8 research outputs found
Revised Conditional t-SNE: Looking Beyond the Nearest Neighbors
Conditional t-SNE (ct-SNE) is a recent extension to t-SNE that allows removal
of known cluster information from the embedding, to obtain a visualization
revealing structure beyond label information. This is useful, for example, when
one wants to factor out unwanted differences between a set of classes. We show
that ct-SNE fails in many realistic settings, namely if the data is well
clustered over the labels in the original high-dimensional space. We introduce
a revised method by conditioning the high-dimensional similarities instead of
the low-dimensional similarities and storing within- and across-label nearest
neighbors separately. This also enables the use of recently proposed speedups
for t-SNE, improving the scalability. From experiments on synthetic data, we
find that our proposed method resolves the considered problems and improves the
embedding quality. On real data containing batch effects, the expected
improvement is not always there. We argue revised ct-SNE is preferable overall,
given its improved scalability. The results also highlight new open questions,
such as how to handle distance variations between clusters.Comment: 20 pages including supplemen
A Coq Library of Undecidable Problems
International audienceWe propose a talk on our library of mechanised reductions to establish undecidability results in Coq. The library is a collaborative effort, growing constantly and we are seeking more outside contributors willing to work on undecidability results in Coq
ExClus : explainable clustering on low-dimensional data representations
Dimensionality reduction and clustering techniques are frequently used to
analyze complex data sets, but their results are often not easy to interpret.
We consider how to support users in interpreting apparent cluster structure on
scatter plots where the axes are not directly interpretable, such as when the
data is projected onto a two-dimensional space using a dimensionality-reduction
method. Specifically, we propose a new method to compute an interpretable
clustering automatically, where the explanation is in the original
high-dimensional space and the clustering is coherent in the low-dimensional
projection. It provides a tunable balance between the complexity and the amount
of information provided, through the use of information theory. We study the
computational complexity of this problem and introduce restrictions on the
search space of solutions to arrive at an efficient, tunable, greedy
optimization algorithm. This algorithm is furthermore implemented in an
interactive tool called ExClus. Experiments on several data sets highlight that
ExClus can provide informative and easy-to-understand patterns, and they expose
where the algorithm is efficient and where there is room for improvement
considering tunability and scalability
ExClus : explainable clustering on low-dimensional data representations
Dimensionality reduction and clustering techniques are frequently used to
analyze complex data sets, but their results are often not easy to interpret.
We consider how to support users in interpreting apparent cluster structure on
scatter plots where the axes are not directly interpretable, such as when the
data is projected onto a two-dimensional space using a dimensionality-reduction
method. Specifically, we propose a new method to compute an interpretable
clustering automatically, where the explanation is in the original
high-dimensional space and the clustering is coherent in the low-dimensional
projection. It provides a tunable balance between the complexity and the amount
of information provided, through the use of information theory. We study the
computational complexity of this problem and introduce restrictions on the
search space of solutions to arrive at an efficient, tunable, greedy
optimization algorithm. This algorithm is furthermore implemented in an
interactive tool called ExClus. Experiments on several data sets highlight that
ExClus can provide informative and easy-to-understand patterns, and they expose
where the algorithm is efficient and where there is room for improvement
considering tunability and scalability
Evaluating representation learning and graph layout methods for visualization
Graphs and other structured data have come to the forefront in machine learning over
the past few years due to the efficacy of novel representation learning methods
boosting the prediction performance in various tasks. Representation learning
methods embed the nodes in a low-dimensional real-valued space, enabling the
application of traditional machine learning methods on graphs. These representations
have been widely premised to be also suited for graph visualization. However, no
benchmarks or encompassing studies on this topic exist. We present an empirical
study comparing several state-of-the-art representation learning methods with two
recent graph layout algorithms, using readability and distance-based measures as
well as the link prediction performance. Generally, no method consistently
outperformed the others across quality measures. The graph layout methods provided
qualitatively superior layouts when compared to representation learning methods.
Embedding graphs in a higher dimensional space and applying t-distributed
stochastic neighbor embedding for visualization improved the preservation of local
neighborhoods, albeit at substantially higher computational cost
Topologically Regularized Data Embeddings
Unsupervised representation learning methods are widely used for gaining
insight into high-dimensional, unstructured, or structured data. In some cases,
users may have prior topological knowledge about the data, such as a known
cluster structure or the fact that the data is known to lie along a tree- or
graph-structured topology. However, generic methods to ensure such structure is
salient in the low-dimensional representations are lacking. This negatively
impacts the interpretability of low-dimensional embeddings, and plausibly
downstream learning tasks. To address this issue, we introduce topological
regularization: a generic approach based on algebraic topology to incorporate
topological prior knowledge into low-dimensional embeddings. We introduce a
class of topological loss functions, and show that jointly optimizing an
embedding loss with such a topological loss function as a regularizer yields
embeddings that reflect not only local proximities but also the desired
topological structure. We include a self-contained overview of the required
foundational concepts in algebraic topology, and provide intuitive guidance on
how to design topological loss functions for a variety of shapes, such as
clusters, cycles, and bifurcations. We empirically evaluate the proposed
approach on computational efficiency, robustness, and versatility in
combination with linear and non-linear dimensionality reduction and graph
embedding methods