关于k-means聚类中‘sample’与‘variable’定义及基因表达场景的疑问

Great question—this is a super common point of confusion when working with high-dimensional biological datasets like gene expression! Let’s break it down clearly using your example: 100 patients, each with expression measurements for 1000 genes. The key thing to remember is that the definitions of "sample" and "variable" depend entirely on what you’re trying to cluster.

1. When clustering patients into 10 groups #

In this scenario, your focus is on grouping individual patients based on their gene expression profiles:

• Sample (or data point): Each patient. You’ve got 100 samples here—each patient is the independent entity you’re analyzing and grouping.
• Variable (or feature): Each gene’s expression level. You’re using 1000 variables to describe every patient—how active each gene is in their tissue/sample.

In k-means terms, each patient is a 1000-dimensional vector (one dimension per gene’s expression value). The algorithm groups these vectors into clusters where patients have similar expression patterns across all genes.

2. When clustering genes into 10 groups #

Now when you flip the goal to group genes, the roles shift entirely—because now you’re looking for genes that behave similarly across patients:

• Sample (or data point): Each gene. You’ve got 1000 samples here, since each gene is the entity you want to cluster.
• Variable (or feature): Each patient’s expression measurement for that gene. So each gene is represented as a 100-dimensional vector (one dimension per patient’s expression value for that gene). K-means will group genes that have matching expression trends across the 100 patients (e.g., genes that are all highly expressed in the same subset of patients).

A quick rule of thumb to avoid mix-ups #

No matter what you’re clustering:

• The samples are the items you’re actually grouping (think of them as the rows in your dataset if you structure it with your target items as rows).
• The variables are the attributes you use to measure similarity between those items (the columns in that same dataset structure).

So to map it directly:

• If your dataset has rows = patients, columns = genes → cluster patients → samples = patients, variables = genes
• If you transpose the dataset to rows = genes, columns = patients → cluster genes → samples = genes, variables = patients

That’s the core of it—your clustering target dictates which is which!

内容的提问来源于stack exchange，提问作者user5054