Search

The insertion, deletion, substitution (IDS) correcting code has garnered increased attention due to significant advancements in DNA storage that emerged recently. Despite this, the pursuit of optimal solutions in IDS-correcting codes remains an open challenge, drawing interest from both theoretical and engineering perspectives. This work introduces a pioneering approach named THEA-code. The proposed method follows a heuristic idea of employing an end-to-end autoencoder for the integrated encoding and decoding processes. To address the challenges associated with deploying an autoencoder as an IDS-correcting code, we propose innovative techniques, including the differentiable IDS channel, the entropy constraint on the codeword, and the auxiliary reconstruction of the source sequence. These strategies contribute to the successful convergence of the autoencoder, resulting in a deep learning-based IDS-correcting code with commendable performance. Notably, THEA-Code represents the first instance of a deep learning-based code that is independent of conventional coding frameworks in the IDS-correcting domain. Comprehensive experiments, including an ablation study, provide a detailed analysis and affirm the effectiveness of THEA-Code.

Recently, DNA storage has emerged as a promising data storage solution, offering significant advantages in storage density, maintenance cost efficiency, and parallel replication capability. Mathematically, the DNA storage pipeline can be viewed as an insertion, deletion, and substitution (IDS) channel. Because of the mathematical terra incognita of the Levenshtein distance, designing an IDS-correcting code is still a challenge. In this paper, we propose an innovative approach that utilizes deep Levenshtein distance embedding to bypass these mathematical challenges. By representing the Levenshtein distance between two sequences as a conventional distance between their corresponding embedding vectors, the inherent structural property of Levenshtein distance is revealed in the friendly embedding space. Leveraging this embedding space, we introduce the DoDo-Code, an IDS-correcting code that incorporates deep embedding of Levenshtein distance, deep embedding-based codeword search, and deep embedding-based segment correcting. To address the requirements of DNA storage, we also present a preliminary algorithm for long sequence decoding. As far as we know, the DoDo-Code is the first IDS-correcting code designed using plausible deep learning methodologies, potentially paving the way for a new direction in error-correcting code research. It is also the first IDS code that exhibits characteristics of being `optimal' in terms of redundancy, significantly outperforming the mainstream IDS-correcting codes of the Varshamov-Tenengolts code family in code rate.

Efficient computation or approximation of Levenshtein distance, a widely-used metric for evaluating sequence similarity, has attracted significant attention with the emergence of DNA storage and other biological applications. Sequence embedding, which maps Levenshtein distance to a conventional distance between embedding vectors, has emerged as a promising solution. In this paper, a novel neural network-based sequence embedding technique using Poisson regression is proposed. We first provide a theoretical analysis of the impact of embedding dimension on model performance and present a criterion for selecting an appropriate embedding dimension. Under this embedding dimension, the Poisson regression is introduced by assuming the Levenshtein distance between sequences of fixed length following a Poisson distribution, which naturally aligns with the definition of Levenshtein distance. Moreover, from the perspective of the distribution of embedding distances, Poisson regression approximates the negative log likelihood of the chi-squared distribution and offers advancements in removing the skewness. Through comprehensive experiments on real DNA storage data, we demonstrate the superior performance of the proposed method compared to state-of-the-art approaches.

Recently, graph (network) data is an emerging research area in artificial intelligence, machine learning and statistics. In this work, we are interested in whether node's labels (people's responses) are affected by their neighbor's features (friends' characteristics). We propose a novel latent logistic regression model to describe the network dependence with binary responses. The key advantage of our proposed model is that a latent binary indicator is introduced to indicate whether a node is susceptible to the influence of its neighbour. A score-type test is proposed to diagnose the existence of network dependence. In addition, an EM-type algorithm is used to estimate the model parameters under network dependence. Extensive simulations are conducted to evaluate the performance of our method. Two public datasets are used to illustrate the effectiveness of the proposed latent logistic regression model.

