Showing papers on "Binary tree published in 2021"
TL;DR: The EIF extension to the model-free anomaly detection algorithm, Isolation Forest, is presented, which resolves issues with assignment of anomaly score to given data points and shows that the robustness of the algorithm is much improved by looking at the variance of scores of data points distributed along constant level sets.
Abstract: We present an extension to the model-free anomaly detection algorithm, Isolation Forest. This extension, named Extended Isolation Forest (EIF), resolves issues with assignment of anomaly score to given data points. We motivate the problem using heat maps for anomaly scores. These maps suffer from artifacts generated by the criteria for branching operation of the binary tree. We explain this problem in detail and demonstrate the mechanism by which it occurs visually. We then propose two different approaches for improving the situation. First we propose transforming the data randomly before creation of each tree, which results in averaging out the bias. Second, which is the preferred way, is to allow the slicing of the data to use hyperplanes with random slopes. This approach results in remedying the artifact seen in the anomaly score heat maps. We show that the robustness of the algorithm is much improved using this method by looking at the variance of scores of data points distributed along constant level sets. We report AUROC and AUPRC for our synthetic datasets, along with real-world benchmark datasets. We find no appreciable difference in the rate of convergence nor in computation time between the standard Isolation Forest and EIF.
125 citations
TL;DR: The proposed target detection method through tree-structured encoding (TD-TSE) for HSIs is proposed, which is not constrained by any model assumptions, which makes it highly practical for the hyperspectral data in real scenes.
Abstract: Target detection aims to locate targets of interest within a specific scene. The traditional model-driven detectors based on signal processing have proved to be very effective. However, the detection performance of such traditional methods relies heavily on the model assumption, which is limited by the discrepancy with real hyperspectral images (HSIs) data. In this article, a target detection method through tree-structured encoding (TD-TSE) for HSIs is proposed. Instead of modeling the target and the background to extract valid features, we construct a binary tree based on the features of the data itself and segment the HSI to improve the separability of the target and the background. For the purpose of highlighting the target and suppressing the background, a novel measurement of separation, distance on tree, is calculated via binary encoding based on the constructed tree structure, and the detection output can be obtained according to such distance. To further reduce the generalization error resulting from random subsampling, the statistical average of the distances on multiple independent trees is estimated to improve the robustness of TD-TSE. The proposed method is not constrained by any model assumptions, which is fundamentally different from the most widely used hyperspectral target detectors in the field of signal processing. Moreover, the construction of binary trees without any labeled samples and the linear complexity of the proposed method make it highly practical for the hyperspectral data in real scenes. Extensive experiments on three benchmark HSI data sets demonstrate the effectiveness of the proposed TD-TSE for hyperspectral target detection.
52 citations
TL;DR: To reduce hardware decoder complexity, virtual pipeline data unit constraints are introduced, which forbid certain multi-type tree splits and a local dual tree is described, which reduces the number of small chroma intra blocks.
Abstract: Versatile Video Coding (VVC) is the latest video coding standard jointly developed by ITU-T VCEG and ISO/IEC MPEG. In this paper, technical details and experimental results for the VVC block partitioning structure are provided. Among all the new technical aspects of VVC, the block partitioning structure is identified as one of the most substantial changes relative to the previous video coding standards and provides the most significant coding gains. The new partitioning structure is designed using a more flexible scheme. Each coding tree unit (CTU) is either treated as one coding unit or split into multiple coding units by one or more recursive quaternary tree partitions followed by one or more recursive multi-type tree splits. The latter can be horizontal binary tree split, vertical binary tree split, horizontal ternary tree split, or vertical ternary tree split. A CTU dual tree for intra-coded slices is described on top of the new block partitioning structure, allowing separate coding trees for luma and chroma. Also, a new way of handling picture boundaries is presented. Additionally, to reduce hardware decoder complexity, virtual pipeline data unit constraints are introduced, which forbid certain multi-type tree splits. Finally, a local dual tree is described, which reduces the number of small chroma intra blocks.
