Kernel Mapping Research Articles

Euler Kernel Mapping for Hyperspectral Image Clustering via Self-Paced Learning

Clustering, as a classical unsupervised artificial intelligence technology, is commonly employed for hyperspectral image clustering tasks. However, most existing clustering methods designed for remote sensing tasks aim to solve a non-convex objective function, which can be optimized iteratively, beginning with random initializations. Consequently, during the learning phase of the clustering model, it may easily fall into bad local optimal solutions and finally hurt the clustering performance. Additionally, prevailing approaches often exhibit limitations in capturing the intricate structures inherent in hyperspectral images and are very sensitive to noise and outliers that widely exist in remote sensing data. To address these issues, we proposed a novel Euler kernel mapping for hyperspectral image clustering via self-paced learning (EKM-SPL). EKM-SPL first employs self-paced learning to learn the clustering model in a meaningful order by progressing samples from easy to complex, which can help to remove bad local optimal solutions. Secondly, a probabilistic soft weighting scheme is employed to measure complexity across the data sample, which makes the optimization process more reasonable. Thirdly, in order to more accurately characterize the intricate structure of hyperspectral images, Euler kernel mapping is used to convert the original data into a reproduced kernel Hilbert space, where the nonlinearly inseparable clusters may become linearly separable. Moreover, we innovatively integrate the coordinate descent technique into the optimization algorithm to circumvent the computational inefficiencies and information loss typically associated with conventional kernel methods. Extensive experiments conducted on classic benchmark hyperspectral image datasets illustrate the effectiveness and superiority of our proposed model.

Double kernel and minimum variance embedded broad learning system based autoencoder for one-class classification

One-class classification methods are often used for anomaly detection in healthcare, quality control in manufacturing, and fraud detection in financial services. Particularly in medical datasets, instances of rare cancers are considerably fewer in comparison to those of healthy individuals. One-class classification methods, which concentrate on learning models using just samples from a specified class, have drawn increasing attention as a solution to this problem. To enhance the model’s ability to capture essential feature information, we propose a novel strategy in this paper. This strategy involves the initial application of double kernel mapping, translating the original features into a new feature space. The autoencoder based on the Broad Learning System is then modified to incorporate the minimum variance so that the model can learn the potential feature information. We validated the effectiveness of our proposed strategy using UCI dataset and concordia digits dataset. To compare the performance with other one-class methods, the average F1 scores and the average G−mean are employed as comparative measures. Based on experimental results, it is evident that DKVBLS-AE not only outperforms but also demonstrates greater stability compared to the existing methods.

Dynamic functional connections analysis with spectral learning for brain disorder detection

Dynamic functional connections (dFCs), can reveal neural activities, which provides an insightful way of mining the temporal patterns within the human brain and further detecting brain disorders. However, most existing studies focus on the dFCs estimation to identify brain disorders by shallow temporal features and methods, which cannot capture the inherent temporal patterns of dFCs effectively. To address this problem, this study proposes a novel method, named dynamic functional connections analysis with spectral learning (dCSL), to explore inherently temporal patterns of dFCs and further detect the brain disorders. Concretely, dCSL includes two components, dFCs estimation module and dFCs analysis module. In the former, dFCs are estimated via the sliding window technique. In the latter, the spectral kernel mapping is first constructed by combining the Fourier transform with the non-stationary kernel. Subsequently, the spectral kernel mapping is stacked into a deep kernel network to explore higher-order temporal patterns of dFCs through spectral learning. The proposed dCSL, sharing the benefits of deep architecture and non-stationary kernel, can not only calculate the long-range relationship but also explore the higher-order temporal patterns of dFCs. To evaluate the proposed method, a set of brain disorder classification tasks are conducted on several public datasets. As a result, the proposed dCSL achieves 5% accuracy improvement compared with the widely used approaches for analyzing sequence data, 1.3% accuracy improvement compared with the state-of-the-art methods for dFCs. In addition, the discriminative brain regions are explored in the ASD detection task. The findings in this study are consistent with the clinical performance in ASD.

