Separable Data Research Articles

Practical Screening Method for Cancer Gene Diagnosis -How to Choose Cancer and Normal Patients by four Principles

We developed a new theory of discriminant analysis (Theory1). Physicians can use it for practical medical diagnoses. Only Revised IP Optimal-LDF (RIP) obtains the minimum number of misclassification (MNM). RIP can discriminate linearly separable data (LSD) theoretically. It discriminated against 169 microarrays with two classes and found that 169 MNMs are zero and LSD. It can split high-dimensional arrays into many small LSD with less than n (patient’s number) genes that are the candidates of multivariate oncogenes. We completed a new theory of high-dimensional gene data analysis (Theory2). A 100-fold Cross-Validation (Method1) can rank all candidates for the importance of diagnosis. Thus, if physicians firstly use Theory2 as the screening method, they can start their medical studies with the correct small sizes of candidates. This paper analyzes four arrays in detail and proposes correctly choosing cancer and normal patients using four principles.

General secure encryption algorithm for separable reversible data hiding in encrypted domain

The separable reversible data hiding in encrypted domain (RDH-ED) algorithm leaves out the embedding space for the information before or after encryption and makes the operation of extracting the information and restoring the image not interfere with each other. The encryption method employed not only affects the embedding space of the information and separability, but is more crucial for ensuring security. However, the commonly used XOR, scram-bling or combination methods fall short in security, especially against known plaintext attack (KPA). Therefore, in or-der to improve the security of RDH-ED and be widely applicable, this paper proposes a high-security RDH-ED encryption algorithm that can be used to reserve space before encryption (RSBE) and free space after encryption (FSAE). During encryption, the image undergoes block XOR, global intra-block bit-plane scrambling (GIBS) and inter-block scrambling sequentially. The GIBS key is created through chaotic mapping transformation. Subsequently, two RDH-ED algorithms based on this encryption are proposed. Experimental results indicate that the algorithm outlined in this paper maintains consistent key communication traffic post key conversion. Additionally, its computational complexity remains at a constant level, satisfying separability criteria, and is suitable for both RSBE and FSAE methods. Simultaneously, while satisfying the security of a single encryption technique, we have expanded the key space to 28Np×Np!×8!Np, enabling resilience against various existing attack methods. Notably, particularly in KPA testing scenarios, the average decryption success rate is a mere 0.0067% and 0.0045%, highlighting its exceptional security. Overall, this virtually unbreakable system significantly enhances image security while preserving an appropriate embedding capacity.

Quantum-enhanced learning with a controllable bosonic variational sensor network

Abstract The emergence of quantum sensor networks has presented opportunities for enhancing complex sensing tasks, while simultaneously introducing significant challenges in designing and analyzing quantum sensing protocols due to the intricate nature of entanglement and physical processes. Supervised learning assisted by an entangled sensor network (SLAEN) (Zhuang and Zhang 2019 Phys. Rev. X 9 041023) represents a promising paradigm for automating sensor-network design through variational quantum machine learning. However, the original SLAEN, constrained by the Gaussian nature of quantum circuits, is limited to learning linearly separable data. Leveraging the universal quantum control available in cavity quantum electrodynamics experiments, we propose a generalized SLAEN capable of handling nonlinear data classification tasks. We establish a theoretical framework for physical-layer data classification to underpin our approach. Through training quantum probes and measurements, we uncover a threshold phenomenon in classification error across various tasks—when the energy of probes exceeds a certain threshold, the error drastically diminishes to zero, providing a significant improvement over the Gaussian SLAEN. Despite the non-Gaussian nature of the problem, we offer analytical insights into determining the threshold and residual error in the presence of noise. Our findings carry implications for radio-frequency photonic sensors and microwave dark matter haloscopes.

Separable Reversible Data Hiding for Encrypted 3D Meshes Based on Self-Organized Blocking and Most Significant Bit Prediction

Separable Reversible Data Hiding for Encrypted 3D Meshes Based on Self-Organized Blocking and Most Significant Bit Prediction

Hybrid genetic optimization for quantum feature map design

Kernel methods are an import class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and does not require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20% larger) that improve further with circuit parameter training.