50 citations
23 May 2021
TL;DR: In this article, the authors present a new protocol for solving the private heavy-hitters problem, in which there are many clients and a small set of data-collection servers, and each client holds a private bitstring.
Abstract: This paper presents a new protocol for solving the private heavy-hitters problem. In this problem, there are many clients and a small set of data-collection servers. Each client holds a private bitstring. The servers want to recover the set of all popular strings, without learning anything else about any client’s string. A web-browser vendor, for instance, can use our protocol to figure out which homepages are popular, without learning any user’s homepage. We also consider the simpler private subset-histogram problem, in which the servers want to count how many clients hold strings in a particular set without revealing this set to the clients.Our protocols use two data-collection servers and, in a protocol run, each client send sends only a single message to the servers. Our protocols protect client privacy against arbitrary misbehavior by one of the servers and our approach requires no public-key cryptography (except for secure channels), nor general-purpose multiparty computation. Instead, we rely on incremental distributed point functions, a new cryptographic tool that allows a client to succinctly secret-share the labels on the nodes of an exponentially large binary tree, provided that the tree has a single non-zero path. Along the way, we develop new general tools for providing malicious security in applications of distributed point functions.A limitation of our heavy-hitters protocol is that it reveals to the servers slightly more information than the set of popular strings itself. We precisely define and quantify this leakage and explain how to ameliorate its effects. In an experimental evaluation with two servers on opposite sides of the U.S., the servers can find the 200 most popular strings among a set of 400,000 client-held 256-bit strings in 54 minutes. Our protocols are highly parallelizable. We estimate that with 20 physical machines per logical server, our protocols could compute heavy hitters over ten million clients in just over one hour of computation.
49 citations
TL;DR: An audit model based on a designed binary tree assisted by edge computing is established, which provides computing capability for the resource-constrained terminals and is more effective to store and manage big data, which is conducive to providing users with more secure IoT services.
48 citations
TL;DR: In this article, the Tucker and hierarchical Tucker tensors are used to represent the reduced density operator and auxiliary density operators. And the binary tree structure of the hierarchical equations of motion (HEOM) can be used to propagate a short matrix product state constructed from these nodes.
Abstract: We develop new methods to efficiently propagate the hierarchical equations of motion (HEOM) by using the Tucker and hierarchical Tucker (HT) tensors to represent the reduced density operator and auxiliary density operators. We first show that by employing the split operator method, the specific structure of the HEOM allows a simple propagation scheme using the Tucker tensor. When the number of effective modes in the HEOM increases and the Tucker representation becomes intractable, the split operator method is extended to the binary tree structure of the HT representation. It is found that to update the binary tree nodes related to a specific effective mode, we only need to propagate a short matrix product state constructed from these nodes. Numerical results show that by further employing the mode combination technique commonly used in the multi-configuration time-dependent Hartree approaches, the binary tree representation can be applied to study excitation energy transfer dynamics in a fairly large system including over 104 effective modes. The new methods may thus provide a promising tool in simulating quantum dynamics in condensed phases.
35 citations
20 Jun 2021
TL;DR: ProtoTree as discussed by the authors combines prototype learning with decision trees, and thus results in a globally interpretable model by design, which can locally explain a single prediction by outlining a decision path through the tree.
Abstract: Prototype-based methods use interpretable representations to address the black-box nature of deep learning models, in contrast to post-hoc explanation methods that only approximate such models. We propose the Neural Prototype Tree (ProtoTree), an intrinsically interpretable deep learning method for fine-grained image recognition. ProtoTree combines prototype learning with decision trees, and thus results in a globally interpretable model by design. Additionally, ProtoTree can locally explain a single prediction by outlining a decision path through the tree. Each node in our binary tree contains a trainable prototypical part. The presence or absence of this learned prototype in an image determines the routing through a node. Decision making is therefore similar to human reasoning: Does the bird have a red throat? And an elongated beak? Then it’s a hummingbird! We tune the accuracy-interpretability trade-off using ensemble methods, pruning and binarizing. We apply pruning without sacrificing accuracy, resulting in a small tree with only 8 learned prototypes along a path to classify a bird from 200 species. An ensemble of 5 ProtoTrees achieves competitive accuracy on the CUB-200-2011 and Stanford Cars data sets. Code is available at github.com/M-Nauta/ProtoTree.
