Efficient Matrix Research Articles

Efficient matrix key homomorphic encryption of medical images

A sure way of providing privacy to sensitive images is to encrypt them, especially when they are stored in a public cloud server. Homomorphic encryption enables arithmetic operations over encrypted data without access to the secret key. This facility can be well harnessed for secure outsourced image processing by exploiting the available computational capabilities of modern cloud servers. This paper presents a new homomorphic image encryption scheme that uses integer matrix keys. The homomorphic operations are carried out in the finite field Zp to avail the advantages of integer arithmetic and to limit the cipher text sizes to reasonable levels. Our method does not use any error vector as in learning with errors (LWE) to improve the security.

Optimizing massively parallel sparse matrix computing on ARM many-core processor

Sparse matrix multiplication is ubiquitous in many applications such as graph processing and numerical simulation. In recent years, numerous efficient sparse matrix multiplication algorithms and computational libraries have been proposed. However, most of them are oriented to x86 or GPU platforms, while the optimization on ARM many-core platforms has not been well investigated. Our experiments show that existing sparse matrix multiplication libraries for ARM many-core CPU cannot achieve expected parallel performance. Compared with traditional multi-core CPU, ARM many-core CPU has far more cores and often adopts NUMA techniques to scale the memory bandwidth. Its parallel efficiency tends to be restricted by NUMA configuration, memory bandwidth cache contention, etc.In this paper, we propose optimized implementations for sparse matrix computing on ARM many-core CPU. We propose various optimization techniques for several routines of sparse matrix multiplication to ensure coalesced access of matrix elements in the memory. In detail, the optimization techniques include a fine-tuned CSR-based format for ARM architecture, co-optimization of Gustavson’s algorithm with hierarchical cache and dense array strategy to mitigate performance loss caused by handling compressed storage formats. We exploit the coarse-grained NUMA-aware strategy for inter-node parallelism and the fine-grained cache-aware strategy for intra-node parallelism to improve the parallel efficiency of sparse matrix multiplication. The evaluation shows that our implementation consistently outperforms the existing library on ARM many-core processor.

MM optimization: Proximal distance algorithms, path following, and trust regions

We briefly review the majorization-minimization (MM) principle and elaborate on the closely related notion of proximal distance algorithms, a generic approach for solving constrained optimization problems via quadratic penalties. We illustrate how the MM and proximal distance principles apply to a variety of problems from statistics, finance, and nonlinear optimization. Drawing from our selected examples, we also sketch a few ideas pertinent to the acceleration of MM algorithms: a) structuring updates around efficient matrix decompositions, b) path following in proximal distance iteration, and c) cubic majorization and its connections to trust region methods. These ideas are put to the test on several numerical examples, but for the sake of brevity, we omit detailed comparisons to competing methods. The current article, which is a mix of review and current contributions, celebrates the MM principle as a powerful framework for designing optimization algorithms and reinterpreting existing ones.

Hybrid weighted communication network node importance evaluation method

Communication networks are used as an important guarantee for information interaction and efficient collaboration within many fields and systems; however, under information technology conditions, the destruction of a number of nodes in a network may have a great impact on the overall operation of the network. Therefore, it is important to accurately determine the critical nodes in the network to enhance the network’s resistance to destruction. Combining the characteristic attributes of the communication network, a node contribution evaluation matrix is proposed based on the efficiency matrix, from the perspective of node receiving information; a node value evaluation matrix is proposed from the perspective of a node providing information to neighboring nodes, and node importance is calculated by integrating the evaluation results of the two matrices and the node’s own attributes. The algorithm is suitable for directed-weighted network node value evaluation, and the effectiveness and accuracy of the algorithm are verified by comparing other algorithms for a small-scale network. In further experimental validation, a hybrid weighted communication network evolution model based on organizational structured networks is proposed, and networks of different sizes are generated for experimental simulation. The results show that when nodes with high importance are removed from the network, they can cause a rapid decrease in the network efficiency and maximum connectivity, confirming the accuracy of the algorithm in evaluating the importance of nodes and identifying critical nodes in the network.

