Transformations Of Vector Spaces Research Articles

Image recovery method for underwater targets with complex polarization characteristics

Polarization imaging techniques have been effective in improving the clarity of turbid underwater images affected by water scattering. These techniques offer valuable additional information compared to traditional methods. However, previous descattering methods have mostly been designed for targets with uniform distribution of polarimetric characteristics. Therefore, targets with complex polarization characteristics have non-uniform distribution of polarization characteristics when dealing with such problems, additional parameter estimation errors can limit the results of image recovery. This paper proposes what we believe is a novel approach to address this issue. The method involves obtaining a new set of images using the polarization images vector space transformation method. The angle of polarization (AOP) of the target reflected light is estimated using the additivity law of the Stokes vector. This information is then combined with the physical model of underwater imaging to recover the underwater images affected by scattering. Experimental results conducted under varying levels of water turbidity validate the effectiveness of the proposed method. Moreover, the proposed method significantly broadens the range of application scenarios.

Classification of tumor types using XGBoost machine learning model: a vector space transformation of genomic alterations

BackgroundMachine learning (ML) represents a powerful tool to capture relationships between molecular alterations and cancer types and to extract biological information. Here, we developed a plain ML model aimed at distinguishing cancer types based on genetic lesions, providing an additional tool to improve cancer diagnosis, particularly for tumors of unknown origin.MethodsTCGA data from 9,927 samples spanning 32 different cancer types were downloaded from cBioportal. A vector space model type data transformation technique was designed to build consistently homogeneous new datasets containing, as predictive features, calls for somatic point mutations and copy number variations at chromosome arm-level, thus allowing the use of the XGBoost classifier models. Considering the imbalance in the dataset, due to large difference in the number of cases for each tumor, two preprocessing strategies were considered: i) setting a percentage cut-off threshold to remove less represented cancer types, ii) dividing cancer types into different groups based on biological criteria and training a specific XGBoost model for each of them. The performance of all trained models was mainly assessed by the out-of-sample balanced accuracy (BACC) and the AUC scores.ResultsThe XGBoost classifier achieved the best performance (BACC 77%; AUC 97%) on a dataset containing the 10 most represented tumor types. Moreover, dividing the 18 most represented cancers into three different groups (endocrine-related carcinomas, other carcinomas and other cancers),such analysis models achieved 78%, 71% and 86% BACC, respectively, with AUC scores greater than 96%. In addition, the model capable of linking each group to a specific cancer type reached 81% BACC and 94% AUC. Overall, the diagnostic potential of our model was comparable/higher with respect to others already described in literature and based on similar molecular data and ML approaches.ConclusionsA boosted ML approach able to accurately discriminate different cancer types was developed. The methodology builds datasets simpler and more interpretable than the original data, while keeping enough information to accurately train standard ML models without resorting to sophisticated Deep Learning architectures. In combination with histopathological examinations, this approach could improve cancer diagnosis by using specific DNA alterations, processed by a replicable and easy-to-use automated technology. The study encourages new investigations which could further increase the classifier’s performance, for example by considering more features and dividing tumors into their main molecular subtypes.

T-Linear Tensor Subspace Learning for Robust Feature Extraction of Hyperspectral Images

Subspace learning has been widely applied for feature extraction of hyperspectral images (HSIs) and achieved great success. However, the current methods still leave two problems that need to be further investigated. First, those methods mainly focus on finding one or multiple projection matrices for mapping the high-dimensional data into a low-dimensional subspace, which can only capture the information from each direction of high-order hyperspectral data separately. Second, the performance of feature extraction is barely satisfactory when the hyperspectral data is severely corrupted by noise. To address these issues, this article presents a t-linear tensor subspace learning (tLTSL) model for robust feature extraction of HSIs based on t-product projection. In the model, t-product projection is a new defined tensor transformation way similar to linear transformation in vector space, which can maximally capture the intrinsic structure of tensor data. The integrated tensor low-rank and sparse decomposition can effectively remove the noise corruption and the learned t-product projection can directly transform the high-order hyperspectral data into a subspace with information from all modes comprehensively considered. Moreover, a proposition related to tensor rank is proofed for interpreting the meaning of the tLTSL model. Extensive experiments are conducted on two different kinds of noise (i.e., simulated and real noise) corrupted HSI data, which validate the effectiveness of tLTSL.