34 citations
TL;DR: A fast decision scheme using a lightweight neural network (LNN) to avoid redundant block partitioning in versatile video coding (VVC) and substantially decreases the encoding complexity of VVC with a slight coding loss under the All Intra configuration.
Abstract: In this paper, we propose a fast decision scheme using a lightweight neural network (LNN) to avoid redundant block partitioning in versatile video coding (VVC). A more versatile block structure, named the multi-type tree (MTT) structure, which includes binary trees (BTs) and ternary trees (TTs), is adopted by VCC, in addition to the traditional quadtree structure. The MTT improved the coding efficiency compared with previous video coding standards. However, the new tree structures, mainly TT, significantly increased the complexity of the VVC encoder. Although widespread application of VVC has been inhibited, this problem has not yet been investigated thoroughly in the literature. In this study, we first determine the statistical characteristics of coded parameters that exhibit correlation with the TT and develop two useful types of features —explicit VVC features (EVFs) and derived VVC features (DVFs) — to facilitate the intra coding of VVC. These features can be obtained efficiently during the intra prediction before the determination of the best block partitioning during rate-distortion optimization in VVC encoding. Our LNN model decides whether to terminate the nested TT block structures subsequent to a quadtree based on the features. The experimental results confirm that the proposed method substantially decreases the encoding complexity of VVC with a slight coding loss under the All Intra configuration. Our code, models, and dataset are available at https://github.com/foriamweak/MTTPartitioning_LNN .
31 citations
TL;DR: In this article, a reliable tree-based data aggregation method is proposed, where sensor nodes are organized in the form of a binary tree and aggregation requests are authenticated by a shared key, and if the request is acknowledged, the aggregation process begins.
Abstract: Aggregating the sensed data by nodes is a natural way to increase the network lifetime and reduce the number of bits sent and received by each sensor node. This paper presents a reliable tree-based data aggregation method. In the proposed method, sensor nodes are organized in the form of a binary tree. Then, aggregation requests are authenticated by a shared key, and if the request is acknowledged, the aggregation process begins. In the proposed method, using dynamic generator polynomial-size for cycle error detection code (CRC), the error generated along the path is detected hop by hop. In case of an error, the request for retransmission will be sent to the previous hop. Also, intermediate nodes apply certain aggregating functions like summation or averaging on the received packages, which cause a reduction in the amount of data transmission on the network. This method reduces the number of sent packets and the amount of energy consumed, so the network has a longer lifetime. Also, this method significantly increased reliability using the CRC code. The proposed method is compared with EESSDA, SDAACA, and LAG methods. The simulation results show that the proposed method has greater superiority over its comparative techniques, particularly on aspects such as energy consumption, network lifetime, and reliability.
30 citations
TL;DR: In this article, an ensemble approach composed of random partitioning binary trees is proposed to detect point-wise and collective (as well as contextual) anomalies, taking into account the frequencies of visits in the leaves of the random trees.
Abstract: In this paper, we propose DiFF-RF, an ensemble approach composed of random partitioning binary trees to detect point-wise and collective (as well as contextual) anomalies. Thanks to a distance-based paradigm used at the leaves of the trees, this semi-supervised approach solves a drawback that has been identified in the isolation forest (IF) algorithm. Moreover, taking into account the frequencies of visits in the leaves of the random trees allows to significantly improve the performance of DiFF-RF when considering the presence of collective anomalies. DiFF-RF is fairly easy to train, and good performance can be obtained by using a simple semi-supervised procedure to setup the extra hyper-parameter that is introduced. We first evaluate DiFF-RF on a synthetic data set to i) verify that the limitation of the IF algorithm is overcome, ii) demonstrate how collective anomalies are actually detected and iii) to analyze the effect of the meta-parameters it involves. We assess the DiFF-RF algorithm on a large set of datasets from the UCI repository, as well as four benchmarks related to network intrusion detection applications. Our experiments show that DiFF-RF almost systematically outperforms the IF algorithm and one of its extended variant, but also challenges the one-class SVM baseline, deep learning variational auto-encoder and ensemble of auto-encoder architectures. Finally, DiFF-RF is computationally efficient and can be easily parallelized on multi-core architectures.