Evaluation of direct sample injection as a fast, no-sample handling, approach for the LC-MS/MS monitoring of pharmaceuticals in different water matrices

The determination of drug residues in water, particularly in environmental water, is a hot topic due to the usual presence of these emerging contaminants in the aquatic environment and their potential negative impact on water quality. The most widely approach applied at present for their determination is the use of a solid phase extraction (SPE) step followed by the LC-MS/MS measurement. This is due to the theoretical need to pre-concentrate the analytes and to produce “clean” sample extracts leading to less inferences in subsequent analysis. However, in LC-MS/MS based methods, the main interferences are not “visible” and are mostly due to matrix effects, which in fact are produced by unknown compounds that co-elute with the analytes and therefore not easily removed by SPE. As an alternative, an increasing trend is observed towards the use of direct injection (DI) of the samples, which is nowadays possible thank to the notable improvement in sensitivity of modern LC-MS/MS instrumentation.In this work, both approaches, SPE and DI, have been evaluated for the determination of 16 pharmaceuticals in three different types of water: groundwater, surface water and effluent wastewater. The study has been performed by using pharmaceutical reference standards and their corresponding isotope-labelled internal standards (ILIS) for efficient matrix effects correction. Both methodologies have been compared in terms of matrix effects, sensitivity, and suitability for the analysis of real-world water samples. Our data show that DI is an efficient alternative to SPE, with satisfactory analyte recoveries for most pharmaceuticals, matrix effects even lower than in SPE, and sufficient sensitivity for most of applications. In addition, the absence of sample treatment minimizes potential errors associated with this step, and there is a notable saving in the analysis time and costs. The analysis of Quality Control (QC) samples included in different sample batch sequences has been used to support the feasibility of using DI in this type of analysis.

GIO: Generating Efficient Matrix and Frame Readers for Custom Data Formats by Example

Data Scientists deal with a wide variety of file data formats and data representations. Probably the most difficult to handle are custom data formats that liberally define their own particular flat or nested structure with multiple custom delimiters, multi-line records, or undocumented semantics of attribute sequences, co-appearances, and repetitions. As a prerequisite for exploratory ML model training, data scientists need to map these data representations into regular frames or matrices. Unfortunately, existing tools and frameworks provide only limited support for aiding this process, which causes redundant manual efforts and unnecessary data quality issues. In this paper, we initiate work on automatic matrix and frame reader generation by example. A user provides a sample of raw text data and its mapped matrix or frame representation. Our GIO framework then first identifies the mapping rules from raw to structured data, and subsequently generates source code of an efficient, multi-threaded reader for reading full raw datasets of this format. In order to facilitate manual improvements, both the mapping rules, and generated reader can be modified as needed. Our experiments show that GIO is able to correctly identify the mapping rules for basic text formats like CSV, LibSVM, MatrixMarket; custom text formats from publishing, automotive, and health care; as well as various nested formats such as JSON and XML. Additionally, the automatically generated readers yield competitive performance compared to hand-coded readers and tuned libraries like RapidJSON.

DC grid load flow solution incorporating generic DC/DC converter topologies

This research proposes a load flow (LF) solver with DC/DC converter models for DC distribution. The solver is based on modified-augmented-nodal-analysis (MANA) formulation and is implemented with the Newton–Raphson (NR) algorithm. The conditions to guarantee the convergence range of the MANA are demonstrated with Kantorovich’s theorem. The proposed formulation is generic and flexible, allowing it to accommodate any arbitrary DC grid configuration. In addition, the formulation is extendable due to MANA’s modular structure, which enables the incorporation of any device without changing the prior formulation. Instead of bus power injections, the summation of line flows and their associated derivatives are used when considering connections with various kinds of buses equipped with various converters. The proposed method is implemented in MATLAB and tested on the modified IEEE 33 bus distribution test feeder. Electromagnetic Transient (EMT) simulations confirmed the accuracy of the proposed method. Moreover, the results are also compared with the recently proposed efficient Laplacian Matrix (eLM) based method. Results suggest that the proposed method is robust and offers superior convergence characteristics with a faster simulation speed.

Hydride generation-smartphone RGB readout and visual colorimetric dual-mode system for the detection of inorganic arsenic in water samples and honeys.

A miniaturized/portable dual-mode colorimetric analytical system was established for inorganic arsenic determination in honey and drinking water samples. Hydride generation (HG) was utilized as a sampling technique for this colorimetric system, because of its high generation efficiency and efficient matrix separation. AsH3 was generated via HG and then reacted with HAuCl4, gold nanoparticles (Au NPs) were formed on the paper sheet, leading the paper color changed from light yellow to dark blue, it could be readout by naked-eye (visual colorimetric mode) and a smartphone (RGB readout mode) simultaneously. The accuracy and potential application for field analysis were further confirmed by the analysis of two water samples, four honey samples and two certified reference water samples (BWB2440-2016 and GBW08650), good recoveries (90-116%) were obtained for those samples and their spiked samples.

