 | 393 | the same mean statistic, but one has larger deviation. In the above perspective of | |

394 | 394 | comparing means, we would have to conclude that they are equal, in practise however, | |

395 | 395 | the difference can be crucial as we can run the highly varying | |

396 | algorithm several times to ensure significantly better results. Matters are made | ||

397 | even more complicated by skewed distributions, where we would need to observe even | ||

396 | algorithm several times to ensure significantly better results. Skewed | ||

397 | distributions complicate the matter even further since | ||

398 | %Matters are made | ||

399 | %even more complicated by skewed distributions, where | ||

400 | we would need to observe | ||

401 | %even | ||

398 | 402 | more statistical parameters in addition to variance to decide which algorithm would | |

399 | 403 | be better at the case at hand. | |

400 | 404 | ||

… | … | ||

527 | 527 | ||

528 | 528 | %}}}1 | |

529 | 529 | ||

530 | \section{\uppercase{Conclusions}} % half a page | ||

530 | \section{\uppercase{Conclusions}}\label{s:conc}%{{{1 % half a page | ||

531 | 531 | ||

532 | 532 | In this text we have presented a novel visualization for comparing evolutionary optimization methods. We claim that this visualisation | |

533 | 533 | can convey more information than average/standard deviation tables and statistical test tables while retaining nearly the same usage of |