27 citations
TL;DR: A fast CU partition decision algorithm based on the improved Directed Acyclic Graph Support Vector Machine (DAG-SVM) model to reduce the complexity of CU partition.
Abstract: One of the biggest changes in H.266/Versatile Video Coding (VVC) is introduced quad-tree with nested multi-type tree (QTMT) coding tree architecture, where the multi-type tree (MTT) structure in H.266/VVC includes binary tree (BT) and ternary tree (TT). Compared with H.265/High Efficiency Video Coding (HEVC) which only is divided by quad-tree (QT), the QTMT architecture makes the coding unit (CU) partition procedure more complexity. In this paper, we design a fast CU partition decision algorithm based on the improved Directed Acyclic Graph Support Vector Machine (DAG-SVM) model to reduce the complexity of CU partition. The video sequences are first encoded on the H.266/VVC and Test Model 4.0 (VTM 4.0), and the characteristics of the video sequences are extracted for training through the improved F-score method, where the correlation between a feature and CU partition is high. Then, the offline training is used for the improved DAG-SVM model. Finally, the trained DAG-SVM model is embedded in VTM 4.0 to early forecast the optimal CU partition modes. Simulation results indicate that the proposed method increases the time savings to 54.74% while maintaining the encoding performance. Furthermore, the proposed method exceeds the latest methods of H.266/VVC.
TL;DR: In this article, a novel image encryption algorithm based on a new permutation scheme and DNA operations is introduced, where SHA 256 and DNA hamming distance participate in the generation of the initial conditions of the 4D chaotic system, which can associate the encryption system with the original image.
Abstract: In this paper, a novel image encryption algorithm based on a new permutation scheme and DNA operations are introduced. In our algorithm, SHA 256 and DNA hamming distance participate in the generation of the initial conditions of the 4D chaotic system, which can associate the encryption system with the original image. In the permutation process, based on the adjustment process of the IAVL (improved balanced binary tree), a new scrambling algorithm is constructed. Then the dynamic block coding rules are designed, in which different image blocks have different coding rules. In the diffusion process, a new diffusion algorithm with intra-block and inter-block is proposed to perform DNA operations on the intermediate encryption result and the key matrix. In the security analysis, the key space of the encryption system is 2933 and the information entropy is about 7.9973. In addition, the NPCR and UACI in the differential attack test are close to the ideal values of 99.6094% and 33.4653%. To further prove the security of the encryption algorithm, the Irregular deviation, Maximum deviation, Energy, Contrast, and Homogeneity tests are introduced into the analysis. Experimental results illustrate that the encryption scheme can against multiple illegal attacks like statistical, brute-force and differential attacks.
TL;DR: In this paper, the authors use a simple model where the dendrite is implemented as a sequence of thresholded linear units to investigate the impacts of binary branching constraints and repetition of synaptic inputs on neural computation.
Abstract: Physiological experiments have highlighted how the dendrites of biological neurons can nonlinearly process distributed synaptic inputs. However, it is unclear how aspects of a dendritic tree, such as its branched morphology or its repetition of presynaptic inputs, determine neural computation beyond this apparent nonlinearity. Here we use a simple model where the dendrite is implemented as a sequence of thresholded linear units. We manipulate the architecture of this model to investigate the impacts of binary branching constraints and repetition of synaptic inputs on neural computation. We find that models with such manipulations can perform well on machine learning tasks, such as Fashion MNIST or Extended MNIST. We find that model performance on these tasks is limited by binary tree branching and dendritic asymmetry and is improved by the repetition of synaptic inputs to different dendritic branches. These computational experiments further neuroscience theory on how different dendritic properties might determine neural computation of clearly defined tasks.