Modular Matrix Multiplication on GPU for Polynomial System Solving

The bottleneck of the SPARSE-FGLM algorithm for Gröbner bases change of order is an iterative matrix - tall and skinny matrix product over a finite prime field. Our contribution is twofold. First, we port existing CPU-only algorithms for matrix products over prime fields to GPU architectures, and carry out a performance analysis of our implementation that shows that we can nearly achieve the maximum theoretical throughput of the hardware. Second, existing CPU-only algorithms could not handle primes with more than 26 bits, other than the GMP-based implementation in FLINT; we overcome this limitation by proposing an efficient multiword matrix product algorithm that can deal with primes with at most 35 bits; we benchmarked it on GPU.

Multi-view fusion guided matrix factorization based one-step efficient subspace clustering

Multi-view clustering that integrates the complementary information from different views for better clustering is a fundamental topic in data engineering. Most existing methods learn latent representations first, and then obtain the final result via post-processing. These two-step strategies may lead to sub-optimal clustering. The existing one-step methods are based on spectral clustering, which is inefficient. To address these problems, we propose a Multi-view fusion guided Matrix factorization based One-step subspace Clustering (MMOC) to perform clustering on multi-view data efficiently and effectively in one step. Specifically, we first propose a matrix factorization based multi-view fusion representation method, which adopts efficient matrix factorization instead of time-consuming spectral representation to reduce the computational complexity. Then we propose a self-supervised weight learning strategy to distinguish the importance of different views, which considers both the gradient and the learning rate to make the learned weights closer to the real situation. Finally, we propose a one-step framework of MMOC, which effectively reduces the information loss by integrating data representation, multi-view data fusion, and clustering into one step. We conduct experiments on 5 real-world datasets. The experimental results show the effectiveness and the efficiency of our MMOC method in comparison with state-of-the-art methods.

Parallel Optimization of BLAS on a New-Generation Sunway Supercomputer

The new-generation Sunway supercomputer has ultra-high computing capacity. But due to the unique heterogeneous architecture of the supercomputer, the open-source versions of basic linear algebra subprograms (BLAS) are insufficient for performance or compatibility. In addition, due to the update of the architecture, BLAS based on the previous Sunway could not fully exploit the performance of the successor. To address the challenges, we propose an optimized BLAS on the new-generation Sunway supercomputer in this paper. Specially, for achieving efficient computation, a parallel optimization method based on the new-generation Sunway for the Level-1 BLAS computing between vectors and the Level-2 BLAS computing between vectors and matrices is first proposed. Then, an adaptive scheduling algorithm for various data sizes is proposed, which is used to balance the tasks of core groups. Finally, to achieve highly efficient general matrix multiplication (GEMM) kernels, a parallel optimization method based on the new-generation Sunway for the Level-3 BLAS computing between matrices is proposed, which includes source-level optimization as well as assembly-level optimization. Experimental results show that the memory bandwidth utilization of the optimized Level-1/2 BLAS exceeds 95%, and the computational efficiency of the optimized GEMM kernel exceeds 94%.

Novel Isotope-Labeled Derivatization Strategy for the Simultaneous Analysis of Fatty Acids and Fatty Alcohols and Its Application in Idiopathic Inflammatory Myopathies and Pancreatic Cancer.

Fatty acids (FAs) and fatty alcohols (FOHs) are essential compounds for maintaining life. Due to the inherent poor ionization efficiency, low abundance, and complex matrix effect, such metabolites are challenging to precisely quantify and explore deeply. In this study, a pair of novel isotope derivatization reagents known as d0/d5-1-(2-oxo-2-(piperazin-1-yl) ethyl) pyridine-1-ium (d0/d5-OPEPI) were designed and synthesized, and an in-depth screening strategy for FAs and FOHs was established based on d0/d5-OPEPI coupled with liquid chromatography-tandem high-resolution mass spectrometry (LC-HRMS/MS). Using this approach, a total of 332 metabolites were identified and annotated (some of the FAs and FOHs were reconfirmed by standards). Our results demonstrated that OPEPI labeling could significantly enhance the MS response of FAs and FOHs via the introduction of permanently charged tags. The detection sensitivities of FAs were increased by 200-2345-fold compared with the nonderivatization method. At the same time, for FOHs, due to the absence of ionizable functional groups, sensitive detection was achieved utilizing OPEPI derivatization. One-to-one internal standards were provided by using d5-OPEPI labeling to minimize the errors in quantitation. Moreover, the method validation results showed that the method was stable and reliable. Finally, the established method was successfully applied to the study of the FA and FOH profiles of two heterogeneous severe clinical disease tissues. This study would improve our understanding of the pathological and metabolic mechanisms of FAs and FOHs for inflammatory myopathies and pancreatic cancer and also prove the generality and accuracy of the developed analytical method for complex samples.

