数据挖掘 - 如何解释余弦相似度的上三角矩阵 - 吾爱随笔录

在Spark中，有一种RowMatrix.columnSimilarities()返回“该矩阵的列之间余弦相似度的 nxn 稀疏上三角矩阵“。

我应该怎么读？如果我尝试从https://stackoverflow.com/a/1750187实现一个示例，如下所示：

JavaRDD<Vector> rows = sc.parallelize(Arrays.asList(
    new DenseVector(new double[]{2, 1, 0, 2, 0, 1, 1, 1}),
    new DenseVector(new double[]{2, 1, 1, 1, 1, 0, 1, 1})
));

RowMatrix mat = new RowMatrix(rows.rdd());  
List<Vector> sims = mat.columnSimilarities().toRowMatrix().rows().toJavaRDD().collect();
for(Vector v: sims) {
    System.out.println(v);
}

我明白了

(8,[6,7],[0.7071067811865475,0.7071067811865475])
(8,[1,2,3,4,5,6,7],[0.9999999999999998,0.7071067811865475,0.9486832980505137,0.7071067811865475,0.7071067811865475,0.9999999999999998,0.9999999999999998])
(8,[2,3,4,5,6,7],[0.7071067811865475,0.9486832980505137,0.7071067811865475,0.7071067811865475,0.9999999999999998,0.9999999999999998])
(8,[7],[0.9999999999999998])
(8,[4,5,6,7],[0.4472135954999579,0.8944271909999159,0.9486832980505137,0.9486832980505137])
(8,[6,7],[0.7071067811865475,0.7071067811865475])
(8,[3,4,6,7],[0.4472135954999579,1.0,0.7071067811865475,0.7071067811865475])

我应该如何解释它？如引用的 StackOverflow 帖子中所述，如何从中获得余弦角 0.822？

谢谢！