Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Insights into Ordinal Embedding Algorithms: A Systematic Evaluation   The objective of ordinal embedding is to find a Euclidean representation of a
set of abstract items, using only answers to triplet comparisons of the form
"Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous
algorithms have been proposed to solve this problem. However, there does not
exist a fair and thorough assessment of these embedding methods and therefore
several key questions remain unanswered: Which algorithms perform better when
the embedding dimension is constrained or few triplet comparisons are
available? Which ones scale better with increasing sample size or dimension? In
our paper, we address these questions and provide the first comprehensive and
systematic empirical evaluation of existing algorithms as well as a new neural
network approach. We find that simple, relatively unknown, non-convex methods
consistently outperform all other algorithms, including elaborate approaches
based on neural networks or landmark approaches. This finding can be explained
by our insight that many of the non-convex optimization approaches do not
suffer from local optima. Our comprehensive assessment is enabled by our
unified library of popular embedding algorithms that leverages GPU resources
and allows for fast and accurate embeddings of millions of data points.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int