1,175 research outputs found
Representation Learning for Scale-free Networks
Network embedding aims to learn the low-dimensional representations of
vertexes in a network, while structure and inherent properties of the network
is preserved. Existing network embedding works primarily focus on preserving
the microscopic structure, such as the first- and second-order proximity of
vertexes, while the macroscopic scale-free property is largely ignored.
Scale-free property depicts the fact that vertex degrees follow a heavy-tailed
distribution (i.e., only a few vertexes have high degrees) and is a critical
property of real-world networks, such as social networks. In this paper, we
study the problem of learning representations for scale-free networks. We first
theoretically analyze the difficulty of embedding and reconstructing a
scale-free network in the Euclidean space, by converting our problem to the
sphere packing problem. Then, we propose the "degree penalty" principle for
designing scale-free property preserving network embedding algorithm: punishing
the proximity between high-degree vertexes. We introduce two implementations of
our principle by utilizing the spectral techniques and a skip-gram model
respectively. Extensive experiments on six datasets show that our algorithms
are able to not only reconstruct heavy-tailed distributed degree distribution,
but also outperform state-of-the-art embedding models in various network mining
tasks, such as vertex classification and link prediction.Comment: 8 figures; accepted by AAAI 201
DiffKendall: A Novel Approach for Few-Shot Learning with Differentiable Kendall's Rank Correlation
Few-shot learning aims to adapt models trained on the base dataset to novel
tasks where the categories are not seen by the model before. This often leads
to a relatively uniform distribution of feature values across channels on novel
classes, posing challenges in determining channel importance for novel tasks.
Standard few-shot learning methods employ geometric similarity metrics such as
cosine similarity and negative Euclidean distance to gauge the semantic
relatedness between two features. However, features with high geometric
similarities may carry distinct semantics, especially in the context of
few-shot learning. In this paper, we demonstrate that the importance ranking of
feature channels is a more reliable indicator for few-shot learning than
geometric similarity metrics. We observe that replacing the geometric
similarity metric with Kendall's rank correlation only during inference is able
to improve the performance of few-shot learning across a wide range of datasets
with different domains. Furthermore, we propose a carefully designed
differentiable loss for meta-training to address the non-differentiability
issue of Kendall's rank correlation. Extensive experiments demonstrate that the
proposed rank-correlation-based approach substantially enhances few-shot
learning performance
Scene Graph Embeddings Using Relative Similarity Supervision
Scene graphs are a powerful structured representation of the underlying
content of images, and embeddings derived from them have been shown to be
useful in multiple downstream tasks. In this work, we employ a graph
convolutional network to exploit structure in scene graphs and produce image
embeddings useful for semantic image retrieval. Different from
classification-centric supervision traditionally available for learning image
representations, we address the task of learning from relative similarity
labels in a ranking context. Rooted within the contrastive learning paradigm,
we propose a novel loss function that operates on pairs of similar and
dissimilar images and imposes relative ordering between them in embedding
space. We demonstrate that this Ranking loss, coupled with an intuitive triple
sampling strategy, leads to robust representations that outperform well-known
contrastive losses on the retrieval task. In addition, we provide qualitative
evidence of how retrieved results that utilize structured scene information
capture the global context of the scene, different from visual similarity
search.Comment: Accepted to AAAI 202
Statistical Phylogenetic Tree Analysis Using Differences of Means
We propose a statistical method to test whether two phylogenetic trees with
given alignments are significantly incongruent. Our method compares the two
distributions of phylogenetic trees given by the input alignments, instead of
comparing point estimations of trees. This statistical approach can be applied
to gene tree analysis for example, detecting unusual events in genome evolution
such as horizontal gene transfer and reshuffling. Our method uses difference of
means to compare two distributions of trees, after embedding trees in a vector
space. Bootstrapping alignment columns can then be applied to obtain p-values.
To compute distances between means, we employ a "kernel trick" which speeds up
distance calculations when trees are embedded in a high-dimensional feature
space, e.g. splits or quartets feature space. In this pilot study, first we
test our statistical method's ability to distinguish between sets of gene trees
generated under coalescence models with species trees of varying dissimilarity.
We follow our simulation results with applications to various data sets of
gophers and lice, grasses and their endophytes, and different fungal genes from
the same genome. A companion toolkit, {\tt Phylotree}, is provided to
facilitate computational experiments.Comment: 17 pages, 6 figure
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