Storing information in DNA molecules is of great interest because of its advantages in longevity, high storage density, and low maintenance cost. A key step in the DNA storage pipeline is to efficiently cluster the retrieved DNA sequences according to their similarities. Levenshtein distance is the most suitable metric on the similarity between two DNA sequences, but it is inferior in terms of computational complexity and less compatible with mature clustering algorithms. In this work, we propose a novel deep squared Euclidean embedding for DNA sequences using Siamese neural network, squared Euclidean embedding, and chi-squared regression. The Levenshtein distance is approximated by the squared Euclidean distance between the embedding vectors, which is fast calculated and clustering algorithm friendly. The proposed approach is analyzed theoretically and experimentally. The results show that the proposed embedding is efficient and robust.

In recent years, Graph Neural Network (GNN) has bloomly progressed for its power in processing graph-based data. Most GNNs follow a message passing scheme, and their expressive power is mathematically limited by the discriminative ability of the Weisfeiler-Lehman (WL) test. Following Tinhofer's research on compact graphs, we propose a variation of the message passing scheme, called the Weisfeiler-Lehman-Tinhofer GNN (WLT-GNN), that theoretically breaks through the limitation of the WL test. In addition, we conduct comparative experiments and ablation studies on several well-known datasets. The results show that the proposed methods have comparable performances and better expressive power on these datasets.

Recent advances in neural networks have made great progress in the hyperspectral image (HSI) classification. However, the overfitting effect, which is mainly caused by complicated model structure and small training set, remains a major concern. Reducing the complexity of the neural networks could prevent overfitting to some extent, but also declines the networks' ability to express more abstract features. Enlarging the training set is also difficult, for the high expense of acquisition and manual labeling. In this paper, we propose an abundance-based multi-HSI classification method. Firstly, we convert every HSI from the spectral domain to the abundance domain by a dataset-specific autoencoder. Secondly, the abundance representations from multiple HSIs are collected to form an enlarged dataset. Lastly, we train an abundance-based classifier and employ the classifier to predict over all the involved HSI datasets. Different from the spectra that are usually highly mixed, the abundance features are more representative in reduced dimension with less noise. This benefits the proposed method to employ simple classifiers and enlarged training data, and to expect less overfitting issues. The effectiveness of the proposed method is verified by the ablation study and the comparative experiments.

To improve the classification performance in the context of hyperspectral image processing, many works have been developed based on two common strategies, namely the spatial-spectral information integration and the utilization of neural networks. However, both strategies typically require more training data than the classical algorithms, aggregating the shortage of labeled samples. In this letter, we propose a novel framework that organically combines the spectrum-based deep metric learning model and the conditional random field algorithm. The deep metric learning model is supervised by the center loss to produce spectrum-based features that gather more tightly in Euclidean space within classes. The conditional random field with Gaussian edge potentials, which is firstly proposed for image segmentation tasks, is introduced to give the pixel-wise classification over the hyperspectral image by utilizing both the geographical distances between pixels and the Euclidean distances between the features produced by the deep metric learning model. The proposed framework is trained by spectral pixels at the deep metric learning stage and utilizes the half handcrafted spatial features at the conditional random field stage. This settlement alleviates the shortage of training data to some extent. Experiments on two real hyperspectral images demonstrate the advantages of the proposed method in terms of both classification accuracy and computation cost.

The shortage of training samples remains one of the main obstacles in applying the artificial neural networks (ANN) to the hyperspectral images classification. To fuse the spatial and spectral information, pixel patches are often utilized to train a model, which may further aggregate this problem. In the existing works, an ANN model supervised by center-loss (ANNC) was introduced. Training merely with spectral information, the ANNC yields discriminative spectral features suitable for the subsequent classification tasks. In this paper, a CNN-based spatial feature fusion (CSFF) algorithm is proposed, which allows a smart fusion of the spatial information to the spectral features extracted by ANNC. As a critical part of CSFF, a CNN-based discriminant model is introduced to estimate whether two paring pixels belong to the same class. At the testing stage, by applying the discriminant model to the pixel-pairs generated by the test pixel and its neighbors, the local structure is estimated and represented as a customized convolutional kernel. The spectral-spatial feature is obtained by a convolutional operation between the estimated kernel and the corresponding spectral features within a neighborhood. At last, the label of the test pixel is predicted by classifying the resulting spectral-spatial feature. Without increasing the number of training samples or involving pixel patches at the training stage, the CSFF framework achieves the state-of-the-art by declining $20\%-50\%$ classification failures in experiments on three well-known hyperspectral images.