Sub-sampling graph neural networks for genomic prediction of quantitative phenotypes.

In genomics, use of deep learning (DL) is rapidly growing and DL has successfully demonstrated its ability to uncover complex relationships in large biological and biomedical data sets. With the development of high-throughput sequencing techniques, genomic markers can now be allocated to large sections of a genome. By analysing allele sharing between individuals, one may calculate realized genomic relationships from single nucleotide polymorphisms (SNPs) data rather than relying on known pedigree relationships under polygenic model. The traditional approaches in genome-wide prediction (GWP) of quantitative phenotypes utilise genomic relationships in fixed global covariance modelling, possibly with some non-linear kernel mapping (for example Gaussian processes). On the other hand, the DL approaches proposed so far for GWP fail to take into account the non-Euclidean graph structure of relationships between individuals over several generations. In this paper, we propose one global convolutional neural network (GCN) and one local sub-sampling architecture (GCN-RS) that are specifically designed to perform regression analysis based on genomic relationship information. A GCN is tailored to non-Euclidean spaces and consists of several layers of graph convolutions. The GCN-RS architecture is designed to further improve the GCN's performance by sub-sampling the graph to reduce the dimensionality of the input data. Through these graph convolutional layers, the GCN maps input genomic markers to their quantitative phenotype values. The graphs are constructed using an iterative nearest neighbour approach. Comparisons show that the GCN-RS outperforms the popular Genomic Best Linear Unbiased Predictor (GBLUP) method on one simulated and three real data sets from wheat, mice and pig with a predictive improvement of 4.4% to 49.4% in terms of test mean squared error (MSE). This indicates that GCN-RS is a promising tool for genomic predictions in plants and animals. Furthermore, GCN-RS is computationally efficient, making it a viable option for large-scale applications.

KGR: A Kernel-Mapping Based Group Recommender System Using Trust Relations

A massive amount of information explosion over the internet has caused a possible difficulty of information overload. To overcome this, Recommender systems are systematic tools that are rapidly being employed in several domains such as movies, travel, E-commerce, and music. In the existing research, several methods have been proposed for single-user modeling, however, the massive rise of social connections potentially increases the significance of group recommender systems (GRS). A GRS is one that jointly recommends a list of items to a collection of individuals based on their interests. Moreover, the single-user model poses several challenges to recommender systems such as data sparsity, cold start, and long tail problems. On the contrary hand, another hotspot for group-based recommendation is the modeling of user preferences and interests based on the groups to which they belong using effective aggregation strategies. To address such issues, a novel “KGR” group recommender system based on user-trust relations is proposed in this study using kernel mapping techniques. In the proposed model, user-trust networks or relations are exploited to generate trust-based groups of users which is one of the important behavioral and social aspects. More precisely, in KGR the group kernels and group residual matrices are exploited as well as seeking a multi-linear mapping between encoded vectors of group-item interactions and probability density function indicating how groups will rate the items. Moreover, to emphasize the relevance of individual preferences of users in a group to which they belong, a hybrid approach is also suggested in which group kernels and individual user kernels are merged as additive and multiplicative models. Furthermore, the proposed KGR is validated on two different trust-based datasets including Film Trust and CiaoDVD. In addition, KGR outperforms with an RMSE value of 0.3306 and 0.3013 on FilmTrust and CiaoDVD datasets which are lower than the 1.8176 and 1.1092 observed with the original KMR.

Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space.

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population-population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important.

Mental health and collective health: an epidemiological analysis of suicides in Brazil

To analyze the temporal behavior of suicides. Cross-sectional, ecological study on suicide registered in the mortality information system. Kernel analysis was used in Quantum Geographic Information System (QGIS), TerraView and the Chi-Square test in R software. In twenty years there were 195,046 suicides, with a mortality rate of 4.94, mainly in the southeast, among males with significant growth, low education, single, aged 20-29, white and by hanging. In the kernel map, the south, southeast and northeast regions concentrate the largest clusters. In part of the South and in the interior of the Southeast there was a reduction in mortality. This study provides information about the worrying scenario of suicide in Brazil over twenty years, identifying the areas and characteristics with the greatest risks. To reduce this suicide scenario, effective public actions and a quality health care network that provides comprehensive, equitable and universal assistance to the mental health of individuals are essential, creating conditions to meet the needs of the social body.

