Dimensionality Reduction Step Research Articles

Unsupervised Anomaly Detection in Sequential Process Data

Abstract: In this study, we present three types of unsupervised anomaly detection to identify anomalous test-takers based on their action sequences in problem-solving tasks. The first method relies on the use of the Isolation Forest algorithm to detect anomalous test-takers based on raw action sequences extracted from process data. The second method transforms raw action sequences into contextual embeddings using the Bidirectional Encoder Representations from Transformers (BERT) model and then applies the Isolation Forest algorithm to detect anomalous test-takers. The third method follows the same procedure as the second method, but it includes an intermediary step of dimensionality reduction for the contextual embeddings before applying the Isolation Forest algorithm for detecting anomalous cases. To compare the outcomes of the three methods, we analyze the log files from test-takers in the US sample ( n = 2,021) who completed the problem-solving in technology-rich environments (PSTRE) section of the Programme for the International Assessment of Adult Competencies (PIAAC) 2012 assessment. The results indicated that different groups of test-takers were flagged as anomalous depending on the representation (raw action sequences vs. contextual embeddings) and dimensionality of action sequences. Also, when the contextual embeddings were used, a larger number of test-takers were flagged by the Isolation Forest algorithm, indicating the sensitivity of this algorithm to the dimensionality of input data.

An integrative multi-omics approach aimed to gain insight on the effect of composition, style, yeast, and wheat species on wheat craft beer flavour

This study was aimed to unravel the effect of raw materials (barley and wheat), wheat concentration (0, 25, 40, and 100 %), wheat species (common and durum), beer style (Blanche and Weiss), and yeast (US-05 and WB-06) on the chemical composition, volatiles, and sensory profile of wheat craft beers by using a multivariate statistical approach. Beer samples were analysed for their composition, volatiles and sensory profile and data were processed using unsupervised multivariate analyses, PLS regression and a multi-omics approach using multi-block PLS-DA. Multi-block variable sparsification was used as an embedded dimension reduction step. The adopted multi-omics approach permitted to correctly classify beers with different styles and wheat concentration, and to accurate classify (95 % accuracy) beers according to yeast type. Wheat species was of lower importance since it permitted a classification with 49 % accuracy which increased to 74 % in Blanche beers, thus suggesting that malting flattened differences determined by wheat species.

Automatic diagnosis of Parkinson's disease using artificial intelligence base on routine T1-weighted MRI.

Parkinson's disease (PD) is the second most common neurodegenerative disease. An objective diagnosis method is urgently needed in clinical practice. In this study, deep learning and radiomics techniques were studied to automatically diagnose PD from healthy controls (HCs). 155 PD patients and 154 HCs were randomly divided into a training set (246 patients) and a testing set (63 patients). The brain subregions identification and segmentation were automatically performed with a VB-net, and radiomics features of billateral thalamus, caudatum, putamen and pallidum were extracted. Five independent machine learning classifiers [Support Vector Machine (SVM), Stochastic gradient descent (SGD), random forest (RF), quadratic discriminant analysis (QDA) and decision tree (DT)] were trained on the training set, and validated on the testing. Delong test was used to compare the performance of different models. Our VB-net could automatically identify and segment the brain into 109 regions. 2,264 radiomics features were automatically extracted from the billateral thalamus, caudatum, putamen or pallidum of each patient. After four step of features dimensionality reduction, Delong tests showed that the SVM model based on combined features had the best performance, with AUCs of 0.988 (95% CI: 0.979 ~ 0.998, specificity = 91.1%, sensitivity =100%, accuracy = 89.4% and precision = 88.2%) and 0.976 (95% CI: 0.942 ~ 1.000, specificity = 100%, sensitivity = 87.1%, accuracy = 93.5% and precision = 88.6%) in the training set and testing set, respectively. Decision curve analysis showed that the clinical benefit of the line graph model was high. The SVM model based on combined features could be used to diagnose PD with high accuracy. Our fully automatic model could rapidly process the MRI data and distinguish PD and HCs in one minute. It greatly improved the diagnostic efficiency and has a great potential value in clinical practice to help the early diagnosis of PD.