Porting fragmentation methods to GPUs using an OpenMP API: Offloading the resolution-of-the-identity second-order Møller-Plesset perturbation method.

Using an OpenMP Application Programming Interface, the resolution-of-the-identity second-order Møller-Plesset perturbation (RI-MP2) method has been off-loaded onto graphical processing units (GPUs), both as a standalone method in the GAMESS electronic structure program and as an electron correlation energy component in the effective fragment molecular orbital (EFMO) framework. First, a new scheme has been proposed to maximize data digestion on GPUs that subsequently linearizes data transfer from central processing units (CPUs) to GPUs. Second, the GAMESS Fortran code has been interfaced with GPU numerical libraries (e.g., NVIDIA cuBLAS and cuSOLVER) for efficient matrix operations (e.g., matrix multiplication, matrix decomposition, and matrix inversion). The standalone GPU RI-MP2 code shows an increasing speedup of up to 7.5× using one NVIDIA V100 GPU with one IBM 42-core P9 CPU for calculations on fullerenes of increasing size from 40 to 260 carbon atoms using the 6-31G(d)/cc-pVDZ-RI basis sets. A single Summit node with six V100s can compute the RI-MP2 correlation energy of a cluster of 175 water molecules using the correlation consistent basis sets cc-pVDZ/cc-pVDZ-RI containing 4375 atomic orbitals and 14 700 auxiliary basis functions in ∼0.85h. In the EFMO framework, the GPU RI-MP2 component shows near linear scaling for a large number of V100s when computing the energy of an 1800-atom mesoporous silica nanoparticle in a bath of 4000 water molecules. The parallel efficiencies of the GPU RI-MP2 component with 2304 and 4608 V100s are 98.0% and 96.1%, respectively.

Research on Spatial Correlation Evolution of Marine Ecological Efficiency Based on Social Network and Spatial Correlation Matrix Model

Most developed countries in the world are maritime powers. This article constructs an ecological efficiency evaluation system based on the characteristics of the ocean itself while taking into account the relationship between land and sea. Based on social network analysis, the relationship between China’s marine ecological efficiency is regarded as a social network system, and the roles and positions played by 11 coastal cities in the network are analyzed from a relational perspective. Next, based on the unexpected super efficiency model to measure the ocean efficiency value in China’s coastal areas, we explore its spatiotemporal evolution characteristics, and measure the ocean ecological efficiency while incorporating ecological environmental pollution as an unexpected output into the evaluation system. Then, the spatial incidence matrix of marine ecological efficiency is calculated through the modified gravity model, and the characteristics of network structure are described with the help of the social network method. In addition, ArcGIS software is used to visualize the spatial evolution process. Finally, QAP regression is used to explore the key factors affecting the spatial correlation network of marine ecological efficiency in China. The results show the following: (1) In terms of time, the marine eco-efficiency of most provinces is not high, and the difference between provinces is obvious, but on the whole, it shows a fluctuating upward trend. (2) From the perspective of space, the overall displacement of the center of marine eco-efficiency in China is large in the north–south direction and small in the east–west direction, and the center of marine eco-efficiency is always concentrated near the Yangtze River Delta. (3) On the whole, the spatial correlation network of China’s marine eco-efficiency is becoming more and more complex. The number of correlation relationships and network density is increasing, and the network framework is gradually maturing. The spatial adjacency matrix, the difference in economic development level, and the difference in population distribution level can significantly promote the formation and development of the spatial correlation network of marine eco-efficiency. However, the differences in the level of opening to the outside world and in the structure of marine industries restrain their spatial networks. The difference between marine science and technology levels is not significant.