TL;DR: The FPGCN provides an effective theoretical method to improve the detection performance of e-nose and a new technology to track the rice quality.
Abstract: The quality of rice produced in different origins is different, and the gas reflects the external sensory information of rice. Based on the electronic nose (e-nose) instrument, the gas information of rice from different origins is obtained. An effective feature processing method is a key issue to improve the detection performance of e-nose. In this work, a fast pearson graph convolutional network (FPGCN) is proposed to identify the features extracted by the e-nose sensors and realize the origin tracking of rice. Based on the pearson correlation coefficient (PCC) value, the correlation between the features is quantified to construct the graph Laplacian matrix of graph convolutional network (GCN). The Chebyshev polynomial is introduced to reduce the computational complexity and parameters of GCN, and combine the binary tree method to speed up the pooling calculation. A multi-layer structure of FPGCN is designed to achieve the gas identification of rice. Compared with the traditional feature processing method, the FPGCN has a better classification result of 98.28%, the best F1-score is 0.9829, and the best Kappa coefficient is 0.9799. In conclusion, the FPGCN provides an effective theoretical method to improve the detection performance of e-nose and a new technology to track the rice quality.
TL;DR: A novel tensorial feature extraction approach called hierarchical multiscale symbolic dynamic entropy is developed, which can be used to assess the dynamic characteristic of the measured vibration data at different hierarchical layers and different scales.
Abstract: Bearing health condition identification plays a crucial role in guaranteeing maximum productivity and reducing maintenance costs. In this article, a novel tensorial feature extraction approach call...
10 May 2021
TL;DR: A novel concept of quantum random access memory employing a quantum walk is provided, which relies on a bucket brigade scheme to access the memory cells, and only O(n) steps are required to access and retrieve data in the form of quantum superposition states.
Abstract: A novel concept of quantum random access memory (qRAM) employing a quantum walk is provided Our qRAM relies on a bucket brigade scheme to access the memory cells Introducing a bucket with chirality left and right as a quantum walker, and considering its quantum motion on a full binary tree, we can efficiently deliver the bucket to the designated memory cells, and fill the bucket with the desired information in the form of quantum superposition states Our procedure has several advantages First, we do not need to place any quantum devices at the nodes of the binary tree, and hence in our qRAM architecture, the cost to maintain the coherence can be significantly reduced Second, our scheme is fully parallelized Consequently, only O(n) steps are required to access and retrieve O(2n) data in the form of quantum superposition states Finally, the simplicity of our procedure may allow the design of qRAM with simpler structures
TL;DR: In this article, a tree model for large-eddy simulations (LES) is presented to represent the effects of trees on drag, transpiration, shading and deposition at resolutions of O(1 m, 0.1 s) whilst minimising the number of model parameters.
TL;DR: This work develops and analyzes a blind modulation identification algorithm for two-path successive relaying systems, and mathematically proves that a group of modulation types exhibits peaks for specific correlation functions while the other group does not.
Abstract: Modulation identification, a major task of intelligent receivers, is of vital importance for applications in military and civilian fields. In this work, we develop and analyze a blind modulation identification algorithm for two-path successive relaying systems. Analytical expressions for the correlation functions adopted as the basis of the proposed algorithm are derived, and the computational cost of the algorithm is addressed. By taking advantage of the space-time redundancy, we mathematically prove that a group of modulation types exhibits peaks for specific correlation functions while the other group does not. Exploiting this feature, we propose a binary tree hypothesis test for decision-making. A packet length estimator is also introduced as an auxiliary task for the proposed algorithm. The proposed algorithm does not require information about channel coefficients and noise power. The identification performance of the proposed algorithm is evaluated through Monte Carlo simulations under different conditions. Results show that the performance of the proposed algorithm is remarkably better than the traditional algorithms.