Identification for nonlinear systems modelled by deep long short-term memory networks based Wiener model

This paper is concerned with modeling and identification methodology for practical nonlinear system via deep long short-term memory (DLSTM) networks-based Wiener model. To determine the unknown parameters and simplify parameters identification procedure for the Wiener model, a two-step identification scheme is implemented applying hybrid signals involving separable signal and random data. First, the separable signal to separate the two blocks in Wiener model is imported, then parameters of the linear block is estimated using correlation function-based least squares technique, which handles the issue that the intermediate variable information in Wiener model cannot be measured. Moreover, integrating the advantages of adaptive stochastic gradient descent algorithm and root mean square propagation, an adaptive momentum estimation technique is created to optimize the DLSTM networks parameters based on available random data, which improves the accuracy of identified Wiener model. Compared with the other existing schemes, the superiority of the proposed method in terms of predictive performance and control results are illustrated by permanent magnet synchronous motors.

Logical specifications of effectively separable data models

It is established that any effectively separable many-sorted universal algebra has an enrichment that is the only (up to isomorphism) model constructed from constants for a suitable computably enumerable set of sentences

Interactive semi-supervised learning for microarray analysis

Microarray technology has generated vast amounts of gene expression data with distinct patterns. Based on the premise that genes of correlated functions tend to exhibit similar expression patterns, various machine learning methods have been applied to capture these specific patterns in microarray data. However, the discrepancy between the rich expression profiles and the limited knowledge of gene functions has been a major hurdle to the understanding of cellular networks. To bridge this gap so as to properly comprehend and interpret expression data, we introduce Relevance Feedback to microarray analysis and propose an interactive learning framework to incorporate the expert knowledge into the decision module. In order to find a good learning method and solve two intrinsic problems in microarray data: high dimensionality and small sample size, we also propose a semi-supervised learning algorithm: Kernel Discriminant-EM (KDEM). This algorithm efficiently utilizes a large set of unlabeled data to compensate for the insufficiency of a small set of labeled data and it extends linear algorithm in Discriminant-EM (DEM) to kernel algorithm to handle nonlinearly separable data in a lower dimensional space. Relevance Feedback technique and KDEM together construct an efficient and effective interactive semi-supervised learning framework for microarray analysis. Extensive experiments on the yeast cell cycle regulation data set and Plasmodium falciparum red blood cell cycle data set show the promise of this approach.

Margin Maximization of Text Classification based on Support Vector Machine

Abstract: This project focuses on developing a margin maximization model for topic categorization using Support Vector Machines (SVM). Topic categorization aims to classify text documents into predefined topic categories. The proposed model leverages SVM's ability to create a hyperplane with maximum margin between different topics, enhancing the classification performance. The project begins with dataset preparation, where a labeled dataset covering a wide range of topics is gathered. The text data undergoes preprocessing, including cleaning, normalization, and conversion into numerical representations. Feature extraction techniques such as TF-IDF or word embeddings are employed to capture important features related to topics. The dataset is split into training and testing sets, with the training set used to train the SVM model. The SVM model is trained with a focus on maximizing the margin, utilizing techniques like soft-margin SVM or the kernel trick to handle non-linear separable data. Hyperparameters of the SVM model are tuned to optimize its performance. The trained SVM model is then used to predict the topics of the testing data, and its performance is evaluated using standard metrics such as accuracy, precision, recall, and F1 score. The findings of this project demonstrate the effectiveness of the margin maximization model for topic categorization using SVM

Novel modified kernel fuzzy c-means algorithm used for cotton leaf spot detection

Image segmentation is a significant and difficult subject that is a prerequisite for both basic image analysis and sophisticated picture interpretation. In image analysis, picture segmentation is crucial. Several different applications, including those related to medicine, facial identification, Cotton disease diagnosis, and map object detection, benefit from image segmentation. In order to segment images, the clustering approach is used. The two types of clustering algorithms are Crisp and Fuzzy. Crisp clustering is superior to fuzzy clustering. Fuzzy clustering uses the well-known FCM approach to enhance the results of picture segmentation. KFCM technique for image segmentation can be utilized to overcome FCM’s shortcomings in noisy and nonlinear separable images. In the KFCM approach, the Gaussian kernel function transforms high-dimensional, nonlinearly separable data into linearly separable data before applying FCM to the data. KFCM is enhancing noisy picture segmentation results. KFCM increases the accuracy rate but ignores neighboring pixels. The Modified Kernel Fuzzy C-Means approach is employed to get over this problem. The NMKFCM approach enhances picture segmentation results by including neighboring pixel information into the objective function. This suggested technique is used to find “blackarm” spots on cotton leaves. A fungal leaf disease called “blackarm” leaf spot results in brown leaves with purple borders. The bacterium can harm cotton plants, causing angular leaf blotches that range in color from red to brown.