О 〈2〉-экспонентах орграфов нелинейности регистровых преобразований

The matrix-graph approach is used to estimate the set of essential and non-linear variables of coordinate functions of the product of transformations of vector spaces. For essential variables, estimates are obtained by multiplying binary mixing matrices (or digraphs) of multiplied transformations, for non-linear variables - by multiplying ternary non-linearity matrices of multiplied transformations or their corresponding non-linearity digraphs, the arcs of which are labeled by the numbers of the set {0,1, 2}. For degrees of a given transformation, the area of non-trivial estimates is limited: for a set of essential variables, by the exponential of the mixing matrix (digraph); for a set of nonlinear variables, the 〈2〉-exponent of the matrix (digraph) of nonlinearity. For the class of transformations of binary shift registers, an attainable estimate of 〈2〉-exponents is obtained, expressed in terms of the length of the shift register and the set of numbers of essential and nonlinear variables of the feedback function. For register transformations whose non-linearity digraph has a loop, an exact formula for the 〈2〉-exponent is obtained. The results can be used to evaluate the nonlinearity characteristics of cryptographic functions built on the basis of iterations of register transformations.

Social Media Engineering for Issues Feature Extraction using Categorization Knowledge Modelling and Rule-based Sentiment Analysis

A company maintains and improves its quality services by paying attention to reviews and complaints from users. The complaints from users are commonly written using human natural language expression so that their messages are computationally difficult to extract and proceed. To overcome this difficulty, in this study, we presented a new system for issues feature extraction from users’ reviews and complaints from social media data. This system consists of four main functions: (1) Data Crawling and Preprocessing, (2) Categorization Knowledge Modelling, (3) Rule-based Sentiment Analysis, and (4) Application Environment. Data Crawling and Preprocessing provides data acquisition from users’ tweets on social media, crawls the data and applies the data preprocessing. Categorization Knowledge Modelling provides text mining of textual data, vector space transformation to create knowledge metadata, context recognition of keyword queries to the knowledge metadata, and similarity measurement for categorization. In the Rule-based Sentiment Analysis, we developed our own rules of computatioal linguistics to measure polarity of sentiment. Application Environment consists of 3 layers: database management, back-end services and front-end services. For applicability of our proposed system, we conducted two kinds of experimental study: (1) categorization performance, and (2) sentiment analysis performance. For categorization performance, we used 8743 tweet data and performed 82% of accuracy. For categorization performance, we made experiments on 217 tweet data and performed 92% of accuracy.

MATRIKS BAKU UNTUK TRANSFORMASI LINIER PADA RUANG VEKTOR DIMENSI TIGA

The linear transformation is a function relating the vector ke . If , then the transformation is called a linear operator. Several examples of linear operators have been introduced since SMA such as reflexive, rotation, compression and expansion and shear. Apart from being introduced in SMA, these linear operators were also introduced to the linear algebra course. Linear transformations studied at the university level include linear transformation in finite dimension vector spaces . The discussion includes how to determine the standard matrix for reflexive linear transformations, rotation, compression and expansion and given shear. Through the column vectors of reflexive, rotation, compression and expansion and shear, a standard matrix of 2x2 size is formed for the corresponding linear transformation. however, in this study, the authors studied linear transformations in dimensioned vector spaces . The results of this study are if known is a vector space with finite and the standard matrix for reflexivity, rotation, expansion, compression and shear is obtained. Each of these linear transformations is performed on x-axis, y-axis and z-axis on to get column vectors. The column vectors as a result of the linear transformation at form the standard matrix for the corresponding linear transformation in the vector space. The standard matrix for linear transformations in the vector space is obtained by determining reflexivity, rotation, expansion, compression and shear. The process of obtaining a standard matrix for linear transformation is carried out by rewriting the standard basis, determining the column vectors, and rearranging them as the standard matrix for each linear transformation in the vector space

Unseen Word Representation by Aligning Heterogeneous Lexical Semantic Spaces

Word embedding techniques heavily rely on the abundance of training data for individual words. Given the Zipfian distribution of words in natural language texts, a large number of words do not usually appear frequently or at all in the training data. In this paper we put forward a technique that exploits the knowledge encoded in lexical resources, such as WordNet, to induce embeddings for unseen words. Our approach adapts graph embedding and cross-lingual vector space transformation techniques in order to merge lexical knowledge encoded in ontologies with that derived from corpus statistics. We show that the approach can provide consistent performance improvements across multiple evaluation benchmarks: in-vitro, on multiple rare word similarity datasets, and invivo, in two downstream text classification tasks.