Spatial-temporal evolution of carbon emissions and spatial-temporal heterogeneity of influencing factors in the Bohai Rim Region, China.

The total change in carbon emissions in the Bohai Rim Region (BRR) plays a guiding role in the policy formulation of carbon emission reduction in northern China. Taking the 43 cities in the BRR as an example, the spatial-temporal evolution of carbon emissions in the BRR was analyzed using kernel density estimation (KDE), map visualization, and standard deviation ellipses, and the spatial autocorrelation model was used to explore the spatial clustering of carbon emissions. On this basis, the spatial-temporal heterogeneity of the factors influencing carbon emissions is explained using a Geodetector. The results are as follows: (i) During the study period, the carbon emissions in the BRR were on the rise, the share of carbon emissions in the Beijing-Tianjin-Hebei region (BTHR) and Liaoning Province was decreasing, and the contribution of Shandong Province was gradually enhanced. The spatial distribution of carbon emissions shows a geographical pattern of "middle-high and low-outside." (ii) Carbon emissions from different regions show the characteristics of BTHR > Shandong Province > Liaoning Province. The high-value carbon emission area continues to move from the northwest of Beijing-Tianjin-Hebei to the southeast. (iii) Municipal carbon emissions showed a significant positive spatial correlation in the later part of the study. The high-high aggregation area is in Tianjin, and the low-low aggregation area is in Liaoning Province. (iv) The level of transport development contributes to carbon emissions with the highest growth rate, followed by industrial structure. There are also regional differences in the dominant influences on municipal carbon emission differences. Population size, urbanization, and economic development level are the core influencing factors of carbon emissions in the BTHR, Shandong Province, and Liaoning Province, respectively. In addition, the explanatory power of the interaction between the level of economic development and other factors on carbon emissions is at a high level.

Tomographic Universality of the Discrete Wigner Function

We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.

Tensor Robust Kernel PCA for Multidimensional Data.

Recently, the tensor nuclear norm (TNN)-based tensor robust principle component analysis (TRPCA) has achieved impressive performance in multidimensional data processing. The underlying assumption in TNN is the low-rankness of frontal slices of the tensor in the transformed domain (e.g., Fourier domain). However, the low-rankness assumption is usually violative for real-world multidimensional data (e.g., video and image) due to their intrinsically nonlinear structure. How to effectively and efficiently exploit the intrinsic structure of multidimensional data remains a challenge. In this article, we first suggest a kernelized TNN (KTNN) by leveraging the nonlinear kernel mapping in the transform domain, which faithfully captures the intrinsic structure (i.e., implicit low-rankness) of multidimensional data and is computed at a lower cost by introducing kernel trick. Armed with KTNN, we propose a tensor robust kernel PCA (TRKPCA) model for handling multidimensional data, which decomposes the observed tensor into an implicit low-rank component and a sparse component. To tackle the nonlinear and nonconvex model, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm. Extensive experiments on real-world applications collectively verify that TRKPCA achieves superiority over the state-of-the-art RPCA methods.

Geography and public health: analysis of the epidemiological dynamics of meningitis in Brazil, between 2010 and 2019.

