We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures and representations can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies.
翻译:我们建议进行未经监督的代言学习和从 dendrogram 中提取特征。 常用的迷你式距离措施相当于用单一联系标准来构建一个弯曲格, 确定一个层次函数和距离函数的具体形式。 因此, 我们将这种方法推广到任意的弯曲格。 我们开发了一个通用框架, 从不同类型的斜度、 级别函数和距离函数中可以推断出不同的距离度量和表达方式。 通过一个适当的嵌入, 我们计算所推断的距离的矢量代表方式, 以便让许多数字机器学习算法能够使用这样的距离。 然后, 为了解决模型选择问题, 我们研究基于坦德罗克的距离的汇总, 分别存在于溶解空间和深层代表空间中。 在第一个方法中, 例如, 对于集群问题, 我们根据不同对象的组合标记标签的一致性, 在混合方法中, 我们用一个有效的关联组合组合组合来生成最后的组合。 然后, 在第二个方法中, 我们研究不同距离和跨层方法的组合, 我们通过最后的排序方法, 展示我们最后的数学结构的组合。