This paper proposes a new convolutional neural network with multiscale processing for detecting ground-glass opacity (GGO) nodules in 3D computed tomography (CT) images, which is referred to as PiaNet for short. PiaNet consists of a feature-extractio
n module and a prediction module. The former module is constructed by introducing pyramid multiscale source connections into a contracting-expanding structure. The latter module includes a bounding-box regressor and a classifier that are employed to simultaneously recognize GGO nodules and estimate bounding boxes at multiple scales. To train the proposed PiaNet, a two-stage transfer learning strategy is developed. In the first stage, the feature-extraction module is embedded into a classifier network that is trained on a large data set of GGO and non-GGO patches, which are generated by performing data augmentation from a small number of annotated CT scans. In the second stage, the pretrained feature-extraction module is loaded into PiaNet, and then PiaNet is fine-tuned using the annotated CT scans. We evaluate the proposed PiaNet on the LIDC-IDRI data set. The experimental results demonstrate that our method outperforms state-of-the-art counterparts, including the Subsolid CAD and Aidence systems and S4ND and GA-SSD methods. PiaNet achieves a sensitivity of 91.75% with only one false positive per scan
The popular softmax loss and its recent extensions have achieved great success in the deep learning-based image classification. However, the data for training image classifiers usually has different quality. Ignoring such problem, the correct classif
ication of low quality data is hard to be solved. In this paper, we discover the positive correlation between the feature norm of an image and its quality through careful experiments on various applications and various deep neural networks. Based on this finding, we propose a contraction mapping function to compress the range of feature norms of training images according to their quality and embed this contraction mapping function into softmax loss or its extensions to produce novel learning objectives. The experiments on various classification applications, including handwritten digit recognition, lung nodule classification, face verification and face recognition, demonstrate that the proposed approach is promising to effectively deal with the problem of learning on the data with different quality and leads to the significant and stable improvements in the classification accuracy.
Suppose that $X_{1}$ and $X_{2}$ are two selfadjoint random variables that are freely independent over an operator algebra $mathcal{B}$. We describe the possible operator atoms of the distribution of $X_{1}+X_{2}$ and, using linearization, we determi
ne the possible eigenvalues of an arbitrary polynomial $p(X_{1},X_{2})$ in case $mathcal{B}=mathbb{C}$.
We study $N$-ary non-commutative notions of independence, which are given by trees and which generalize free, Boolean, and monotone independence. For every rooted subtree $mathcal{T}$ of the $N$-regular tree, we define the $mathcal{T}$-free product o
f $N$ non-commutative probability spaces and we define the $mathcal{T}$-free additive convolution of $N$ non-commutative laws. These $N$-ary convolution operations form a topological symmetric operad which includes the free, Boolean, monotone, and anti-monotone convolutions, as well as the orthogonal and subordination convolutions. Using the operadic framework, the proof of convolution identities (such as the relation between free, monotone, and subordination convolutions studied by Lenczewski) can be reduced to combinatorial manipulations of trees. We also develop a theory of $mathcal{T}$-free independence that closely parallels the free, Boolean, and monotone cases, provided that the root vertex has more than one neighbor. In particular, we study the case where the root vertex of $mathcal{T}$ has $n$ children and each other vertex has $d$ children, and we relate the $mathcal{T}$-free convolution powers to free and Boolean convolution powers and the Belinschi-Nica semigroup.
We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relations have a matricial extension property so that we can easily study t
heir associated convolutions via Voiculescus fully matricial function theory. Based the matricial extension property, we show that many results can be generalized to multi-variable cases. Besides free, Boolean and monotone independence convolutions, we will focus on two important convolutions, which are orthogonal and subordination additive convolutions. We show that the operator-valued subordination functions, which come from the free additive convolutions or the operator-valued free convolution powers, are reciprocal Cauchy transforms of operator-valued random variables which are uniquely determined up to Voiculescus fully matricial function theory. In the end, we study relations between certain convolutions and transforms in $C^*$-operator valued probability.
We show that the limit laws of random matrices, whose entries are conditionally independent operator valued random variables having equal second moments proportional to the size of the matrices, are operator valued semicircular laws. Furthermore, we
prove an operator valued analogue of Voiculescus asymptotic freeness theorem. By replacing conditional independence with Boolean independence, we show that the limit laws of the random matrices are Operator-valued Bernoulli laws.
In this paper, we introduce the notion of free-free-Boolean independence relation for triples of algebras. We define free-free-Boolean cumulants ans show that the vanishing of mixed cumulants is equivalent to free-free-Boolean independence. A free-free -Boolean central limit law is studied.
In this paper, we develop the notion of free-Boolean independence in an amalgamation setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence with amalgama
tion. We also provide a characterization of free-Boolean independence by conditions in terms of mixed moments. In addition, we study free-Boolean independence over a $C^*$-algebra and prove a positivity property.
We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce free-Boolean c
umulants and show that free-Boolean independence is equivalent to the vanishing of mixed cumulants.
We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal distributional symme
tries which means the corresponding de Finetti type theorem fails if a sequence of random variables satisfy more symmetry relations other than the maximal one. In addition, we define Boolean quantum semigroups in analogous to the easy quantum groups, by universal conditions on matrix coordinate generators and an orthogonal projection. Then, we show a general de Finetti type theorem for Boolean independence.