To analyze the spatiotemporal epidemiological dynamics of meningitis in Brazil, between 2010 and 2019. Descriptive ecological study with cases and deaths due to meningitis in Brazil (2010-2019) in the National Notifiable Diseases Information System (Sistema de Informações de Agravos de Notificação - SINAN). The following analyses were performed: (I) frequency analyses of cases and deaths, prevalence rates, mortality, lethality, Fisher's exact test, and chi-square test; (II) Prais-Winstein regression; and (III) Global, Local Moran's index, and Kernel density. 182,126 cases of meningitis were reported in Brazil, of which 16,866 (9.26%) resulted in death, with prevalence rates of 9.03/100,000 inhabitants, mortality of 0.84/100,000 inhabitants, and lethality of 9.26%. There was a noted trend of decreasing prevalence rates (-9.5%, 95% confidence interval - 95%CI -13.92; -4.96, p<0.01) and mortality (-11.74%, 95%CI -13.92; -9.48, p<0.01), while lethality remained stable (-2.08%, 95%CI -4.9; 0.8; p<0.1941). The majority of cases were viral meningitis (45.7%), among 1-9 years old (32.2%), while the highest proportion of deaths was due to bacterial meningitis (68%), among 40-59 years old (26.3%). In the Moran and Kernel maps of prevalence and mortality rates, municipalities in the South, Southeast, and the capital of Pernambuco in the Northeast stood out with high rates; as for lethality, the North, Northeast, and Southeast coastal areas were highlighted. A decrease in meningitis cases and deaths was found in this study; however, the lethality rate was higher in areas with lower prevalence, emphasizing the need to enhance actions for identifying, monitoring, and providing health care for cases, as well as expanding vaccination coverage.

The application of blood flow sound contrastive learning to predict arteriovenous graft stenosis of patients with hemodialysis.

End-stage kidney disease (ESKD) presents a significant public health challenge, with hemodialysis (HD) remaining one of the most prevalent kidney replacement therapies. Ensuring the longevity and functionality of arteriovenous accesses is challenging for HD patients. Blood flow sound, which contains valuable information, has often been neglected in the past. However, machine learning offers a new approach, leveraging data non-invasively and learning autonomously to match the experience of healthcare professionas. This study aimed to devise a model for detecting arteriovenous grafts (AVGs) stenosis. A smartphone stethoscope was used to record the sound of AVG blood flow at the arterial and venous sides, with each recording lasting one minute. The sound recordings were transformed into mel spectrograms, and a 14-layer convolutional neural network (CNN) was employed to detect stenosis. The CNN comprised six convolution blocks with 3x3 kernel mapping, batch normalization, and rectified linear unit activation function. We applied contrastive learning to train the pre-training audio neural networks model with unlabeled data through self-supervised learning, followed by fine-tuning. In total, 27,406 dialysis session blood flow sounds were documented, including 180 stenosis blood flow sounds. Our proposed framework demonstrated a significant improvement (p<0.05) over training from scratch and a popular pre-trained audio neural networks (PANNs) model, achieving an accuracy of 0.9279, precision of 0.8462, and recall of 0.8077, compared to previous values of 0.8649, 0.7391, and 0.6538. This study illustrates how contrastive learning with unlabeled blood flow sound data can enhance convolutional neural networks for detecting AVG stenosis in HD patients.

Kernel Mapping Methods of Convolutional Neural Network in 3D NAND Flash Architecture

A flash memory is a non-volatile memory that has a large memory window, high cell density, and reliable switching characteristics and can be used as a synaptic device in a neuromorphic system based on 3D NAND flash architecture. We fabricated a TiN/Al2O3/Si3N4/SiO2/Si stack-based Flash memory device with a polysilicon channel. The input/output signals and output values are binarized for accurate vector-matrix multiplication operations in the hardware. In addition, we propose two kernel mapping methods for convolutional neural networks (CNN) in the neuromorphic system. The VMM operations of two mapping schemes are verified through SPICE simulation. Finally, the off-chip learning in the CNN structure is performed using the Modified National Institute of Standards and Technology (MNIST) dataset. We compared the two schemes in terms of various parameters and determined the advantages and disadvantages of each.

