45 research outputs found
2-manifold recognition is in logspace
We prove that the homeomorphism problem for 2 manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected s, t-connectivity problem in graphs
2-manifold recognition is in logspace
We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected -connectivity problem in graphs
R3MC: A Riemannian three-factor algorithm for low-rank matrix completion
We exploit the versatile framework of Riemannian optimization on quotient
manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank
matrix completion. The underlying search space of fixed-rank matrices is
endowed with a novel Riemannian metric that is tailored to the least-squares
cost. Numerical comparisons suggest that R3MC robustly outperforms
state-of-the-art algorithms across different problem instances, especially
those that combine scarcely sampled and ill-conditioned data.Comment: Accepted for publication in the proceedings of the 53rd IEEE
Conference on Decision and Control, 201
-softmax: Improving Intra-class Compactness and Inter-class Separability of Features
Intra-class compactness and inter-class separability are crucial indicators
to measure the effectiveness of a model to produce discriminative features,
where intra-class compactness indicates how close the features with the same
label are to each other and inter-class separability indicates how far away the
features with different labels are. In this work, we investigate intra-class
compactness and inter-class separability of features learned by convolutional
networks and propose a Gaussian-based softmax (-softmax) function
that can effectively improve intra-class compactness and inter-class
separability. The proposed function is simple to implement and can easily
replace the softmax function. We evaluate the proposed -softmax
function on classification datasets (i.e., CIFAR-10, CIFAR-100, and Tiny
ImageNet) and on multi-label classification datasets (i.e., MS COCO and
NUS-WIDE). The experimental results show that the proposed
-softmax function improves the state-of-the-art models across all
evaluated datasets. In addition, analysis of the intra-class compactness and
inter-class separability demonstrates the advantages of the proposed function
over the softmax function, which is consistent with the performance
improvement. More importantly, we observe that high intra-class compactness and
inter-class separability are linearly correlated to average precision on MS
COCO and NUS-WIDE. This implies that improvement of intra-class compactness and
inter-class separability would lead to improvement of average precision.Comment: 15 pages, published in TNNL