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2010年12月1日水曜日

Further investigations into a proposed peak Touhou music phenomenon;
以前指摘された東方同人音楽隆盛の上限に対するさらなる調査
ダウンロード数から見た海外での東方ブーム

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/* /jp/のhghgdさんからメールを頂いたので翻訳しました。 */
/* 私は統計については無知で理解するのに時間がかかったのですが、興味深いデータです。 */
/* torrentファイルのダウンロード数とファイルサイズを表にして計測しています。 */


>> No.6457743

Doujin game fan music enthusiasts and connoisseurs were alarmed [1] when [2] suggested we have reached ``peak touhou'', i.e. the point in time when the global rate of Touhou music production has hit its maximum and will not further increase. For a slightly more thorough analysis of this phenomenon, we have scraped release count data of Touhou related albums from vgmdb [3] and reworked the data from the torrent's size. The vgmdb search result dataset consists of 2286 album release dates from Dec 30, 2002 through Dec 31, 2010 (presumed announced). It has the following properties:

Min. 1st Qu. Median Mean 3rd Qu. Max.
1.000 1.000 1.000 9.181 4.000 166.000

[2]に示すデータが我々に、”東方ブームの上限”、つまり世界的な東方同人音楽の生産率が最大限に達し、もうさらに伸びることはないだろうということを指し示したとき、同人ゲーム音楽の熱狂的なファンや玄人たちは[1]に示すスレッドにおいて警鐘を鳴らした。この現象に対し幾許かの分析を通して、[3]に示すvgmdbから関係している東方のアルバムがダウンロードされている数を取り出して、そしてそのtorrentのサイズからデータを再構成した。vgmdbにおける検索結果のデータは2002年の12月30日から2010年の12月31日まで(事前に告知されている)にリリースされた2286のアルバムで構成されている。それらは以下のような性質を持っている。

最小値 第1四半期 中央値 平均 第3四半期 最大値
1.000  1.000   1.000 9.181  4.000  166.000

>> No.6457753
File: 32 KB, 800x800, figure1_touhou_music_distribution.png [View same] [iqdb]

Its cumulative fractional distribution function is plotted in figure 1. Only little growth occurred in 2003 and 2004. Much more, almost linear growth can be observed from 2005 through 2008. In 2009 notably more albums were released. The (incomplete) data for 2010 suggests that there might be far less releases in that year. The green dotted line indicates the date the data was collected (Nov 5, 2010). Please note that it is possible that a smaller part of the albums released shortly before the data was collected might be indexed by VGMdb.

その次第に増加が見られる断片的な分布関数は図1に示されている。2003から2004年にはわずかな増加しか見られない。さらに、2005から2008年にはほとんど直線的な増加が観察される。2009年にはさらに著しくアルバムがリリースされている。2010年のデータ(不完全)は年内にほとんどリリースがないであろうということを示唆している。緑の点線はデータが収集された日時(2010年11月5日)を示している。VGMdbの目録に追加されたデータが集められる前に、アルバムのわずかな部分しかリリースされていない可能性があることを注意して欲しい。

>> No.6457765
File: 47 KB, 1200x800, figure2_touhou_music.png [View same] [iqdb]

When we collate the data by months we can get another view on the release patterns. That dataset has the these basic properties:

Min. 1st Qu. Median Mean 3rd Qu. Max.
1.00 4.00 8.50 29.19 39.75 173.00

The combined plot of monthly releases and torrent size in figure 2 clearly reveals the well-known correlation of overperforming months during which major events (Comiket and Reitaisai) took place. These months have remained remarkably levelled in release count from Reitaisai 2 (March 2005) through Comiket 72 (summer 2007), followed by a steep, though not regular, incline up to 2009's Reitaisai.

