KMeans Algorithm

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# KMeans Algorithm
### By ChengMingbo
### 2017-8-18
.footnote[powered by <a href="https://github.com/gnab/remark"><font color=yellow>remark.js</font></a>] 
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I am a note, will be only shown when under presentation mode

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# Outline
* Classification and Clustering
* Applications
* KMeans
* Other Cluster Algorithm
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# Classification and Clustering
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## classify
<div align=center>
<img src="http://cmb.oss-cn-qingdao.aliyuncs.com/2017-08-18-classify.png" height=90% width=90% />
</div>

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## clustering
<div align=center>
<img src="http://cmb.oss-cn-qingdao.aliyuncs.com/2017-08-18-clustering.png" height=90% width=90% />
</div>

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# Applications

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## Applications
.left-column[
- Google News
]
.right-column[<img src='http://cmb.oss-cn-qingdao.aliyuncs.com/2017-08-18-gnews.png' width=100% height=100%>]

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## Applications
.left-column[
- Google News
- Marketing
]
.right-column[<img src='http://cmb.oss-cn-qingdao.aliyuncs.com/2017-08-18-marketing.png' width=100% height=100%/>]

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## Applications
.left-column[
- Google News
- Marketing
- Vibration Detection
]
.right-column[<img src='http://cmb.oss-cn-qingdao.aliyuncs.com/2017-08-18-vibration.png' width=100% height=100%/>]

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# KMeans

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## KMeans Cartoon

.center[![](http://cmb.oss-cn-qingdao.aliyuncs.com/2017-08-18-kmeans.gif)]

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## Algorithm
.pseudocode[
1. Initialize cluster centroids $\mu_1, \mu_2, \cdots, \mu_k \in R^n$ randomly.
2. Repeat until convergence{

For every i, set
$$c^i := \arg\min_j ||x^i-\mu_j ||^2$$
    For every j, set
$$\mu_j := \frac{\sum_i 1 (c^i = j) x^i}{\sum_i 1 (c^i = j)}$$
}
]

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## Algorithm

```octave

centroid1 = X(floor(rand*200),:)
	centroid2 = X(floor(rand*200),:)

while(1)
		for i=1:length(X)
			d1 = norm(X(i,:)-centroid1); %Euclidean distance
			d2 = norm(X(i,:)-centroid2);

if d1 < d2
				class1 = [class1; X(i,:)];
			else
				class2 = [class2; X(i,:)];
			end
		end

m1 = mean(class1);
		m2 = mean(class2);

if norm(m1-centroid1) <0.01  &&  norm(m2-centroid2) <0.01
			break
		end

centroid1 = m1;
		centroid2 = m2;
	end
```
???
>
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# Other Cluster Algorithm

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## Clustering Alogrithm
- Guassian Mixture Model
- Affinity Propagation
- DBSCAN
- Latent Dirichlet Allocation

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- Guassian Mixture Model

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- Guassian Mixture Model

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- DBSCAN

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- Latent Dirichlet Allocation

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# Summary 
* Classification and Clustering
* Applications
* KMeans
* Other Cluster Algorithm

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# Thanks!
# Q&A

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# Snacks
## Remark.js HowTo