13 - 5 - Choosing the Number of Clusters (8 min).srt

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In this video I'd like to
在这个视频中
(字幕整理：中国海洋大学 黄海广,haiguang2000@qq.com )

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talk about one last detail
详细讨论一下

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of K-means clustering which is
K均值方法聚类中

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how to choose the number of
如何去选择聚类

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clusters, or how to choose
类别数目 或者说是如何去选择

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the value of the parameter
参数K的值

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capsule K. To be
说实话

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honest, there actually isn't a
其实上没有一个

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great way of answering this
非常好的方法回答这个问题

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or doing this automatically and
或者能够自动做这件事情

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by far the most common way
到目前为止 用来决定聚类

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of choosing the number of clusters,
数目最常用的方法

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is still choosing it manually
任然是通过

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by looking at visualizations or by
看可视化的图或者通过

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looking at the output of the clustering algorithm or something else.
查看聚类算法的输出结果或者其他一些东西来手动地决定聚类的类别数量

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But I do get asked
但是 我也确实经常被问及

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this question quite a lot of
这样的问题

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how do you choose the number of
你是如何来选择聚类的数量的

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clusters, and so I just want
我只是想

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to tell you know what
告诉你

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are peoples' current thinking on
现在人们所思考的

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it although, the most
最为常见的

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common thing is actually to
一件事实际上是

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choose the number of clusters by hand.
手动去选择聚类的数目

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A large part of
其中一大部分

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why it might not always
为什么选择聚类

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be easy to choose the
数量并不容易

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number of clusters is that
的原因是

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it is often generally ambiguous how many clusters there are in the data.
通常在数据集中有多少个聚类是不清楚的

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Looking at this data set
看这样一个数据集

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some of you may see
有些人可能会看到

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four clusters and that
四个聚类

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would suggest using K equals 4.
那么这就意味着需要使用K=4

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Or some of you may
或者有些人可能

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see two clusters and
会看到两个聚类

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that will suggest K equals
这个条件下就意味着K等于

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2 and now this may see three clusters.
2 现在这有可能是3个聚类

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And so, looking at the
那么

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data set like this, the
相类似于这样的数据集

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true number of clusters, it actually
其真实的类别数对我来说实际上

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seems genuinely ambiguous to me,
相当地模棱两可的

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and I don't think there is one right answer.
我并不认为只有一个正确的答案

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And this is part of our supervised learning.
这就是我们监督学习的一部分

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We are aren't given labels, and
我们不知道分类

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so there isn't always a clear cut answer.
因此总是没有一个清晰的答案

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And this is one of the
这是其中的一个

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things that makes it more difficult
使得（决定聚类数目）

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to say, have an automatic
拥有一个自动化

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algorithm for choosing how many clusters to have.
算法来决定聚类数目变得困难的原因

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When people talk about ways of
当人们在讨论

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choosing the number of clusters,
选择聚类数目的方法时

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one method that people sometimes
有一个可能会

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talk about is something called the Elbow Method.
谈及的方法叫作“肘部法则”

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Let me just tell you a little bit about that,
让我告诉你一些关于这个法则的内容

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and then mention some of its advantages but also shortcomings.
之后会提及到它的一些优点和缺点

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So the Elbow Method,
关于“肘部法则”

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what we're going to do is vary
我们所需要做的是改变

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K, which is the total number of clusters.
K值 也就是聚类类别数目的总数

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So, we're going to run K-means
我们用一个聚类来运行K均值聚类方法

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with one cluster, that means really,
这就意味着

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everything gets grouped into a
所有的数据都会分到一个

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single cluster and compute the
聚类里 然后计算

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cost function or compute the distortion
成本函数或者计算畸变函数

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J and plot that here.
J 并将其画在这儿

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And then we're going to run K
之后我们又用两个聚类来运行K

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means with two clusters, maybe
均值聚类 也许

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with multiple random initial agents, maybe not.
有多个随机的初始中心 也许没有

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But then, you know,
但是之后 你知道的

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with two clusters we should
有两个聚类 我们

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get, hopefully, a smaller distortion,
所期望得到的是一个较小的畸变值

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and so plot that there.
把它画在这儿

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And then run K-means with three
之后用选用3个聚类来运行K均值聚类

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clusters, hopefully, you get even
你期望得到一个更

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smaller distortion and plot that there.
小的畸变值 并把它画在这儿

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I'm gonna run K-means with four, five and so on.
之后再用4，5等聚类数来运行均值聚类

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And so we end up with
最后我们就能得到

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a curve showing how the
一条曲线显示

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distortion, you know, goes
随着我们的聚类数量的增多

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down as we increase the number of clusters.
畸变值是如何下降的

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And so we get a curve that maybe looks like this.
我们可能会得到一条类似于这样的曲线

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And if you look at this
看看这条

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curve, what the Elbow Method does
曲线 这就是“肘部法则”所做的

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it says "Well, let's look at this plot.
让我们来看这样一个图

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Looks like there's a clear elbow there".
看起来就好像有一个很清楚的肘在那儿

