We propose a novel algorithm for the task of supervised discriminative
distance learning by nonlinearly embedding vectors into a low dimensional
Euclidean space. We work in the challenging setting where supervision is with
constraints on similar and dissimilar pairs while training. The proposed method
is derived by an approximate kernelization of a linear Mahalanobis-like
distance metric learning algorithm and can also be seen as a kernel neural
network. The number of model parameters and test time evaluation complexity of
the proposed method are O(dD) where D is the dimensionality of the input
features and d is the dimension of the projection space - this is in contrast
to the usual kernelization methods as, unlike them, the complexity does not
scale linearly with the number of training examples. We propose a stochastic
gradient based learning algorithm which makes the method scalable (w.r.t. the
number of training examples), while being nonlinear. We train the method with
up to half a million training pairs of 4096 dimensional CNN features. We give
empirical comparisons with relevant baselines on seven challenging datasets for
the task of low dimensional semantic category based image retrieval.

提出了一种新颖的算法，用于通过非线性嵌入向量到低维欧氏空间中进行监督判别距离学习，该方法可以被视为核神经网络，并且可以通过类似于线性 Mahalanobis 距离度量学习算法的近似核化得出，该方法的模型参数数量和测试时间评估复杂度均为 O (dD)，其中 D 是输入特征的维度，d 是投影空间的维数，在具有数十万个训练对的 CNN 特征的数据集上进行了实证比较。