We first show that the commonly used dimensionality reduction (DR) methods
such as t-SNE and LargeVis poorly capture the global structure of the data in
the low dimensional embedding. We show this via a number of tests for the DR
methods that can be easily applied by any practitioner to the dataset at hand.
Surprisingly enough, t-SNE performs the best w.r.t. the commonly used measures
that reward the local neighborhood accuracy such as precision-recall while
having the worst performance in our tests for global structure. We then
contrast the performance of these two DR method against our new method called
TriMap. The main idea behind TriMap is to capture higher orders of structure
with triplet information (instead of pairwise information used by t-SNE and
LargeVis), and to minimize a robust loss function for satisfying the chosen
triplets. We provide compelling experimental evidence on large natural datasets
for the clear advantage of the TriMap DR results. As LargeVis, TriMap scales
linearly with the number of data points.

我们展示了经常使用的降维方法，如 t-SNE 和 LargeVis，不能很好地捕捉低维度嵌入中数据的全局结构，并提出了一种名为 TriMap 的新方法，使用三元组信息来捕获更高级别的结构，通过实验证明 TriMap DR 结果具有明显的优势。

利用三元组实现更加全局准确的降维方法

A more globally accurate dimensionality reduction method using triplets

We study the problem of visualizing large-scale and high-dimensional data in
a low-dimensional (typically 2D or 3D) space. Much success has been reported
recently by techniques that first compute a similarity structure of the data
points and then project them into a low-dimensional space with the structure
preserved. These two steps suffer from considerable computational costs,
preventing the state-of-the-art methods such as the t-SNE from scaling to
large-scale and high-dimensional data (e.g., millions of data points and
hundreds of dimensions). We propose the LargeVis, a technique that first
constructs an accurately approximated K-nearest neighbor graph from the data
and then layouts the graph in the low-dimensional space. Comparing to t-SNE,
LargeVis significantly reduces the computational cost of the graph construction
step and employs a principled probabilistic model for the visualization step,
the objective of which can be effectively optimized through asynchronous
stochastic gradient descent with a linear time complexity. The whole procedure
thus easily scales to millions of high-dimensional data points. Experimental
results on real-world data sets demonstrate that the LargeVis outperforms the
state-of-the-art methods in both efficiency and effectiveness. The
hyper-parameters of LargeVis are also much more stable over different data
sets.

本文提出了一种叫做 LargeVis 的技术，旨在解决将大规模和高维数据可视化在低维空间的问题。与 t-SNE 相比，LargeVis 构建精确近似的 K 最近邻图的计算成本更低，并采用了一个原则上的概率模型来进行可视化，整个过程易于扩展到数百万个高维数据点。实验结果表明，LargeVis 在效率和效果方面均优于现有的先进方法。