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Right, this is, would be by
对吧 这就

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analogy to the human arm where,
类比于人的手臂

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you know, if you imagine that
想象一下

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you reach out your arm,
如果你伸出你的胳膊

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then, this is your
那么这就是你的

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shoulder joint, this is your
肩关节 这就是你的

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elbow joint and I guess, your hand is at the end over here.
肘关节 我猜你的手就在这里的终端

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And so this is the Elbow Method.
这就是“肘部法则”

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Then you find this sort of pattern
你会发现这种模式

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where the distortion goes down rapidly
它的畸变值会迅速下降

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from 1 to 2, and 2 to
从1到2 从2到

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3, and then you reach an
3 之后你会

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elbow at 3, and then
在3的时候达到一个肘点 在此之后

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the distortion goes down very slowly after that.
畸变值就下降的非常慢

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And then it looks like, you
看起来就像

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know what, maybe using three
使用3个聚类来

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clusters is the right
进行聚类是正确的

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number of clusters, because that's
这是因为那个点

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the elbow of this curve, right?
是曲线的肘点

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That it goes down, distortion goes
畸变值下降

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down rapidly until K equals
得很快知道K等于

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3, really goes down very slowly after that.
3 之后就下降得很慢

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So let's pick K equals 3.
那么我们就选K等于3

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If you apply the Elbow Method,
当你应用“肘部法则” 的时候

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and if you get a plot
如果你得到了一个

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that actually looks like this,
像这样的图

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then, that's pretty good, and
那么这非常好

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this would be a reasonable way
这将是一种用来

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of choosing the number of clusters.
选择聚类个数的合理方法

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It turns out the Elbow Method
而事实证明“肘部法则”

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isn't used that often, and one
并不那么常用 其中一个

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reason is that, if you
原因是如果你

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actually use this on
把这种方法用到

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a clustering problem, it turns out that
一个聚类问题上 事实证明

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fairly often, you know,
这种想象是相当常见的

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you end up with a curve
你最后得到了一条

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that looks much more ambiguous, maybe something like this.
看上去相当模棱两可的曲线 也许就像这样

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And if you look at this,
请看这个

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I don't know, maybe there's
我不知道 也许没有

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no clear elbow, but it
一个清晰的肘点 但是

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looks like distortion continuously goes down,
看上去畸变值是连续下降的

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maybe 3 is a
也许3是比较

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good number, maybe 4 is
好的一个数字 也许4是

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a good number, maybe 5 is also not bad.
一个比较好的数字 也许5也并不糟糕

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And so, if you actually
那么如果你在

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do this in a practice, you know,
实际操作中做这样一个事情的话

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if your plot looks like the one on the left and that's great.
如果你的图像左边这个的话 那么就太好了

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It gives you a clear answer, but
它会给你一个清晰的答案 但是

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just as often, you end
通常 你最终

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up with a plot that looks
得到的图是像

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like the one on the right and
右边的那个

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is not clear where the
并不能清晰指定

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ready location of the elbow
肘点合适的位置

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is. It  makes it harder to
这使得

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choose a number of clusters using this method.
用这个方法来选择聚类数目变得较为困难

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So maybe the quick summary
对于“肘部法则”快速的小结

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of the Elbow Method is that is worth the shot
就是它使一个值得尝试的方法

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but I wouldn't necessarily,
但是我不会必然地

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you know, have a very high
对它有很高的

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expectation of it working for any particular problem.
期望来解决任何一个特定的问题

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Finally, here's one other way
最后 有另外一种方法

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of how, thinking about how
引导你如何

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you choose the value of K,
选择K值

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very often people are running
通常人们运行

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K-means in order you
K均值聚类方法是为了

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get clusters for some later
得到一些聚类用于后面的

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purpose, or for some sort of downstream purpose.
一些用途 或者是一些下游的目的

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Maybe you want to use K-means
也许你会用K均值聚类方法

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in order to do market segmentation,
来做市场分割

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like in the T-shirt sizing example that we talked about.
如我们之前谈论的T恤尺寸的例子

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Maybe you want K-means to organize
也许你会用K均值聚类来使得

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a computer cluster better, or
电脑的聚类变得更好 或者

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maybe a learning cluster for some
也有可能是用于某种不同目的一个

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different purpose, and so,
学习聚类 等等

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if that later, downstream purpose,
如果是后续下游的目的

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such as market segmentation. If
如市场分割 如果

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that gives you an evaluation metric,
那能给你一个评估标准

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then often, a better
那么通常 更好

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way to determine the number of
的方式是决定聚类的数量

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clusters, is to see
来看

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how well different numbers of
不同的聚类数值能

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clusters serve that later downstream purpose.
为后续下游的目的提供多好的结果

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Let me step through a specific example.
让我们来涉足一个特别的例子

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Let me go through the T-shirt
让我重新举例T恤尺寸

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size example again, and I'm
的例子 我

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trying to decide, do I want three T-shirt sizes?
尝试决定我是否需要3种T恤尺寸

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So, I choose K equals 3, then
因此我选择K等于3 那么