SiameseDeNPEnetwork framework for fault detection of batch process

AbstractIn batch processes, it is crucial to ensure safe production by fault detection. However, the long batch duration, limited runs, and strong nonlinearity of the data pose challenges. Incipient faults with small amplitudes further complicate the detection process. To achieve safe production, motivated by deep learning strategies, we propose a new fault detection method of batch process called Siamese deep neighbourhood preserving embedding network (SDeNPE). First, the DeNPE network is constructed by means of NPE and kernel functions, which utilizes the different types of kernel functions in the kernel mapping layer to extract diverse deep nonlinear features and overcome strong nonlinearity in the process data. Then, the Siamese network is used to obtain the different features between the data and improve the recognition of incipient faults. In addition, the deep extraction and Siamese network allow for batches of training data reduction without diminishing the performance of fault detection. Finally, we utilize monitoring statistics to complete the fault detection process. Two batch process cases involving the penicillin fermentation process and the semiconductor etching process demonstrate the superior fault detection performance of the proposed SDeNPE over the other comparison methods.

One Health Approach to Leptospirosis: Dogs as Environmental Sentinels for Identification and Monitoring of Human Risk Areas in Southern Brazil.

Leptospirosis has been a neglected, widespread and reemerging zoonotic disease of global importance. The One Health holistic approach combining human, animal and environmental health has been important for control and prevention of zoonotic disease. An urban municipality in Southern Brazil with a high prevalence of leptospirosis was selected by convenience, with asymptomatic human and canine individuals serologically tested using MAT against 30 Leptospira spp. serovars. Epidemiological questionnaires were assessed along with the historical national database, with associated risk factors to dog and human seropositivity analyzed using multiple logistic regression. The spatial distribution of retrospective human leptospirosis cases was analyzed using a Kernel map and overlapped dog seropositivity and historical flooding areas, demonstrating that domestic and asymptomatic dogs may be important environmental sentinels for leptospirosis in such urban areas, even in the absence of human seropositivity and low canine seropositivity. Associated risk factors for leptospirosis in dogs and humans according to multiple regression included healthy dogs (p = 0.02, odds ratio-OR = 0.17, confidence interval of 95%CI 0.03-0.71) with indoor access (p = 0.059, OR = 5.12, 95%CI 1.10-37.7) and human males (p = 0.042, OR = 2.44, 95%CI 1.08-6.11) with presenting calf pain (p = 0.005, OR = 3.14, 95%CI 1.46-7. 14), jaundice (p < 0.001, OR = 4.61, 95%CI 2.11-10.10) and renal failure (p = 0.008, OR = 4.49, 95%CI 1.49-13.76). The greater the rain precipitation (above 3 mm of average annual precipitation), the higher the number of leptospirosis cases in humans. In conclusion, dog active serosurvey and rain precipitation should be systematically reported and plotted altogether as a basis for the early detection and monitoring of human risk areas. Such findings may serve as a basis for public health policies in Brazil and other endemic countries worldwide.

GraphAGILE: An FPGA-Based Overlay Accelerator for Low-Latency GNN Inference

This paper presents GraphAGILE, a domain-specific FPGA-based overlay accelerator for graph neural network (GNN) inference. GraphAGILE consists of (1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a novel unified architecture design</i> with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">instruction set</i> , and (2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a compiler</i> built upon the instruction set that can quickly generate optimized code. Due to the proposed instruction set architecture (ISA) and the compiler, GraphAGILE does not require any FPGA reconfiguration when performing inference on various GNN models and input graphs. For the architecture design, we propose a novel hardware module named Adaptive Computation Kernel (ACK), that can execute various computation kernels of GNNs, including general matrix multiplication (GEMM), sparse-dense matrix multiplication (SpDMM), and sampled dense-dense matrix multiplication (SDDMM). The compiler takes the specifications of a GNN model and the graph meta data (e.g., the number of vertices and edges) as input, and generates a sequence of instructions for inference execution. We develop the following compiler optimizations to reduce inference latency: (1) computation order optimization that automatically reorders the computation graph to reduce the total computation complexity, (2) layer fusion that merges adjacent layers to reduce data communication volume, (3) data partitioning with a partition-centric execution scheme that partitions the input graph to fit the available on-chip memory of FPGA, (4) kernel mapping that automatically selects execution mode for ACK, and performs task scheduling to overlap computation with data communication and achieves dynamic load balance. We implement GraphAGILE on a state-of-the-art FPGA platform, Xilinx Alveo U250. GraphAGILE can execute widely used GNN models, including GCN, GAT, GIN, GraphSAGE, SGC and other GNN models supported by GraphGym. Experimental results show that GraphAGILE achieves up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$47.1\times$</tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3.9\times$</tex-math></inline-formula> ) reduction in end-to-end latency, including the latency of compilation and hardware execution, compared with the state-of-the-art implementations on CPU (GPU), and achieves up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.9\times$</tex-math></inline-formula> reduction in hardware execution latency compared with the state-of-the-art FPGA accelerators.