TL;DR: A switching rule of the BT topology is developed to cope with the emergent failures of target sensing and the formation scalabilities and a multitask framework is constructed which is compatible with the local control protocols.
Abstract: Cooperative target enclosing problem with multiple unmanned microaerial vehicles is addressed. A local controller based on a binary-tree (BT) communication topology is presented for the target enclosing formation. A sufficient condition is derived for the formation stability by a recursive Lyapunov method. In this article, a switching rule of the BT topology is developed to cope with the emergent failures of target sensing and the formation scalabilities. Besides, in order to accommodate the enclosure in complicated environments, a multitask framework is constructed which is compatible with the local control protocols. Comparative experiments on both simulations and platforms demonstrate the effectiveness of the theoretical results.
TL;DR: In this article, the authors prove that the sequence of random variables Cn 2−(n+1)−mn, where mn is an explicit constant, converges in distribution as n→∞.
Abstract: Let Tn denote the binary tree of depth n augmented by an extra edge connected to its root. Let Cn denote the cover time of Tn by simple random walk. We prove that the sequence of random variables Cn 2−(n+1)−mn, where mn is an explicit constant, converges in distribution as n→∞, and identify the limit.
TL;DR: GRMT (Generative Reconstruction of Mutation Tree from scratch), a method for inferring tumor mutation tree from SCS data using the k-Dollo parsimony model, which enables GRMT to efficiently recover the chronological order of mutations and scale well to large datasets.
Abstract: Single-cell sequencing (SCS) now promises the landscape of genetic diversity at single cell level, and is particularly useful to reconstruct the evolutionary history of tumor. There are multiple types of noise that make the SCS data notoriously error-prone, and significantly complicate tumor tree reconstruction. Existing methods for tumor phylogeny estimation suffer from either high computational intensity or low-resolution indication of clonal architecture, giving a necessity of developing new methods for efficient and accurate reconstruction of tumor trees. We introduce GRMT (Generative Reconstruction of Mutation Tree from scratch), a method for inferring tumor mutation tree from SCS data. GRMT exploits the k-Dollo parsimony model to allow each mutation to be gained once and lost at most k times. Under this constraint on mutation evolution, GRMT searches for mutation tree structures from a perspective of tree generation from scratch, and implements it to an iterative process that gradually increases the tree size by introducing a new mutation per time until a complete tree structure that contains all mutations is obtained. This enables GRMT to efficiently recover the chronological order of mutations and scale well to large datasets. Extensive evaluations on simulated and real datasets suggest GRMT outperforms the state-of-the-arts in multiple performance metrics. The GRMT software is freely available at https://github.com/qasimyu/grmt.
TL;DR: In this article, the traverse symplectic correlation-gram (TSCgram) is proposed to overcome the shortcomings existing in Autogram and based on that, a novel fault diagnosis method for rolling bearing is proposed.
Abstract: Resonance demodulation is a commonly used method to obtain fault information, whose main challenge is to seek a suitable frequency band for demodulation. Autogram is a recently proposed method for optimal demodulation frequency band (ODFB) selection, in which the frequency domain is divided by a binary tree structure. However, the frequency band information obtained by Autogram is easily missed. To solve this issue, a 1/3 binary tree structure is employed to segment the frequency domain and improve the segmentation accuracy of Autogram. Despite this, the frequency bands with different position information cannot be fully obtained through the above-mentioned structure yet. In this article, the traverse symplectic correlation-gram (TSCgram) is proposed to overcome the shortcomings existing in Autogram and based on that, a novel fault diagnosis method for rolling bearing is proposed. First, the frequency domain of the raw vibration signal of rolling bearing is accurately divided through the traversal segmentation structure. Then, the concept of symplectic correlation is introduced to reduce the interference of noise, as well as other unrelated components on the traditional kurtosis, thus further improving the accuracy of ODFB detection. Finally, the band position corresponding to the maximum symplectic correlation kurtosis (SCK) value is chosen as the ODFB for fault diagnostics of rolling bearing. Also, the proposed method is applied to the simulated and measured data analysis by comparing it with fast kurtogram and Autogram methods. The comparison and analysis results indicate that the fault diagnostic effect of the proposed TSCgram method is better than the comparing methods.