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I might have small, medium and large T-shirts.
可能会有小号 中号 大号三类T恤

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Or maybe, I want to choose
或者我可以选择

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K equals 5, and then I
K等于5 那么我就

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might have, you know, extra
可能会有 特小

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small, small, medium, large
号 小号 中号 大号

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and extra large T-shirt sizes.
和特大号尺寸的T恤

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So, you can have like 3 T-shirt sizes or four or five T-shirt sizes.
所以 你可能有3种T恤尺寸或者4种或者5种

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We could also have four T-shirt
我们也可以有四种T恤

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sizes, but I'm just
尺寸，但是我只是

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showing three and five here,
在这里展示了3和5这两种情况

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just to simplify this slide for now.
只是为了是这张幻灯片变得简洁一些

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So, if I run K-means with
因此如果我用K等于

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K equals 3, maybe I end
3来运行K均值方法 最后我可能会得到

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up with, that's my small
这是小号

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and that's my
这是

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medium and that's my large.
中号 这是大号

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Whereas, if I run K-means with
然而 如果我用

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5 clusters, maybe I
5个聚类来运行K均值方法 也许我

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end up with, those are
最后会得到 这些是

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my extra small T-shirts, these
超小号T恤 这些

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are my small, these are
是小号 这些是

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my medium, these are my
中号 这些是

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large and these are my extra large.
大号 这些是超大号

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And the nice thing about this
这个例子的一个亮点

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example is that, this then
是这之后

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maybe gives us another way
可能会给我们一种方法

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to choose whether we want
来选择究竟我们想要的

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3 or 4 or 5 clusters,
聚类数目是3或4 还是5

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and in particular, what you can
特别的 你所能

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do is, you know, think
做的是去从

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about this from the perspective
T恤商业的角度

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of the T-shirt business and
去思考 并且

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ask: "Well if I have
提出问题 “如果我有

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five segments, then how well
5个分段 那么

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will my T-shirts fit my
我的T恤将如何很好地区满足

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customers and so, how many T-shirts can I sell?
我的顾客呢？我可以卖出多少T恤？

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How happy will my customers be?"
我的顾客将会有多高兴呢？”

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What really makes sense, from the
其中正真有意义的是 从

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perspective of the T-shirt business,
T恤的商业角度去考虑

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in terms of whether, I
也就是我是否需要

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want to have Goer T-shirt sizes
更多的T恤尺寸

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so that my T-shirts fit my customers better.
来更好地满足我的顾客

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Or do I want to have fewer
或者我是否想要更少的

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T-shirt sizes so that
T恤尺码以便

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I make fewer sizes of T-shirts.
我制造更少尺码的T恤

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And I can sell them to the customers more cheaply.
且我可以将它们卖得更加便宜一些

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And so, the t-shirt selling
因此T恤销售的

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business, that might give you
商业可能会给你

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a way to decide, between three clusters versus five clusters.
一种方法来决定究竟是采用3还是5

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So, that gives you an
这就是给你的

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example of how a
一个例子 一个

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later downstream purpose like
后续的下游目的 如

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the problem of deciding what
决定

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T-shirts to manufacture, how that
生产什么样的T恤 来

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can give you an evaluation metric for choosing the number of clusters.
给你一个评价标准来选择聚类数量

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For those of you that are
对于你们正在

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doing the program exercises, if
编程练习的同学来说 如果

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you look at this week's
你去看一下这周的

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program exercise associative K-means, that's
K均值方法相关的编程练习 是

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an example there of using K-means for image compression.
一个将K均值用于图片压缩的例子

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And so if you were trying to
如果你尝试

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choose how many clusters
选择多少个聚类

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to use for that problem, you could
来解决这个问题的话 你也可以

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also, again use the
再一次用到

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evaluation metric of image compression
图片压缩的评估标准

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to choose the number of clusters, K?
来选择聚类数目K

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So, how good do you want the
你想要图片

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image to look versus, how much
看起来有多好 还是

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do you want to compress the file
你想要压缩图片大小

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size of the image, and,
的多少

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you know, if you do the
如果你做

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programming exercise, what I've just
编程练习 我刚刚

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said will make more sense at that time.
所说的可以在那时候起到更好的作用

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So, just summarize, for the
总结一下 对于

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most part, the number of
大部分时候

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customers K is still chosen
聚类数目仍然是通过

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by hand by human input or human insight.
手动 人工输入或我们的经验来决定

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One way to try to
一种可以尝试的

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do so is to use
方法是使用

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the Elbow Method, but I
“肘部原则” 但是我

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wouldn't always expect that to
并不总是期望它能

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work well, but I think
很有效果 但是我认为

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the better way to think about
更好的方法是思考

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how to choose the number of
如何去选择聚类

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clusters is to ask, for
基于

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what purpose are you running K-means?
运行K均值聚类的目的来决定

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And then to think, what is
然后想一想

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the number of clusters K that
聚类的数目所能

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serves that, you know, whatever
提供的东西

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later purpose that you actually run the K-means for.
无论你后续运行K均值聚类的目的是什么