そこで、月ごとのデータを収集すればリリースの傾向において他の見解を得ることができる。そのデータセットにおいては以下のような基本プロパティを持つ。

最小値 第1四半期 中央値 平均 第3四半期 最大値
 1.00   4.00   8.50  29.19  39.75   173.00

月ごとのリリース数とtorrentのファイルサイズを合成した図2は、大規模なイベント(コミケや例大祭)が行われた月に見られる数値の大幅な増大とのよく知られている相関性を明らかにしてくれる。これらの月は第二回例大祭(2005年3月)から第72回コミックマーケット(2007年夏)までそのリリース数において著しく一様である、しかしここでグラフは急勾配ながらも一様ではないカーブを描き、2009年の例大祭までその勾配を上げ続ける。

>> No.6457776

The next three months with events again have release counts in roughly the same range. Summer Comiket 2010 on the other hand has fewer albums. Of course no final judgment for 2010 can be given until after Winter Comiket (end of December), especially given the observation that Winter Comikets seem to have slightly more releases throughout the observed period on average.
The ``peak'' observed by rwx is not as apparant in this chart as it is a plot of totals, not differences, as is his. The growth in 2009 and 2010 appears to be quite linear, though.
The dotted lines are ``LOESS'' smoothed fit curves with a smoother span (or alpha) of 1/2 for both datasets. The fit curves are for illustrative purposes only, as the standard deviation in the releases is obviously very high.

イベントを抱えた次の三ヶ月では、またリリース数においてグラフは大方同じような山を描くだろう。一方で2010年の夏コミで出展されるアルバムの数はわずかである。もちろん冬コミ(12月の終わり)まで最終的な判断は与えることができないだろうが、観察された期間において平均的にわずかながらより多くのリリース数が見込まれている。rwx氏によって観察された「ピーク」というものは、彼が用意した図表と変りない図を表示しているが、それほど明確に示されていないことがわかる。しかしながら、2009年と2010年のグラフの伸びは直線的なのである。点線は「LOESS」を使って、二つの値(ダウンロード量とアルバム数)の二分の一の値を曲線あてはめによって滑らかにした曲線である。その回帰曲線は説明のためだけに作成したもので、そのリリース数における標準偏差は明らかに高い。

※(LOESS:locally weighted scatterplot smoothingの略):局所回帰モデル?
参考:http://en.wikipedia.org/wiki/LOESS
曲線あてはめ、回帰曲線…curve fitting

>> No.6457798

For now the available data remains inconclusive. While no clear indication of a peak could be found, it cannot be ruled out either. Slowdown in the growth rate in 2010 might be a temporary plateau phenomenon (as in the 2005 - 2007 period) and very recent data (which is highly important for trend observation) might be subject to data entry lagging behind releases in VGMdb.

References
[1]
Archived thread 6386321 from /jp/http://archive.easymodo.net/cgi-board.pl/jp/thread/6386321
[2]
rwx: Touhou lossless music collection v.09 (2010.10.24), http://www.nyaatorrents.org/?page=torrentinfo&tid=167750
[3]
Search for ``touhou'' in the ``Any field contains'' field on VGMdb, http://vgmdb.net/search?do=results&id=81614&field=&&page=1 and the following pages

The author can be contacted on rizon, nick is hghgd.
Disclaimer: I'm not actually good at data analysis nor do I claim authority on Touhou music matters, I just happen to like some of it.

現在、利用可能なデータは未だに確定的ではない。ピークについてのいかなる指摘も未だに見つけられない一方で、それについて完全に否定することもできない。2010年における伸び幅の減少は一時的な停滞現象なのかもしれない(2005-2007年にかけての現象のように)そしてごく最近のデータ(傾向の観察のために非常に重要である)はVFMdbから遅れて入手したデータに従っている。

参考文献リスト
[1]
Archived thread 6386321 from /jp/, http://archive.easymodo.net/cgi-board.pl/jp/thread/6386321
[2]
rwx: Touhou lossless music collection v.09 (2010.10.24), http://www.nyaatorrents.org/?page=torrentinfo&tid=167750
[3]
Search for ``touhou'' in the ``Any field contains'' field on VGMdb, http://vgmdb.net/search? do=results&id=81614&field=&&page=1 and the following pages

筆者とはrizonにて連絡を取れます。ニックネームはhghgdです。
注意:私は実際データの解析は得意ではなく、東方音楽の問題について権利を主張するものではありません。私 はただそれが気に入っているだけです。



/* なぜhghgdさんがこのようなことを述べたのかというと、参考文献にもあるようなことがrwx氏によって以前述べられていたからなのです。 */
/* 問題を総括すると、rwx氏がダウンロードの総量のみで東方の衰退を述べていたのに対し、hghgd氏は月ごとのデータと出された東方のアルバムの数を集計して、イベントの時期と重ねあわせることで、東方ブームの衰退が明確に言い表されるものでないことを述べているものと思われます。 */

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