Correlation Joins over Time Series Data Streams Utilizing Complementary Dimension Reduction and Transformation

A common analysis task over a stream of time series is to find all pairs of windows whose correlation is above a given threshold. For a large number of streams, doing so naively, i.e., checking the Cartesian product, is too expensive. In essence, finding correlated pairs in a non-naive way boils down to a high-dimensional similarity join in a Euclidean space. While there are similarity join algorithms, such as Quickjoin and ε-kdB tree, they are inefficient for high-dimensional data. We propose CorrJoin, short for Correlation Join, that combines a complementary dimension reduction and transformation step with a subsequent double-filtering step. In the first step, we reduce the dimensionality of data stream windows by combining a fast but inaccurate method, Piecewise Aggregate Approximation (PAA), with an accurate and slow one, Singular Value Decomposition (SVD). Not only does SVD compensate for the weaknesses of PAA, it also transforms the data to make the first filter based on bucketing more effective. The second filter, which uses Euclidean distances, reduces the number of false positives before computing exact correlations. Our experiments reveal that in common settings, CorrJoin is an order of magnitude faster than state-of-the-art approaches (up to 20 times faster than Quickjoin).

Similarity-assisted variational autoencoder for nonlinear dimension reduction with application to single-cell RNA sequencing data

BackgroundDeep generative models naturally become nonlinear dimension reduction tools to visualize large-scale datasets such as single-cell RNA sequencing datasets for revealing latent grouping patterns or identifying outliers. The variational autoencoder (VAE) is a popular deep generative method equipped with encoder/decoder structures. The encoder and decoder are useful when a new sample is mapped to the latent space and a data point is generated from a point in a latent space. However, the VAE tends not to show grouping pattern clearly without additional annotation information. On the other hand, similarity-based dimension reduction methods such as t-SNE or UMAP present clear grouping patterns even though these methods do not have encoder/decoder structures.ResultsTo bridge this gap, we propose a new approach that adopts similarity information in the VAE framework. In addition, for biological applications, we extend our approach to a conditional VAE to account for covariate effects in the dimension reduction step. In the simulation study and real single-cell RNA sequencing data analyses, our method shows great performance compared to existing state-of-the-art methods by producing clear grouping structures using an inferred encoder and decoder. Our method also successfully adjusts for covariate effects, resulting in more useful dimension reduction.ConclusionsOur method is able to produce clearer grouping patterns than those of other regularized VAE methods by utilizing similarity information encoded in the data via the highly celebrated UMAP loss function.

FastSRM: A fast, memory efficient and identifiable implementation of the shared response model

The shared response model (SRM) provides a simple but effective framework to analyze fMRI data of subjects exposed to naturalistic stimuli. However, when the number of subjects or runs is large, fitting the model requires a large amount of memory and computational power, which limits its use in practice. Furthermore, SRM is not identifiable, which makes the shared response difficult to interpret. In this work, we implement an identifiable version of SRM and show on real data that it improves the stability of the recovered shared response. We then introduce FastSRM, which relies on a dimension reduction step and yields the same solution as the original algorithm. We show experimentally using synthetic and real fMRI data that FastSRM is considerably faster and more memory efficient than current implementations. The experiments performed in this article are fully reproducible: our code available at https://github.com/hugorichard/FastSRM allows you to download the data, run the experiments and plot the figures. For a more pleasant reading of the math equations, we advise the reader to read the version of this article formatted with latex:https://github.com/hugorichard/FastSRM/blob/master/paper/main.pdf.

DNA Chromatogram Classification Using Entropy-Based Features and Supervised Dimension Reduction Based on Global and Local Pattern Information

Gene sequence classification can be seen as a challenging task due to the nonstationary, noisy and nonlinear characteristics of sequential data. The primary goal of this research is to develop a general solution approach for supervised DNA chromatogram (DNAC) classification in the absence of sufficient training data. Today, deep learning comes to the fore with its achievements, however this requires a lot of training data. Finding enough training data can be exceedingly challenging, particularly in the medical area and for rare disorders. In this paper, a novel supervised DNAC classification method is proposed, which combines three techniques to classify hepatitis virus DNA trace files as HBV and HCV. The features that are capable of reflecting the complex-structured sequential data are extracted based on both embedding and spectral entropies. After the supervised dimension reduction step, not only global behavior of the entropy features but also local behavior of the entropy features is taken into account for classification purpose. A memory-based learning, which cannot lose any information coming from training data as its nature, is being used as a classifier. Experimental results show that the proposed method achieves good results that although 19% training data is used, a performance of 92% is obtained.