Cross-Lingual Entity Linking for Web Tables

This paper studies the problem of linking string mentions from web tables in one language to the corresponding named entities in a knowledge base written in another language, which we call the cross-lingual table linking task. We present a joint statistical model to simultaneously link all mentions that appear in one table. The framework is based on neural networks, aiming to bridge the language gap by vector space transformation and a coherence feature that captures the correlations between entities in one table. Experimental results report that our approach improves the accuracy of cross-lingual table linking by a relative gain of 12.1%. Detailed analysis of our approach also shows a positive and important gain brought by the joint framework and coherence feature.

The Past is Not a Foreign Country: Detecting Semantically Similar Terms across Time

Numerous archives and collections of past documents have become available recently thanks to mass scale digitization and preservation efforts. Libraries, national archives, and other memory institutions have started opening up their collections to interested users. Yet, searching within such collections usually requires knowledge of appropriate keywords due to different context and language of the past. Thus, non-professional users may have difficulties with conceptualizing suitable queries, as, typically, their knowledge of the past is limited. In this paper, we propose a novel approach for the temporal correspondence detection task that requires finding terms in the past which are semantically closest to a given input present term. The approach we propose is based on vector space transformation that maps the distributed word representation in the present to the one in the past. The key problem in this approach is obtaining correct training set that could be used for a variety of diverse document collections and arbitrary time periods. To solve this problem, we propose an effective technique for automatically constructing seed pairs of terms to be used for finding the transformation. We test the performance of proposed approaches over short as well as long time frames such as 100 years. Our experiments demonstrate that the proposed methods outperform the best-performing baseline by 113 percent for the New York Times Annotated Corpus and by 28 percent for the Times Archive in MRR on average, when the query has a different literal form from its temporal counterpart.

Precipitation data fusion using vector space transformation and artificial neural networks

We have developed a new methodology to fuse several precipitation datasets, available from different estimation techniques. The method is based on artificial neural networks and vector space transformation function. The final merged product is statistically superior to any of the individual datasets over a seasonal period. The results have been tested against ground-based measurements of rainfall over a study area. This method is shown to have average success rates of 85% in the summer, 68% in the fall, 77% in the spring, and 55% in the winter.

Inverse problems in dynamic cognitive modeling

Inverse problems for dynamical system models of cognitive processes comprise the determination of synaptic weight matrices or kernel functions for neural networks or neural/dynamic field models, respectively. We introduce dynamic cognitive modeling as a three tier top-down approach where cognitive processes are first described as algorithms that operate on complex symbolic data structures. Second, symbolic expressions and operations are represented by states and transformations in abstract vector spaces. Third, prescribed trajectories through representation space are implemented in neurodynamical systems. We discuss the Amari equation for a neural/dynamic field theory as a special case and show that the kernel construction problem is particularly ill-posed. We suggest a Tikhonov-Hebbian learning method as regularization technique and demonstrate its validity and robustness for basic examples of cognitive computations.

Continuous modules are clean

A ring R is said to be clean if every element of R is a sum of an idempotent and a unit. The class of clean rings is quite large and includes, for instance, semiperfect rings (and thus finite rings), and rings of linear transformations of vector spaces. We prove that the endomorphism ring of every continuous (or discrete) module is clean.

On lacets and their manifolds

By topological lacet we mean the embedding, with self-intersections, of a closed curve in a 2-manifold, such that (1) all self-intersections are simple double points at which the curve crosses itself, and (2) the complement of the curve in the 2-manifold is a 2-colorable family of discs. Such embeddings are characterized, up to homotopy, by a combinatorial lacet, that is, by a double occurrence word Δ on an alphabet P and a bipartition (K,L) of the set P, P representing the set of self-intersections of the curve, Δ their sequence in one complete run along the curve, and K,L the two types of reentry possible at a crossing. Passing by the construction of a map associated to the lacet, we show that every combinatorial lacet is representable on a 2-manifold. Beginning with a problem on curves in the plane posed and partially solved by Gauss (1840), and introducing certain linear transformations of vector spaces over GF(2) , depending on Δ and (K,L), Rosenstiehl [C. R. Acad. Sci. Paris Ser. A 283 (1976) 551] and Lins et al. [Aequationes Math. 33 (1987) 81] characterized combinatorial lacets representable in the Euclidean plane and projective plane, respectively, by a simple property of the enlacement graph of pairs of letters in Δ. We prove here that a characterisation of the same sort extends naturally to the case of arbitrary 2-manifolds. In particular, we present procedures for determining if a combinatorial lacet is representable on the torus, or on the Klein bottle.