In this paper, we propose a spectral-spatial feature extraction and classification framework based on artificial neuron network (ANN) in the context of hyperspectral imagery. With limited labeled samples, only spectral information is exploited for training and spatial context is integrated posteriorly at the testing stage. Taking advantage of recent advances in face recognition, a joint supervision symbol that combines softmax loss and center loss is adopted to train the proposed network, by which intra-class features are gathered while inter-class variations are enlarged. Based on the learned architecture, the extracted spectrum-based features are classified by a center classifier. Moreover, to fuse the spectral and spatial information, an adaptive spectral-spatial center classifier is developed, where multiscale neighborhoods are considered simultaneously, and the final label is determined using an adaptive voting strategy. Finally, experimental results on three well-known datasets validate the effectiveness of the proposed methods compared with the state-of-the-art approaches., Comment: 17 pages, 10 figures

Given a sequence $s=(s_1,s_2,\ldots)$ of positive integers, the inversion sequences with respect to $s$, or $s$-inversion sequences, were introduced by Savage and Schuster in their study of lecture hall polytopes. A sequence $(e_1,e_2,\ldots,e_n)$ of nonnegative integers is called an $s$-inversion sequence of length $n$ if $0\leq e_i < s_i$ for $1\leq i\leq n$. Let I(n) be the set of $s$-inversion sequences of length $n$ for $s=(1,4,3,8,5,12,\ldots)$, that is, $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\geq1$, and let $P_n$ be the set of signed permutations on $\{1^2,2^2,\ldots,n^2\}$. Savage and Visontai conjectured that when $n=2k$, the ascent number over $I_n$ is equidistributed with the descent number over $P_k$. For a positive integer $n$, we use type $B$ $P$-partitions to give a characterization of signed permutations over which the descent number is equidistributed with the ascent number over $I_n$. When $n$ is even, this confirms the conjecture of Savage and Visontai. Moreover, let $I'_n$ be the set of $s$-inversion sequences of length $n$ for $s=(2,2,6,4,10,6,\ldots)$, that is, $s_{2i}=2i$ and $s_{2i-1}=4i-2$ for $i\geq1$. We find a set of signed permutations over which the descent number is equidistributed with the ascent number over $I'_n$., Comment: 14 pages, 1 figure

Let $W$ be a Coxeter group, and for $u,v\in W$, let $R_{u,v}(q)$ be the Kazhdan-Lusztig $R$-polynomial indexed by $u$ and $v$. In this paper, we present a combinatorial proof of the inversion formula on $R$-polynomials due to Kazhdan and Lusztig. This problem was raised by Brenti. Based on Dyer's combinatorial interpretation of the $R$-polynomials in terms of increasing Bruhat paths, we reformulate the inversion formula in terms of $V$-paths. By a $V$-path from $u$ to $v$ with bottom $w$ we mean a pair $(\Delta_1,\Delta_2)$ of Bruhat paths such that $\Delta_1$ is a decreasing path from $u$ to $w$ and $\Delta_2$ is an increasing path from $w$ to $v$. We find a reflection principle on $V$-paths, which leads to a combinatorial proof of the inversion formula. Moreover, we give two applications of the reflection principle. First, we restrict this involution to $V$-paths from $u$ to $v$ with maximal length. This provides a direct interpretation for the equi-distribution property that any nontrivial interval $[u,v]$ has as many elements of even length as elements of odd length. This property was obtained by Verma in his derivation of the M\"obius function of the Bruhat order. Second, using the reflection principle for the symmetric group, we obtain a refinement of the inversion formula by restricting the summation to permutations ending with a given element., Comment: 14 pages, 2 figures