Low-dimensional data-based surrogate model of a continuum-mechanical musculoskeletal system based on non-intrusive model order reduction

Over the last decades, computer modeling has evolved from a supporting tool for engineering prototype design to an ubiquitous instrument in non-traditional fields such as medical rehabilitation. This area comes with unique challenges, e.g. the complex modeling of soft tissue or the analysis of musculoskeletal systems. Conventional modeling approaches like the finite element (FE) method are computationally costly when dealing with such models, limiting their usability for real-time simulation or deployment on low-end hardware, if the model at hand cannot be simplified without losing its expressiveness. Non-traditional approaches such as surrogate modeling using data-driven model order reduction are used to make complex high-fidelity models more widely available regardless. They often involve a dimensionality reduction step, in which the high-dimensional system state is transformed onto a low-dimensional subspace or manifold, and a regression approach to capture the reduced system behavior. While most publications focus on one dimensionality reduction, such as principal component analysis (PCA) (linear) or autoencoder (nonlinear), we consider and compare PCA, kernel PCA, autoencoders, as well as variational autoencoders for the approximation of a continuum-mechanical system. In detail, we demonstrate the benefits of the surrogate modeling approach on a complex musculoskeletal system of a human upper-arm with severe nonlinearities and physiological geometry. We consider both, the model’s deformation and the internal stress as the two main quantities of interest in a FE context. By doing so we are able to create computationally low-cost surrogate models which capture the system behavior with high approximation quality and fast evaluations.

BRAQUE: Bayesian Reduction for Amplified Quantization in UMAP Embedding

Single-cell biology has revolutionized the way we understand biological processes. In this paper, we provide a more tailored approach to clustering and analyzing spatial single-cell data coming from immunofluorescence imaging techniques. We propose Bayesian Reduction for Amplified Quantization in UMAP Embedding (BRAQUE) as an integrative novel approach, from data preprocessing to phenotype classification. BRAQUE starts with an innovative preprocessing, named Lognormal Shrinkage, which is able to enhance input fragmentation by fitting a lognormal mixture model and shrink each component towards its median, in order to help further the clustering step in finding more separated and clear clusters. Then, BRAQUE's pipeline consists of a dimensionality reduction step performed using UMAP, and a clustering performed using HDBSCAN on UMAP embedding. In the end, clusters are assigned to a cell type by experts, using effects size measures to rank markers and identify characterizing markers (Tier 1), and possibly characterize markers (Tier 2). The number of total cell types in one lymph node detectable with these technologies is unknown and difficult to predict or estimate. Therefore, with BRAQUE, we achieved a higher granularity than other similar algorithms such as PhenoGraph, following the idea that merging similar clusters is easier than splitting unclear ones into clear subclusters.

Abstract WMP120: Development Of Smartphone Enabled Machine Learning Algorithms For Autonomous Stroke Detection

Background: We developed an automated smart phone application for detection of acute stroke using machine learning (ML) algorithms for recognition of facial asymmetry, arm weakness, and speech changes. Methods: We analysed prospectively collected data from patients admitted to 4 major metropolitan stroke centers with confirmed diagnosis of acute stroke. Speech and facial data were captured via video recording and arm data was captured via device sensors. A. Face. This module extracts 68 facial landmark points that are passed through a dimensionality reduction step and an asymmetry classifier. We implemented and compared 26 classification methods with neurologists' clinical impression and determined Quadratic Discriminative Analysis as the best one in terms of accuracy and interpretability. B. Arm. Using data extracted from 3D accelerometer, gyroscope, and magnetometer , we designed a grasp agnostic classifier based on AdaBoost to process motion trajectories and detect arm weakness.C. Speech. We developed an algorithm based on frequency analysis and Mel Frequency Cepstral Coefficients (MFCC) to detect abnormal/slurred speech. All tests were conducted within 72 hours of admission. Each of the three ML outputs was correlated with neurologists’ clinical impression. Results: Among the 269 analysed patients, 41% were female, the median age was 71, % had hemorrhagic and % had ischemic stroke. Final analyses of 18311 facial images revealed 99.42% sensitivity, 93.67% specificity, and 97.11% accuracy in detection of facial asymmetry. The results for 43 arm trajectories revealed 71.42% sensitivity, 72.41% specificity, and 72.09% accuracy in detection of arm weakness. Preliminary analysis of MFCC algorithms confirmed adequate features for abnormal speech detection Conclusions: Our preliminary results confirm that smartphone enabled ML-algorithms can reliably identify acute stroke features with accuracy comparable to neurologists’ clinical impression.