Separable Reversible Data Hiding in Encrypted Images for Remote Sensing Images.

High security and effectiveness are critical performance metrics in the data transmission process for satellite remote sensing images, medical images, and so on. Previously, the receiver could gain a high-quality cover image (lossy) after decryption in a separable manner to balance embedding capacity (EC) and security. Completely separable, reversible data hiding in encrypted image (SRDH-EI) algorithms are proposed to address this issue. In this study, the cover image was preprocessed at the sender's end. The pre-embedded pixels and most significant bits (MSB) were compressed via two coding methods to reserve space. Additionally, the header data were embedded for marking. Finally, auxiliary data and secret data were embedded in a forward "Z" and reverse "Z" shape before and after encryption, respectively. The receiver could extract secret data and decrypt the cover image separately using the keys and markers. The experimental results demonstrate that the algorithm reached a high EC for remote sensing images by utilizing pixel correlation at multiple positions within the groups. The cover image could maintain its entropy during the data embedding process, ensuring security. The decrypted image could be recovered without distortion, furthermore, the receiver could achieve complete separability, so it has good application prospects for remote sensing images.

On inference in high-dimensional logistic regression models with separated data

Summary Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the data are separable. Such conclusions are not vacuous, but an honest portrayal of the limitations of the data. Finite confidence sets are only achievable when additional, perhaps implicit, assumptions are made. Under a notional double-asymptotic regime in which the dimension of the logistic coefficient vector increases with the sample size, the present paper considers the implications of enforcing a natural constraint on the vector of logistic transformed probabilities. We derive a relationship between the logistic coefficients and a notional parameter obtained as a probability limit of an ordinary least-squares estimator. The latter exists even when the data are separable. Consistency is ascertained under weak conditions on the design matrix.

Separable and reversible data hiding scheme for medical images using modified Logistic and interpolation

The interpolation technique (IT) is a fundamental tool for image processing and is commonly utilized. Various IT-based reversible data hiding (RDH) schemes for encrypted medical images have been proposed in recent years. However, these schemes have encountered issues such as simplistic encryption, low embedding rate, or incomplete separation. A high-capacity IT-based separable RDH scheme for medical images is proposed to address these issues. First, the original Logistic map is modified by adding extra parameters to increase the complexity of the key. Additionally, an encryption method via bit reorganization and diffusion is presented to encrypt the original image. Second, an improved interpolation method based on the neighbor pixel mean is proposed to interpolate the encrypted (ciphertext) image to generate a cover (interpolated) image for embedding the data. Finally, a new data embedding method is developed using the modulo-operation congruence theorem. Experimental results showed that the modified Logistic map exhibits excellent chaotic characteristics, the metrics of the proposed encryption method are close to the theoretical values, and the proposed data hiding method acquires high embedding capacity and image quality. Furthermore, the proposed scheme is a fully reversible and separable technique that achieves superior performance in comparison to various IT-based encrypted RDH schemes.

Separable high-capacity reversible data hiding in encrypted images based on multiple predictive compression coding

Separable high-capacity reversible data hiding in encrypted images based on multiple predictive compression coding

Cluster-based data relabelling for classification

Linear classifiers are generally simpler and more explainable than their nonlinear variants. They can achieve satisfactory classification performance on linearly separable data, but not on nonlinear data. So, linear classifiers need extending, typically by modification of their algorithms, resulting in their nonlinear variants. In this paper we present one general method, cluster-based data relabelling (CBDR), that allows linear classifiers to work effectively on nonlinear data. CBDR partitions the data set into several non-overlapping class-specific clusters and relabels data by the clusters. A linear classifier can then be applied to the relabelled data to seek cluster-based linear decision boundaries instead of class-based decision boundaries. Extensive experimentation has demonstrated that CBDR can significantly enhance the classification performance of linear classifiers, and even outperform their nonlinear variants. Further experimentation has demonstrated that CBDR can also improve the classification performance of nonlinear classifiers. Most significant outperformance was observed on imbalanced data in both cases.