High-quality single amplicon sequencing method for illumina MiSeq platform using pool of ‘N’ (0–10) spacer-linked target specific primers without PhiX spike-in

BackgroundIllumina sequencing platform requires base diversity in the initial 11 cycles for efficient cluster identification and colour matrix estimation. This limitation yields low-quality data for amplicon libraries having homogeneous base composition. Spike-in of PhiX library ensures base diversity but reduces the overall number of sequencing reads for data analysis. To overcome such low diversity issues during amplicon sequencing on illumina platforms, we developed a high throughput single amplicon sequencing method by introducing ‘N’ (0–10) spacers in target gene amplification primers that are pooled for simple handling.ResultWe evaluated the efficiency of ‘N’ (0–10) spacer-linked primers by targeting bacterial 16S V3-V4 region, demonstrating heterogeneous base library construction. The addition of ‘N’ (0–10) spacers causes sequencing frameshift at every base that leads to base diversity and produces heterogeneous high quality reads within a single amplicon library. We have written a python based command-line software,“MetReTrim”, to trim the ‘N’ (0–10) spacers from the raw reads (https://github.com/Mohak91/MetReTrim). We further demonstrated the accuracy of this method by comparative mock community analysis with standard illumina V3-V4 primer method. The ZymoBIOMICS™ microbial community DNA standard was used as a control for this study. We performed data analysisusing the DADA2 pipeline where taxonomy was assigned using SILVA database as reference. We observed no difference between the communities represented by our method and standard illumina V3-V4 primer method.ConclusionThis method eliminates the need for PhiX spike-in for single amplicon sequencing on illumina MiSeq platform. This allows for sequencing of more number of samples in a run and a reduction in the overall cost. Given that Illumina sequencing works on SBS chemistry irrespective of the platform (such as HiSeq, MiSeq, NextSeq, NovaSeq, etc.) we propose that this strategy of using ‘N’ (0–10) spacer-linked primer design can be adopted for generating high-quality single locus amplicon sequencing in a high throughput manner across the illumina platform subject to further validation.

Earlier proteoglycan turnover promotes higher efficiency matrix remodeling in MRL/MpJ tendons.

While most mammalian tissue regeneration is limited, the Murphy Roths Large (MRL/MpJ) mouse has been identified to regenerate several tissues, including tendon. Recent studies have indicated that this regenerative response is innate to the tendon tissue and not reliant on a systemic inflammatory response. Therefore, we hypothesized that MRL/MpJ mice may also exhibit a more robust homeostatic regulation of tendon structure in response to mechanical loading. To assess this, MRL/MpJ and C57BL/6J flexor digitorum longus tendon explants were subjected to stress-deprived conditions in vitro for up to 14 days. Explant tendon health (metabolism, biosynthesis, and composition), matrix metalloproteinase (MMP) activity, gene expression, and tendon biomechanics were assessed periodically. We found a more robust response to the loss of mechanical stimulus in the MRL/MpJ tendon explants, exhibiting an increase in collagen production and MMP activity consistent with previous in vivo studies. This greater collagen turnover was preceded by an early expression of small leucine-rich proteoglycans and proteoglycan-degrading MMP-3, promoting efficient regulation and organization of newly synthesized collagen and allowing for more efficient overall turnover in MRL/MpJ tendons. Therefore, mechanisms of MRL/MpJ matrix homeostasis may be fundamentally different from that of B6 tendons and may indicate better recovery from mechanical microdamage in MRL/MpJ tendons. We demonstrate here the utility of the MRL/MpJ model in elucidating mechanisms of efficient matrix turnover and its potential to shed light on new targets for more effective treatments for degenerative matrix changes brought about by injury, disease, or aging.

In situ formation of AuNPs in liquid bead-headspace microextraction of arsine for colorimetric sensing of trace As(III)

A simple yet sensitive colorimetric method based on in situ formation of AuNPs in liquid bead-headspace microextraction of arsine has been developed for ultrasensitive sensing of trace As(III). Taking advantage of our self-designed sensing device, the strong reductant AsH3 generated from the hydride generation of As(III) passed through a platform and reacted with a liquid bead (60 μL, containing HAuCl4, KI, PVP and PVA) for the formation of AuNPs inside. Due to the synergistic reduction of iodine ions and the stabilization of polymers, AuNPs could be formed quickly, and the color of liquid-bead changed from yellow to red, which deepened in proportion to the As(III) concentration. Under the optimal experimental conditions, a linear range of 10–500 µg/L with a correlation coefficient up to 0.999 was achieved. Trace As(III) as low as 5 μg/L could produce visible color change. Combining the advantages of hydride generation, headspace liquid-phase microextraction and AuNPs-based colorimetric assay, including efficient matrix separation and analyte enrichment, rapid mass transfer, and visual observation of color change, the proposed sensor features high sensitivity, great selectivity, strong stability and simplicity, enabling successful applications for As(III) detection in water samples.

