# K-Nearest Neighbors

### A Quick Review

<figure><img src="/files/94IopdoJnAuevAz4gIT1" alt=""><figcaption></figcaption></figure>

1. The k-nearest neighbors method is a supervised learning approach that does not need to fit a model to the data.
2. Data points are classified based on the categories of the k nearest neighbors in the training data set.
3. In Biopython, the k-nearest neighbors method is available in Bio.kNN.
4. k is the number of neighbors k that will be considered for the classification.
5. For classification into two classes, choosing an odd number for k lets you avoid tied votes
6. No exact physical or biological rules to define the best value of k
7. Apply different values of K to a part of training data Then evaluate the performance using the other part of training data
8. Low values of k such as 1 or 2 can be noisy and subject to outliers
9. High values of k smooth over things. But you do not want k to be too big because small clusters will be out weighed by other clusters

### Basic Flow of KNN

Import KNN module from Biopython

```
 
from Bio import kNN
```

Define a list containing the distance and the score of similarity in expression profile between the 2 genes

```
xs =      [[-53, -200.78],
          [117, -267.14],
          [57, -163.47],
          [16, -190.30],
          [11, -220.94],
          [85, -193.94],
          [16, -182.71],
          [15, -180.41],
          [-26, -181.73],
          [58, -259.87],
          [126, -414.53],
          [191, -249.57],
          [113, -265.28],
          [145, -312.99],
          [154, -213.83],
          [147, -380.85],
          [93, -291.13]]
```

Define a list specifies if the gene pair belongs to the same operon (1) or different operons (0)

```
ys =     [1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          0,
          0,
          0,
          0,
          0,
          0,
          0]
```

Define the number of nereast neightours.Choosing an odd number for k lets you avoid tied votes

```
k = 3
```

Create and initialize a k-nearest neighbors model

The function name train is a bit deceiving since no model training is done

This function simply stores xs, ys, and k in model.

```
model = kNN.train(xs, ys, k)
```

\
Using a k-nearest neighbors model for classification Classify yxcE, yxcD

```
pair1 = [6, -173.143442352]
kNN.classify(model, pair1)
```

```
Out[1]: 1
```

Classify yxiB and yxiA

```
pair2 = [309, -271.005880394]
kNN.classify(model, pair2)
```

```
Out[2]: 0
```

This is consistent with the results from logistic regression

Hooray! Let's celebrate again!!!

### Fancier Analyses

To run the code in this section, the following keys steps must be run ahead of time

1. Import KNN module from Biopython
2. Define a list containing the distance and the score of similarity in expression profile between the 2 genes
3. Define a list specifies if the gene pair belongs to the same operon (1) or different operons (0)

#### Print Classification Output in Intuitive Ways

classify yxcE, yxcD

```
pair1 = [6, -173.143442352]
print("yxcE, yxcD:", kNN.classify(model, pair1))
```

Output:

```
yxcE, yxcD: 1
```

Classify yxiB and yxiA

```
pair2 = [309, -271.005880394]
print("yxiB, yxiA:", kNN.classify(model, pair2))
```

Output:

```
yxiB, yxiA: 0
```


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