Integrating Coordinate Transformation and Random Sampling Into High-Capacity Reversible Data Hiding in Encrypted Polygonal Models

Reversible data hiding in encrypted media involves using algorithms to perform data encryption to improve the privacy of the original media and hide data for covert communication or access control. This study explores the feasibility of applying coordinate transformation and random sampling to enhance the embedding rate and total embedding capacity of separable reversible data hiding in encrypted polygonal models based on multiple most significant bit (multi-MSB) prediction and Huffman coding. We first transform each vertex coordinate value of the input model into a decimal value between 0 and 1 and then convert the value into numerous binary digits with a user-defined compression threshold. Thereafter, the random sampling concept is used to generate embeddable vertices with only partial neighboring vertices as a reference. Thus, the embedding rate and total embedding capacity can both be increased considerably. The multi-MSB prediction technique is adopted to obtain the embedding capacity of each embeddable vertex, each vertex coordinate value in the proposed study can have a respective embedding length. Finally, the auxiliary information compressed through Huffman coding and an encrypted secret message are embedded in the multi-MSB of each embeddable vertex coordinate value through bit substitution. The experimental results of this study indicate the feasibility of the proposed algorithm.

Fast Convergence in Learning Two-Layer Neural Networks with Separable Data

Fast Convergence in Learning Two-Layer Neural Networks with Separable Data

Implicit Annealing in Kernel Spaces: A Strongly Consistent Clustering Approach.

Kernel k-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Its merits are thoroughly validated on a suite of simulated datasets and real data benchmarks that feature nonlinear and multi-view separation. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from the non-convexity of the underlying objective function. In this paper, we generalize recent results leveraging a general family of means to combat sub-optimal local solutions to the kernel and multi-kernel settings. Called Kernel Power k-Means, our algorithm uses majorization-minimization (MM) to better solve this non-convex problem. We show that the method implicitly performs annealing in kernel feature space while retaining efficient, closed-form updates. We rigorously characterize its convergence properties both from computational and statistical points of view. In particular, we characterize the large sample behavior of the proposed method by establishing strong consistency guarantees as well as finite-sample bounds on the excess risk of the estimates through modern tools in learning theory. The proposal's efficacy is demonstrated through an array of simulated and real data experiments.

Further tests of sequence-sensitive models in a modified garner task using separable dimensions.

In the study of perceptual categorization, a key distinction is made between separable and integral dimensions. Separable dimensions are easy to attend in isolation, while integral dimensions are not. Little et al. (2016) showed that when trial-by-trial responses are analyzed, a consistent pattern of sequential effects was found in a modified Garner paradigm using integral-dimension stimuli. The present experiments investigated whether these pronounced sequential effects are also found with separable-dimension stimuli. Four experiments using two different types of separable dimensions were conducted. The results indicated that similar patterns of sequential effects were present for separable-dimension stimuli, but, unlike for integral dimensions, the effect of a change in the irrelevant dimension in the filtering task was not found. Further, for separable dimensions, the overall pattern of sequential effects did not vary between the Garner tasks (i.e., control, correlated, and filtering). To explain these results, we fit a sequence-sensitive exemplar model and compared the fits of this model to a novel sequence-sensitive feature model, in which only the relevant feature influences the categorization decision. We found that the full exemplar model provided a more compelling account of both our separable dimension data and the integral dimension data of Little et al. (2016). These findings provide a more complete understanding of perceptual categorization and add to the growing body of literature on the prevalence and critical implications of strong sequential effects in cognitive tasks. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

A Novel Two-Stage Fault-Detection Method Based on Constrained RVM and Integrating LDA With Minimax Probability Machine

This article presents a novel two-stage fault-detection (FD) method composed of a preclassifier and a reclassifier for complex industrial processes, where the preclassifier is developed by combining linear discriminant analysis and minimax probability machine to reduce dimensionality and classify fully separable data with low computation time. For overlapping data that cannot be separated by the preclassifier, a reclassifier is designed by constructing a constrained relevance vector machine (RVM), according to Neyman–Pearson principle, to decrease the missed alarm rate. The reclassifier has a lower computational load than traditional RVM due to the amount and dimensionality of reclassified data reduced by the first stage, thereby a balance between detection accuracy and computational burden of the whole FD method can be achieved. Finally, an industrial benchmark of Tennessee–Eastman process is utilized to verify the effectiveness of the proposed FD method.