TL;DR: It is shown that in the subspace of binary algebraic measure trees, weak convergence of sample shapes, sample subtree masses and sample distance matrices are all equivalent and define a compact, metrizable topology.
Abstract: In this paper we present with algebraic trees a novel notion of (continuum) trees which generalizes countable graph-theoretic trees to (potentially) uncountable structures. For that purpose we focus on the tree structure given by the branch point map which assigns to each triple of points their branch point. We give an axiomatic definition of algebraic trees, define a natural topology, and equip them with a probability measure on the Borel-$\sigma$-field.Under an order-separability condition, algebraic (measure) trees can be considered as tree structure equivalence classes of metric (measure) trees (i.e.\ subtrees of R-trees). Using Gromov-weak convergence (i.e.\ sample distance convergence) of the particular representatives given by the metric arising from the distribution of branch points, we define a metrizable topology on the space of equivalence classes of algebraic measure trees.
In many applications, binary trees are of particular interest. We introduce on that subspace with the sample shape and the sample subtree mass convergence two additional, natural topologies. Relying on the connection to triangulations of the circle, we show that all three topologies are actually the same, and the space of binary algebraic measure trees is compact. To this end, we provide a formal definition of triangulations of the circle, and show that the coding map which sends a triangulation to an algebraic measure tree is a continuous surjection onto the subspace of binary algebraic non-atomic measure trees.
01 Aug 2021
TL;DR: This paper proposes a recursive Transformer model based on differentiable CKY style binary trees to emulate this composition process, and extends the bidirectional language model pre-training objective to this architecture, attempting to predict each word given its left and right abstraction nodes.
Abstract: Human language understanding operates at multiple levels of granularity (e.g., words, phrases, and sentences) with increasing levels of abstraction that can be hierarchically combined. However, existing deep models with stacked layers do not explicitly model any sort of hierarchical process. In this paper, we propose a recursive Transformer model based on differentiable CKY style binary trees to emulate this composition process, and we extend the bidirectional language model pre-training objective to this architecture, attempting to predict each word given its left and right abstraction nodes. To scale up our approach, we also introduce an efficient pruning and growing algorithm to reduce the time complexity and enable encoding in linear time. Experimental results on language modeling and unsupervised parsing show the effectiveness of our approach.
TL;DR: In this article, it was shown that an Ω-dendriform structure on typed binary trees can be obtained if Ω has four products satisfying certain axioms, e.g., a diassociative semigroup.
TL;DR: Li et al. as mentioned in this paper proposed a reversible data hiding scheme for the encrypted images (RDHEI) based on vector quantization (VQ) prediction and parametric binary tree labeling (PBTL).
Abstract: In this paper, we propose a reversible data hiding scheme for the encrypted images (RDHEI) based on vector quantization (VQ) prediction and parametric binary tree labeling (PBTL). VQ compression is a lossy image compression method, the difference between the original image and the decompressed image is small when the length of codebook is sufficient. Thus, VQ can be applied as a tool for pixel value prediction. Based on VQ prediction, PBTL method is applied to label the embeddable and non-embeddable pixels. Through adaptive setting of parameters, the modified PBTL can provide optimal pixel labeling strategies and thus maximize the overall embedding capacity. Furthermore, the VQ index and the secret data are stream ciphered to avoid leakage of the image content and secret information. Different metrics are used to show that the marked encrypted images are highly secure. In comparison with several state-of-the-art schemes, our scheme outperforms the related works in embedding rate for two commonly applied image databases. In addition, extraction of the secret data and recovery of the original image can be operated separately according to authorization.
TL;DR: It is shown that the Ehrhart polynomial of these polytopes, and therefore the Hilbert series of the ideals, depends only on the number of leaves of the underlying binary tree, and not on the topology of the tree itself.