Application of Fuzzy algorithms in conjunction with 1 H-NMR spectroscopy for alcoholic beverages differentiation.

According to recent statistics elaborated at the European Union level, wine represents one of the most falsified commodities. In this context, the development of reliable classification models for alcoholic beverages differentiation requires, besides sensitive analytical tools, the use of the most suitable data processing methods like those based on advanced statistical tools or artificial intelligence. The present study aims to establish a new innovative approach for alcoholic beverages differentiation (wines and fruit distillates) able to increase the discrimination rate of the developed models. Thus, a data dimensionality reduction step, performed on the obtained 1 H-NMR profiles, was applied. This stage consisted in the application of Fuzzy Principal Component Analysis (FPCA) before themodel development through discriminant analysis. The enhancement of the classification potential given by the application of FPCA as compared to Principal Component Analysis (PCA) was discussed. The association between 1 H-NMR spectroscopy and an appropriate statistical approach proved to be a very effective tool for alcoholic beverages differentiation. In order to develop reliable metabolomic approaches for the differentiation of wines and fruit distillates, 1 H-NMR spectroscopic data were exploited in corroboration with fuzzy algorithms for data dimensionality reduction. The study proved the efficiency of using FPCA scores over those obtained through the widely applied PCA. Based on the proposed approach, it was proved that for wine classification a perfect separation was obtained according to the geographical origin, cultivar and vintage. A percentage of 100% correctly classified samples was also achieved for botanical and geographical differentiation of fruit distillates. This article is protected by copyright. All rights reserved.

A probabilistic view on modelling weather regimes

AbstractThe statistical modelling of weather regimes encompasses the definition of a framework involving a dimensionality reduction step to reduce the highly sparse feature space of weather anomaly maps, and unsupervised learning techniques to correctly categorize regimes. Across the literature's methodology, the two stages stick to a recurrent scheme: Empirical Orthogonal Functions or Principal Component Analysis are used to assess the former; a standard K‐Means clustering algorithm maps each datapoint to the closest‐matching regime. However, such a combination has to cope with an overall reduction in the modelling accuracy. In our study, we re‐think both the two steps in favour of a more dynamic methodology which we apply to the last 42‐years winters' geopotential anomaly maps in the North Atlantic‐European zone. The dimensionality reduction is tackled by means of Variational Autoencoders, leading to better compressed feature spaces, enhancing the datapoints separability. Finally, we employ two probabilistic clustering methods based on Gaussian and Dirichlet Process mixture models, enabling a more faithful recognition of weather regimes, and allowing to reproduce their dynamics and transitions.

Sequential Active Learning of Low-Dimensional Model Representations for Reliability Analysis

To date, the analysis of high-dimensional, computationally expensive engineering models remains a difficult challenge in risk and reliability engineering. We use a combination of dimensionality reduction and surrogate modeling termed partial least squares--driven polynomial chaos expansion (PLS-PCE) to render such problems feasible. Standalone surrogate models typically perform poorly for reliability analysis. Therefore, in a previous work, we have used PLS-PCEs to reconstruct the intermediate densities of a sequential importance sampling approach to reliability analysis. Here, we extend this approach with an active learning procedure that allows for improved error control at each importance sampling level. To this end, we formulate an estimate of the combined estimation error for both the subspace identified in the dimension reduction step and the surrogate model constructed therein. With this, it is possible to adapt the training set so as to optimally learn the subspace representation and the surrogate model constructed therein. The approach is gradient-free and thus can be directly applied to black box--type models. We demonstrate the performance of this approach with a series of low- (2 dimensions) to high- (869 dimensions) dimensional example problems featuring a number of well-known caveats for reliability methods besides high dimensions and expensive computational models: strongly nonlinear limit-state functions, multiple relevant failure regions, and small probabilities of failure.

NIR-Based Intelligent Sensing of Product Yield Stress for High-Value Bioresorbable Polymer Processing.

