In the spectral clustering algorithm, k-means clustering is applied to the distinct rows, denoted as $a_i$, of the $n \times k$ matrix $M$. Since matrix $M$ contains exactly $n$ rows, each row has a one-to-one correspondence with one of the $n$ original data points represented in the similarity graph. Consequently, the cluster assigned to the $i$-th row of $M$ is directly assigned to the $i$-th original data point. This process demonstrates how spectral clustering efficiently handles high-dimensional data by first mapping it to a lower-dimensional representation before performing k-means.