Neural kernel mapping SVM model based on multi-head self-attention for classification of Chinese meteorological disaster warning texts

Neural kernel mapping SVM model based on multi-head self-attention for classification of Chinese meteorological disaster warning texts

Contrastive deep support vector data description

In comparison with support vector data description (SVDD), deep SVDD (DSVDD) is more suitable for dealing with large-scale data sets. DSVDD uses mapping network to replace the role of kernel mapping in SVDD. Moreover, the objective of DSVDD is to simultaneously learn the optimal connection weights of mapping network and the minimum volume of hypersphere. To further improve the performance of DSVDD for tackling large-scale data sets and obtain the discriminative features of the given samples in a self-supervised learning manner, contrastive DSVDD (CDSVDD) is proposed in this study. In the pre-training phase of CDSVDD, the contrastive loss and the rotation prediction loss are jointly minimized to achieve the optimal feature representations. Furthermore, the learned feature representations are utilized to determine the hypersphere center. In the training phase of CDSVDD, the distances between the obtained feature representations and the hypersphere center together with the contrastive loss are simultaneously minimized to derive the optimal network connection weights, the minimum volume of hypersphere and the optimal feature representations. In addition, CDSVDD can efficiently solve the hypersphere collapse problem of DSVDD. The ablation study on CDSVDD verifies that compared with the case of determining the hypersphere center by the feature representations of the original samples, the hypersphere center determined by the feature representations of the augmented samples makes CDSVDD achieve better hypersphere boundary and more compact feature representations. Experimental results on the four benchmark data sets demonstrate that the proposed CDSVDD acquires better detection performance in comparison with its six pertinent methods.

Approximate Gaussian kernel mapping incremental LSSVR based on knowledge transfer and its industrial application

Aiming at the problem of diversified and time-varying data in industrial energy forecast, an incremental least squares support vector regression model based on approximate Gaussian kernel mapping and knowledge transfer is proposed. Firstly, an incremental learning method based on historical parameter transfer is designed, which is applied to single output and multiple output least squares support vector regression models respectively. It can update the prediction model quickly and meet the requirements of real-time. In order to further improve the prediction accuracy, the approximate Gaussian kernel mapping based on Taylor series theory is used to extend the proposed model to the nonlinear case, which effectively solves the problem of kernel matrix storage. At the same time, the training process is optimized through Sherman–Morrison–Woodbury (SMW) formula, which improves the solution efficiency in enhancing the flexibility of the model. Experiments on industrial energy data show that the proposed method can improve the adaptive ability and prediction accuracy of the model, and improve energy efficiency.

Dimensionality reduction of large datasets with explicit feature maps

Learning algorithms are often equipped with kernels that enable them to deal with non-linearities in the data, which ensures increased performance in practice. However, traditional kernel based methods suffer from the problem of scalability. As a workaround, explicit kernel maps have been proposed in the past. Previously for the task of streaming Kernel Principal Component Analysis (KPCA), an explicit kernel map has been combined with a matrix sketching technique to obtain scalable dimensionality reduction (DR) algorithm. This algorithm is limited by two issues, both pertaining to the explicit kernel map and the matrix sketching algorithms respectively. As a solution, two new scalable DR algorithms called ECM-SKPCA and Euler-SKPCA are proposed. The efficacy of the proposed algorithms as scalable DR algorithms is demonstrated via the task of classification with many publicly available datasets. The results indicate that the proposed algorithms produce more effective features than the previous algorithm for the classification task. Furthermore, ECM-SKPCA is also demonstrated to be much faster than all other algorithms.