PLA (polylactide) is a bioresorbable polymer used in implantable medical and drug delivery devices. Like other bioresorbable polymers, PLA needs to be processed carefully to avoid degradation. In this work we combine in-process temperature, pressure, and NIR spectroscopy measurements with multivariate regression methods for prediction of the mechanical strength of an extruded PLA product. The potential to use such a method as an intelligent sensor for real-time quality analysis is evaluated based on regulatory guidelines for the medical device industry. It is shown that for the predictions to be robust to processing at different times and to slight changes in the processing conditions, the fusion of both NIR and conventional process sensor data is required. Partial least squares (PLS), which is the established ’soft sensing’ method in the industry, performs the best of the linear methods but demonstrates poor reliability over the full range of processing conditions. Conversely, both random forest (RF) and support vector regression (SVR) show excellent performance for all criteria when used with a prior principal component (PC) dimension reduction step. While linear methods currently dominate for soft sensing of mixture concentrations in highly conservative, regulated industries such as the medical device industry, this work indicates that nonlinear methods may outperform them in the prediction of mechanical properties from complex physicochemical sensor data. The nonlinear methods show the potential to meet industrial standards for robustness, despite the relatively small amount of training data typically available in high-value material processing.

Targeting predictors in random forest regression

Random forest (RF) regression is an extremely popular tool for analyzing high-dimensional data. Nonetheless, its benefits may be lessened in sparse settings due to weak predictors, and a pre-estimation dimension reduction (targeting) step is required. We show that proper targeting controls the probability of placing splits along strong predictors, thus providing an important complement to RF’s feature sampling. This is supported by simulations using finite representative samples. Moreover, we quantify the immediate gain from targeting in terms of the increased strength of individual trees. Macroeconomic and financial applications show that the bias–variance trade-off implied by targeting, due to increased correlation among trees in the forest, is balanced at a medium degree of targeting, selecting the best 5%–30% of commonly applied predictors. Improvements in the predictive accuracy of targeted RF relative to ordinary RF are considerable, up to 21%, occurring both in recessions and expansions, particularly at long horizons.

Joint dimension reduction and clustering analysis of single-cell RNA-seq and spatial transcriptomics data.

Dimension reduction and (spatial) clustering is usually performed sequentially; however, the low-dimensional embeddings estimated in the dimension-reduction step may not be relevant to the class labels inferred in the clustering step. We therefore developed a computation method, Dimension-Reduction Spatial-Clustering (DR-SC), that can simultaneously perform dimension reduction and (spatial) clustering within a unified framework. Joint analysis by DR-SC produces accurate (spatial) clustering results and ensures the effective extraction of biologically informative low-dimensional features. DR-SC is applicable to spatial clustering in spatial transcriptomics that characterizes the spatial organization of the tissue by segregating it into multiple tissue structures. Here, DR-SC relies on a latent hidden Markov random field model to encourage the spatial smoothness of the detected spatial cluster boundaries. Underlying DR-SC is an efficient expectation-maximization algorithm based on an iterative conditional mode. As such, DR-SC is scalable to large sample sizes and can optimize the spatial smoothness parameter in a data-driven manner. With comprehensive simulations and real data applications, we show that DR-SC outperforms existing clustering and spatial clustering methods: it extracts more biologically relevant features than conventional dimension reduction methods, improves clustering performance, and offers improved trajectory inference and visualization for downstream trajectory inference analyses.

Intelligent recommender system based on quantum clustering and matrix completion

AbstractFaster than classical algorithms, quantum algorithms benefit from the superposition property of quantum information to offer significant speedup to complex algorithms. Therefore, quantum computing can be used to help machine learning algorithms by boosting their performance and accelerate the processing of time‐consuming ones. Clustering algorithms are very complex unsupervised learning algorithms. Indeed, the similarity calculation (distance) between input vectors is a resource‐consuming step, especially when working with large datasets. In this article, we propose a new better‐performing recommender system that operates as a combination of an adapted quantum K‐means algorithm and the singular value decomposition (SVT) algorithm. We integrate the developed quantum clustering algorithm to a prediction process of the proposed recommender system using matrix completion. To the best of our knowledge, no system with such details was proposed in the literature. The system was applied on the MovieLens dataset without a dimensionality reduction step and evaluated according to measures of information retrieval systems. The results of the quantum K‐means algorithm show that the quantum version leads to a logarithmic reduction of the time complexity compared to the classical algorithm. The proposed system has proved to be better than the previous tested ones in terms of precision and recall.