TL;DR: Zhang et al. as mentioned in this paper proposed a hierarchical mixture model that integrates self-attention with an inference tree structure for constructing a point cloud generator, which is capable of generating realistic point clouds in an unsupervised manner.
Abstract: Point clouds are fundamental in the representation of 3D objects. However, they can also be highly unstructured and irregular. This makes it difficult to directly extend 2D generative models to three-dimensional space. In this paper, we cast the problem of point cloud generation as a topological representation learning problem. To infer the representative information of 3D shapes in the latent space, we propose a hierarchical mixture model that integrates self-attention with an inference tree structure for constructing a point cloud generator. Based on this, we design a novel Generative Adversarial Network (GAN) architecture that is capable to generate realistic point clouds in an unsupervised manner. The proposed adversarial framework (SG-GAN) relies on self-attention mechanism and Graph Convolution Network (GCN) to hierarchically infer the latent topology of 3D shapes. Embedding and transferring the global topology information in a tree framework allows our model to capture and enhance the structural connectivity. Furthermore, the proposed architecture endows our model with partially generating 3D structures. Finally, we propose two gradient penalty methods to stabilize the training of SG-GAN and overcome the possible mode collapse of GAN networks. To demonstrate the performance of our model, we present both quantitative and qualitative evaluations and show that SG-GAN is more efficient in training and it exceeds the state-of-the-art in 3D point cloud generation.
TL;DR: In this article, a high capacity reversible data hiding technique using a parametric binary tree labeling scheme is proposed, which efficiently exploits intra-block correlation, based on the prediction mean of the block by symmetry or asymmetry.
Abstract: In this paper, a high capacity reversible data hiding technique using a parametric binary tree labeling scheme is proposed. The proposed parametric binary tree labeling scheme is used to label a plaintext image’s pixels as two different categories, regular pixels and irregular pixels, through a symmetric or asymmetric process. Regular pixels are only utilized for secret payload embedding whereas irregular pixels are not utilized. The proposed technique efficiently exploits intra-block correlation, based on the prediction mean of the block by symmetry or asymmetry. Further, the proposed method utilizes blocks that are selected for their pixel correlation rather than exploiting all the blocks for secret payload embedding. In addition, the proposed scheme enhances the encryption performance by employing standard encryption techniques, unlike other block based reversible data hiding in encrypted images. Experimental results show that the proposed technique maximizes the embedding rate in comparison to state-of-the-art reversible data hiding in encrypted images, while preserving privacy of the original contents.
13 May 2021
TL;DR: A binary tree of classifiers for multi-label classification that preserves label dependencies and handles class imbalance is proposed, which has shown significant performance improvement on fourteen datasets against fourteen existing multi- label classifiers.
Abstract: This article proposes a binary tree of classifiers for multi-label classification that preserves label dependencies and handles class imbalance. At each node, the input data is strategically split into two subsets for its subsequent child nodes, keeping the label correlations intact. A novel approach of partitioning the data based on label-set proximity has also been proposed. Various data appropriate classifiers are trained to learn the binary partition at every internal node. The tree of classifiers grows iteratively depending on two parameters – multi-label entropy and sample cardinality, computed on the data at the current node. During training, the decision at any node is based on these parameters and the branching out is restricted, if deemed unnecessary. Specific classifiers at the leaf nodes perform the final classification task and assign appropriate label-sets to the unlabelled data. The proposed system aims to appropriately split the data and build the hierarchical structure such that the training and classification tasks become simpler. Also, the problem of class imbalance leads to the irregular splitting of data and excessive branching out of the tree which is handled through the novel use of suitable classifiers and parameters at the intermediate and leaf nodes. The proposed method has shown significant performance improvement on fourteen datasets against fourteen existing multi-label classifiers. Two-tailed Wilcoxon signed rank test statistics show that for $T_{Wilcoxon}(14,0.2)=31$ the proposed method outperforms all the other comparison models.