R语言dbscan包kNNdist函数：距离公式、输出逻辑及计算维度问询

Let's break down how this function works, using your iris example to make everything concrete and easy to follow.

Key Questions Answered #

1. Distance Formula (and whether it uses Euclidean distance) #

By default, kNNdist uses Euclidean distance to calculate distances between samples. This is the standard straight-line distance in multi-dimensional space, calculated as:

sqrt(sum((x_i - y_i)^2)) for all feature dimensions i

You can confirm this with your data: take row 1 (5.1, 3.5, 1.4, 0.2) and row 5 (5.0, 3.6, 1.4, 0.2):

sqrt((5.1-5.0)^2 + (3.5-3.6)^2 + (1.4-1.4)^2 + (0.2-0.2)^2) = sqrt(0.01 + 0.01) ≈ 0.1414

This exactly matches the first value in the first row of your x output (0.1414214), which is the closest neighbor distance for sample 1.

Note: You can override the distance metric with the metric parameter (e.g., metric = "manhattan" for Manhattan distance), but Euclidean is the default.

2. How the Output is Generated #

The output matrix x is structured as follows:

• Rows: One row for each sample in your input data (10 rows, matching your 10 iris samples)
• Columns: For each sample, the columns hold the sorted distances to its k-nearest neighbors (here, k=5). Column 1 is the distance to the closest neighbor, column 2 to the second closest, up to column 5 for the 5th closest.

For example, the first value in row 2 of x is 0.1732051 — that's the distance between sample 2 (4.9, 3.0, 1.4, 0.2) and its closest neighbor (sample 10: 4.9, 3.1, 1.5, 0.1):

sqrt((4.9-4.9)^2 + (3.0-3.1)^2 + (1.4-1.5)^2 + (0.2-0.1)^2) = sqrt(0 + 0.01 + 0.01 + 0.01) ≈ 0.1732

Perfectly matches the output.

3. Calculation Direction (Rows vs Columns) #

kNNdist treats each row as a single sample/observation, and each column as a feature/variable. All distance calculations happen between pairs of rows (samples), not columns. So it computes distances across rows to find neighbors for each sample row.

Example Code Recap #

Here's your original code formatted for readability:

library("dbscan")
# Take first 10 iris samples, exclude the species column
i <- iris[1:10,-5]
i
# Calculate distances to the 5 nearest neighbors for each sample
x <- kNNdist(i,k = 5)
x

内容的提问来源于stack exchange，提问作者Jaray