Peak-climbing is also called “mode-seeking” or “valley-seeking”.

Method

With Grid (Mesh), summarise the number of points for each block (cell).

For example, there are $6\times 6$ cells, each cell has at most $8=3^2-1$ neighbors.

Start with any cell. Find the $Max$ of your neighbors and shoot to the $Max$ with an arrow (which means “yield”) if the $Max$ is larger than you. Repeat this procedure with all cells.

In the end, a “peak” is a cell that shoots to no one and many cells shoot to. View a “peak” as the center of a cluster and the members of this cluster are the cells that point to this “peak”.

For example, we can find that there are two clusters in the matrix above. One is at the upper-left and the other is at the lower-right.

Strength

• No need to decide the number of cluster ($k$).

Limitations

• The number of clusters ($k$) is fixed.
• When the number of cells is too large, the number of peaks will also grow; when the number of cells is too small (e.g., $3 \times 3$), then there may be only 1 peak.
• Not appropriate when the data is high-dimensional.
  • 2-dim: $3^2 -1=8$ neighbors
  • $d$-dim: $3^d- 1=242$ neighbors