推荐树由一组节点N组成,其中N = {n1,n2,...,n | N |}表示| N |个体非叶或叶节点。除根节点以外的N中的每个节点都有一个父节点和一个任意数量的子节点。具体而言,语料库C中的每个项目ci对应于树中唯一的一个叶节点,而那些非叶节点是粗粒度概念。不失一般性,我们假设noden1总是根节点。举个例子树在图2的右下角示出,其中
每个圆圈表示一个节点并且节点的数量是它在树中的索引。该树总共有8个叶节点,每个叶节点对应于语料库中的一个itemin。尽管给出的例子是一个完整的二叉树,但我们并没有强加完整的和二元的作为我们模型中树的类型的限制。
给定一个推荐树和一个优化模型,在
算法1中描述了详细的层次预测算法。检索过程是分层和自上而下的。假设所需的候选项目号是k。对于大小为| C |的语料库C,最多遍历2 * k * log | C |节点可以在完整的二叉树中得到最终的建议集。需要遍历的节点数量是对数关系w.r.t.语料库大小,这使先进的二进制概率模型成为可能。
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