Dictionary learning allows model-free pseudotime estimation of transcriptomic data

BackgroundPseudotime estimation from dynamic single-cell transcriptomic data enables characterisation and understanding of the underlying processes, for example developmental processes. Various pseudotime estimation methods have been proposed during the last years. Typically, these methods start with a dimension reduction step because the low-dimensional representation is usually easier to analyse. Approaches such as PCA, ICA or t-SNE belong to the most widely used methods for dimension reduction in pseudotime estimation methods. However, these methods usually make assumptions on the derived dimensions, which can result in important dataset properties being missed. In this paper, we suggest a new dictionary learning based approach, dynDLT, for dimension reduction and pseudotime estimation of dynamic transcriptomic data. Dictionary learning is a matrix factorisation approach that does not restrict the dependence of the derived dimensions. To evaluate the performance, we conduct a large simulation study and analyse 8 real-world datasets.ResultsThe simulation studies reveal that firstly, dynDLT preserves the simulated patterns in low-dimension and the pseudotimes can be derived from the low-dimensional representation. Secondly, the results show that dynDLT is suitable for the detection of genes exhibiting the simulated dynamic patterns, thereby facilitating the interpretation of the compressed representation and thus the dynamic processes. For the real-world data analysis, we select datasets with samples that are taken at different time points throughout an experiment. The pseudotimes found by dynDLT have high correlations with the experimental times. We compare the results to other approaches used in pseudotime estimation, or those that are method-wise closely connected to dictionary learning: ICA, NMF, PCA, t-SNE, and UMAP. DynDLT has the best overall performance for the simulated and real-world datasets.ConclusionsWe introduce dynDLT, a method that is suitable for pseudotime estimation. Its main advantages are: (1) It presents a model-free approach, meaning that it does not restrict the dependence of the derived dimensions; (2) Genes that are relevant in the detected dynamic processes can be identified from the dictionary matrix; (3) By a restriction of the dictionary entries to positive values, the dictionary atoms are highly interpretable.

Content-Based Video Retrieval With Prototypes of Deep Features

The rapid development in the area of information and communication technologies has enabled the transfer of high-resolution, large-sized videos, and video applications have also evolved according to data quality levels. Content-based video retrieval (CBVR) is an essential video application because it can be applied to various domains, such as surveillance, education, sports, and medicine. In this paper, we propose a CBVR method based on prototypical category approximation (PCA-CBVR), which calculates prototypes of deep features for each category to predict the user’s query video category without a classifier. We also undertake fine searching to retrieve the video most similar to the user’s query video from the predicted category database of videos. The proposed PCA-CBVR approach is efficient in terms of its computational cost and maintains meaningful information of the videos. It does not need to train a classifier even when the database is updated and uses all deep features without any dimension reduction step, such as those in CBVR studies. Moreover, we conduct fine-tuning of the 3D CNN feature extractor based on a few-shot learning approach for better domain adaptation ability and apply salient frame sampling instead of uniform frame sampling to improve the performance of the PCA-CBVR method. We demonstrate the performance capability of the proposed PCA-CBVR approach through experiments on various benchmark video datasets, in this case the UCF101, HMDB51, and ActivityNet datasets.

A Distribution-Dependent Mumford–Shah Model for Unsupervised Hyperspectral Image Segmentation

Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the acquisition of labeled training data is very time-consuming, unsupervised methods become crucial in hyperspectral image analysis. The spectral variability and noise in hyperspectral data make this task very challenging and define special requirements for such methods. Here, we present a novel unsupervised hyperspectral segmentation framework. It starts with a denoising and dimensionality reduction step by the well-established Minimum Noise Fraction (MNF) transform. Then, the Mumford-Shah (MS) segmentation functional is applied to segment the data. We equipped the MS functional with a novel robust distribution-dependent indicator function designed to handle the characteristic challenges of hyperspectral data. To optimize our objective function with respect to the parameters for which no closed form solution is available, we propose an efficient fixed point iteration scheme. Numerical experiments on four public benchmark datasets show that our method produces competitive results, which outperform three state-of-the-art methods substantially on three of these datasets.