Extension of the Unit Disk Gyrogroup into the Unit Ball of Any Real Inner Product Space

The group of all holomorphic automorphisms of the complex unit disk consists of Möbius transformations involving translation-like holomorphic automorphisms and rotations. The former are calledgyrotranslations. As opposed to translations of the complex plane, which are associative-commutative operations (i.e., their composition law is associative and commutative) forming a group, gyrotranslations of the complex unit disk fail to form a group. Rather, left gyrotranslations are gyroassociative-gyrocommutative operations (i.e., their composition law is gyroassociative and gyrocommutative) forming agyrogroup. The complex unit disk gyrogroup has previously been studied by the author (Aequationes Math.47, 1994, 240–254). Employing analogies shared by complex numbers and linear transformations of vector spaces, we extend in this article the complex disk gyrogroup and its Möbius transformations into the ball of any real inner product space and its generalized Möbius transformations. A gyrogroup is a mathematical object which first arose in the study of relativistic velocities which, under velocity addition, form a nongroup gyrogroup, as opposed to prerelativistic velocities, which form a group under velocity addition. It has been discovered that the mathematical regularity, seemingly lost in the transition from prerelativistic to relativistic velocities, is concealed in a relativistic effect known as Thomas precession. In its abstract context, Thomas precession is called Thomas gyration, giving rise to our “gyroterminology.” Our gyroterminology, developed by the author (Amer. J. Phys.59, 1991, 824–834), involves terms like gyrogroups, gyroassociative-gyrocommutative laws, and gyroautomorphisms, in which we extensively use the prefix “gyro.”

Noise compensation for linear prediction via orthogonal transformation

An efficient method is presented for compensating for the bandwidth broadening effect while performing linear prediction of noise-contaminated speech signals. This method takes advantage of an orthogonal transformation in vector space. The computational load is negligible, but the improvement as manifested by the sharpened formant peaks is considerable.

Isomorphisms of semigroups of transformations

If M is a centered operand over a semigroup S, the suboperands of M containing zero are characterized in terms of S‐homomorphisms of M. Some properties of centered operands over a semigroup with zero are studied.A Δ‐centralizer C of a set M and the semigroup S(C, Δ) of transformations of M over C are introduced, where Δ is a subset of M. When Δ = M, M is a faithful and irreducible centered operand over S(C, Δ). Theorems concerning the isomorphisms of semigroups of transformations of sets Mi over Δi‐centralizers Ci, i = 1, 2 are obtained, and the following theorem in ring theory is deduced: Let Li, i = 1, 2 be the rings of linear transformations of vector spaces (Mi, Di) not necessarily finite dimensional. Then f is an isomorphism of L1 → L2 if and only if there exists a 1 − 1 semilinear transformation h of M1 onto M2 such that fT = hTh−1 for all T ∈ L1.

Completely semisimple ring semigroups

AbstractLet R be a ring in which the multiplicative semigroup is completely semisimple. If R has the maximum (respectively, minimum) condition on principal multiplicative ideals. then R is semiprime artinian (respectively, a direct sum of dense rings of finite-rank linear transformations of vector spaces over division rings).

On nonlinear transformations in vector spaces. Colineation and conformal groups

The sets of special colineations and conformal transformations of a pseudo-orthogonal vector space can be given only a Lie groupoid structure, rather than a Lie group structure because of the non-vanishing denominators. With every such groupoid one can associate a unique Lie group, which, however, no longer consists of transformations. For one-parameter subgroups one can define infinitesimal transformations and a bilinear composition, called Lie bracket, which reduces for linear transformations to the commutator. In the special cases of colineations and conformal transformations on pseudo-orthogonal vector spaces of arbitrary finite dimension and signatures, covering homomorphisms onto matrix groups are given together with the corresponding Lie algebra isomorphisms.