Cobalt, nitrogen co-doped microporous carbon matrix derived from metal organic frameworks toward high specific capacity room temperature sodium sulfur batteries

Room-temperature sodium-sulfur (RT Na–S) batteries have been getting increasing attention in the field of energy storage system thanks to their advantages of high specific capacity, good safety, low cost and environmental friendliness. However, limited by the low conductivity, large volume change and complex reaction, the utilization rate of active sulfur is still unacceptable, which delays the practical application of RT Na–S battery. Herein, derived from CoZn-ZIFs, a cobalt, nitrogen co-doped microporous carbon matrix (Co,N-MPC) has been devised to exploit capacity of active sulfur as fully as possible. In the case of appropriate Co content, the affluent micropores limit the size of sulfur and inhibit the volume change. And the well-dispersed Co and N elements improve the adsorption of the matrix to sulfur species and promote their transformation process. Owing to their synergistic effect, the S@Co,N-MPC-10% electrode presents stable cycling (1134.63 mAh g−1 after 100 cycles at 0.2 C) and high rate capacity (835.01 mAh g−1 at 3.0 C). This work might provide beneficial insights to the development of efficient sulfur matrixes of RT Na–S batteries.

Exploring Neuromorphic Computing Based on Spiking Neural Networks: Algorithms to Hardware

Neuromorphic Computing, a concept pioneered in the late 1980s, is receiving a lot of attention lately due to its promise of reducing the computational energy, latency, as well as learning complexity in artificial neural networks. Taking inspiration from neuroscience, this interdisciplinary field performs a multi-stack optimization across devices, circuits, and algorithms by providing an end-to-end approach to achieving brain-like efficiency in machine intelligence. On one side, neuromorphic computing introduces a new algorithmic paradigm, known as Spiking Neural Networks (SNNs), which is a significant shift from standard deep learning and transmits information as spikes (“1” or “0”) rather than analog values. This has opened up novel algorithmic research directions to formulate methods to represent data in spike-trains, develop neuron models that can process information over time, design learning algorithms for event-driven dynamical systems, and engineer network architectures amenable to sparse, asynchronous, event-driven computing to achieve lower power consumption. On the other side, a parallel research thrust focuses on development of efficient computing platforms for new algorithms. Standard accelerators that are amenable to deep learning workloads are not particularly suitable to handle processing across multiple timesteps efficiently. To that effect, researchers have designed neuromorphic hardware that rely on event-driven sparse computations as well as efficient matrix operations. While most large-scale neuromorphic systems have been explored based on CMOS technology, recently, Non-Volatile Memory (NVM) technologies show promise toward implementing bio-mimetic functionalities on single devices. In this article, we outline several strides that neuromorphic computing based on spiking neural networks (SNNs) has taken over the recent past, and we present our outlook on the challenges that this field needs to overcome to make the bio-plausibility route a successful one.

Secure Shapley Value for Cross-Silo Federated Learning

The Shapley value (SV) is a fair and principled metric for contribution evaluation in cross-silo federated learning (cross-silo FL), wherein organizations, i.e., clients, collaboratively train prediction models with the coordination of a parameter server. However, existing SV calculation methods for FL assume that the server can access the raw FL models and public test data. This may not be a valid assumption in practice considering the emerging privacy attacks on FL models and the fact that test data might be clients' private assets. Hence, we investigate the problem of secure SV calculation for cross-silo FL. We first propose HESV , a one-server solution based solely on homomorphic encryption (HE) for privacy protection, which has limitations in efficiency. To overcome these limitations, we propose SecSV , an efficient two-server protocol with the following novel features. First, SecSV utilizes a hybrid privacy protection scheme to avoid ciphertext-ciphertext multiplications between test data and models, which are extremely expensive under HE. Second, an efficient secure matrix multiplication method is proposed for SecSV. Third, SecSV strategically identifies and skips some test samples without significantly affecting the evaluation accuracy. Our experiments demonstrate that SecSV is 7.2--36.6× as fast as HESV, with a limited loss in the accuracy of calculated SVs.