Unit 6 4 k-Means Clustering Example knowitvideos English Japanese

Unit 6 4 k-Means Clustering ExampleYouTube↗ IA↗(long shot)
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Let me explain k-means by an example.

例を挙げてk－means法を解説しましょう

Suppose we're given the following data points in a 2-dimensional space.

こちらの二次元空間にデータ点があると仮定します

K-means estimates for a fixed number of k. Here k = 2.

k－means法はクラスタの定数から予測をしますクラスタ数は2とします

The best centers of clusters representing those data points.

クラスタの重心は空間内のデータ点を表し

Those are found interatively by the following algorithm.

それは次のアルゴリズムによって確認できます

Step 1: Guess cluster centers at random, as shown over here with the 2 stars.

ステップ1：クラスタはこの2つの星のようにランダムに集まると仮定します

Step 2: Assign to each cluster center, even though they are randomly chosen,

ステップ2：クラスタがランダムに置かれていても

the most likely corresponding data points.

データ点に対応して重心を割り当てます

This is done by minimizing Euclidian distance.

ユークリッド距離を最小にして実行すると

In particular, each cluster center represents half of the space.

ここで各クラスタの重心は空間を分割します

And the line that separates the space between the left and right cluster center

クラスタの重心を左右に分割する線形は等距離線で

is the equidistant line, often called a Voronoi graph.

この図は“ボロノイ図”と言います

All the data points on the left correspond to the red cluster,

左側には赤のクラスタに分類されたデータ点があり

and the ones on the right to the green cluster.

右側は緑のクラスタです

Step 3: Given now we have a correspondence between the data points and cluster centers,

ステップ3：データ点とクラスタの重心点の間には関係があると仮定し

find the optimal cluster center that corresponds to the points associated with the cluster center.

データ点の重心点に伴う最適なクラスタの重心点を求めます

Our red cluster center has only 2 data points attached.

赤のクラスタの重心に関連するデータ点は2つです

So the optimal cluster center would be the halfway point in the middle.

この場合2点の中間が最適な重心点となります

Our right cluster center has more than 2 points attached;

緑のクラスタには2点以上のデータがあり

yet it isn't placed optimally, as you can see as they move with the animation back and forth.

重心点が最適ではないためこのように移動します

By minimizing the joint quadratic distance to all of those points,

すべてのデータ点をつなぐ二次元の距離を最小化することで

the new cluster center has attained the center of those data points.

新たな重心点がデータ点の中心に到達します

Now the final step is iterate. Go back and reassign cluster centers.

最終ステップでクラスタの重心点の割り当てを繰り返し行うと

Now the Voronoi diagram has shifted, and the points are associated differently,

ボロノイ図は移動しデータ点の関係も変化します

and then reevaluate what the optimal cluster center looks like given the associated points.

ここで分類されたデータ点の最適な重心点が再評価され

And in both cases we see significant motion.

2つの分類が大きく変化します

Repeat. Now this is the clustering.

この手法を“クラスタリング”と呼び

The point association doesn't change, and as a result, we just converged.

データ点の変化が止まればこれを最適として収束します

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