Matrix factorization is at the heart of many machine learning algorithms, for example, dimensionality reduction (e.g. kernel PCA) or recommender systems relying on collaborative filtering. Understanding a singular value decomposition (SVD) of a matrix as a neural network optimization problem enables us to decompose large matrices efficiently while dealing naturally with missing values in the given matrix. But most importantly, it allows us to learn the connection between data points' feature vectors and the matrix containing information about their pairwise relations. In this paper we introduce a novel neural network architecture termed Similarity Encoder (SimEc), which is designed to simultaneously factorize a given target matrix while also learning the mapping to project the data points' feature vectors into a similarity preserving embedding space. This makes it possible to, for example, easily compute out-of-sample solutions for new data points. Additionally, we demonstrate that SimEc can preserve non-metric similarities and even predict multiple pairwise relations between data points at once.
翻译:矩阵化是许多机器学习算法的核心, 例如, 维度减缩( 内核五氯苯甲醚) 或依靠协作过滤的推荐系统。 了解一个矩阵的单值分解( SVD) 是一个神经网络优化问题, 使我们能够在自然处理给定矩阵中缺失的值的同时, 有效地分解大型矩阵。 但最重要的是, 它能让我们了解数据点特性矢量与包含其对称关系信息的矩阵之间的联系。 在本文中, 我们引入了一个新的神经网络结构, 名为“ 相似 Encoder ” ( SimEc), 旨在同时将特定目标矩阵化, 同时学习将数据点特性矢量投射成类似性, 以保存嵌入空间 。 这使我们有可能, 例如, 很容易对新数据点的分布式解决方案进行计算 。 此外, 我们证明 SimEc 可以保存非计量的相似性, 甚至一次预测数据点之间的多重对称关系 。