Nonlinear Clustering Research Articles

Adriatic-Ionian air temperature and precipitation patterns derived from self-organizing maps: relation to hemispheric indices

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 78:149-163 (2019) - DOI: https://doi.org/10.3354/cr01565 Adriatic-Ionian air temperature and precipitation patterns derived from self-organizing maps: relation to hemispheric indices Frano Matić1,*, Hrvoje Kalinić2, Ivica Vilibić1, Branka Grbec1, Karla Morožin3 1Institute of Oceanography and Fisheries, 21000 Split, Croatia 2Faculty of Science, University of Split, 21000 Split, Croatia 3Department of Marine Studies, University of Split, 21000 Split, Croatia *Corresponding author: fmatic@izor.hr ABSTRACT: Normalized anomalies in air temperature and precipitation patterns derived from monthly data series collected at 28 in situ meteorological stations in the Adriatic-Ionian region between 1961 and 2015 were mapped by using the self-organizing map (SOM) method—an unsupervised neural network method—and connected with hemispheric indices in the atmosphere. Four indices were used: North Atlantic Oscillation (NAO), East Atlantic (EA), East Atlantic/West Russia (EAWR) and Scandinavian (SCA). Two experiments were conducted: the first combined normalized temperature anomalies with the indices, and the second combined normalized precipitation anomalies with the indices. Precipitation data better fit the SOM model than temperature data, while the SOM model has the best performance at a 3 × 3 matrix size. Region-wide negative precipitation anomalies are related to a combination of positive NAO and EAWR, and negative SCA indices, and vice versa. Positive air temperature anomalies are related to the positive EA index and vice versa. The mapped relations between the NAO index and precipitation anomalies indicate a nonlinear connection, because positive index values resemble 2 different precipitation patterns. The SOM-based nonlinear clustering might be useful in determining and forecasting precipitation and air temperature patterns from hemispheric indices. KEY WORDS: Self-organizing maps · Air temperature · Precipitation · Hemispheric indices · Central Mediterranean Full text in pdf format PreviousNextCite this article as: Matić F, Kalinić H, Vilibić I, Grbec B, Morožin K (2019) Adriatic-Ionian air temperature and precipitation patterns derived from self-organizing maps: relation to hemispheric indices. Clim Res 78:149-163. https://doi.org/10.3354/cr01565 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 78, No. 2. Online publication date: August 08, 2019 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2019 Inter-Research.

Parallel Computation Performingkernel-Based Clustering Algorithm using Particle Swarm Optimization for the Big Data Analytics

Digital data has been accelerating day by day with a bulk of dimensions. Analysis of such an immense quantity of data popularly termed as big data, which requires tremendous data analysis scalable techniques. Clustering is an appropriate tool for data analysis to observe hidden similar groups inside the data. Clustering distinct datasets involve both Linear Separable and Non-Linear Separable clustering algorithms by defining and measuring their inter-point similarities as well as non-linear similarity measures. Problem Statement: Yet there are many productive clustering algorithms to cluster linearly; they do not maintain quality clusters.Kernel-based algorithms make use of non-linear similarity measures to define similarity while forming clusters specifically with arbitrary shapes and frequencies. Existing System:Current Kernel-based clustering algorithms have few restraints concerning complexity, memory, and performance. Time and Memory will increase equally when the size of the dataset increase. It is challenging to elect kernel similarity function for different datasets. We have classical random sampling and low-rank matrix approximation linear clustering algorithms with high cluster quality and low memory essentials. Proposed work: in our research, we have introduced a parallel computation performing Kernel-based clustering algorithm using Particle Swarm Optimization approach. This methodology can cluster large datasets having maximum dimensional values accurately and overcomes the issues of high dimensional datasets.

A Scalable Framework for Data-Driven Subspace Representation and Clustering

This paper considers the problem of subspace clustering which segments data samples into their underlying subspaces. While existing subspace clustering algorithms have been successfully applied to various problems, they are not applicable for large-scale or streaming data due to their expensive computational cost. As a remedy, we propose a unified scalable pipeline to reduce the complexity of all sub-tasks in subspace clustering. We first present a robust incremental summary representation, assuming that a subspace can be represented by sparse factors. Based on the summary representation, we propose a fully scalable learning pipeline by integrating the affinity learning task with post-processing and spectral clustering, such that the overall time complexity is linear in the number of samples. Moreover, the proposed framework is integrated with kernel methods for nonlinear subspace clustering. An extensive set of experimental studies demonstrate that the proposed framework gives an order-of-magnitude speed-up over existing subspace clustering baselines with competitive clustering performance.

Evaluation of regional flood quantiles at ungauged sites by employing nonlinearity-based clustering approaches.

Water resource engineers extensively use regional flood frequency analysis to compute the discharge at ungauged sites with limited flow records in the river basins. Frequency and magnitude are the two important factors required to be analyzed for an effective assessment of flood disaster risk management. Globally, many linear clustering techniques are employed to categorize the watershed which are ineffective when dealing with noise and outliers. The present study overcomes this by proposing a relatively new nonlinear clustering algorithm based on hierarchical estimation of densities (NLCAHD) for the Cauvery basin, where the Homogeneity test (H) is enforced to identify the group of stations with same populations. Discordancy measure is carried out for screening the data in order to eliminate the conflicting sites from the group. The whole basin is classified into six homogeneous clusters, while the goodness of fit measure tests the data to distinguish the preferred distribution for the purpose of calculating the growth curves. A comparative study is made with the other linear algorithms such as K-means and C-means, which reveals the better performance of the proposed nonlinear model for identifying the homogeneous regions, in arriving at precise estimates of flood quantiles for various return periods up to 160 years.

Joint correntropy metric weighting and block diagonal regularizer for robust multiple kernel subspace clustering

Nonlinear kernel-based subspace clustering methods that can reveal the multi-cluster nonlinear structure of samples are an emerging research topic. However, the existing kernel subspace clustering methods have the following three flaws: 1) their clustering performance is largely determined by the chosen kernel function; 2) they may lack robustness in the presence of non-Gaussian noise and impulsive noise; and 3) their learned affinity matrix can not hold the desired block diagonal property for clustering purpose, which possibly leads to incorrect clustering when using spectral clustering. In this paper, we propose a Joint Robust Multiple Kernel Subspace Clustering (JMKSC) method for data clustering, which has two primary innovations. First, our multiple kernel weighting strategy introduces the correntropy metric weighting instead of a fixed, or inappropriately assigned weighting, which is more robust to the non-Gaussian noise and contributes to learning the optimal consensus kernel. Second, our method encourages acquiring an affinity matrix with the optimal block diagonal property based on the block diagonal regularizer (BDR) and the self-expressiveness property. Experiments on several different types of datasets confirm that the proposed JMKSC significantly outperforms several state-of-the-art single kernel and multiple kernel subspace clustering methods in terms of accuracy, NMI and purity.

ETHOS – an Effective Theory of Structure Formation: detecting dark matter interactions through the Lyman-α forest

ABSTRACT We perform a series of cosmological hydrodynamic simulations to investigate the effects of non-gravitational dark matter (DM) interactions on the intergalactic medium (IGM). In particular, we use the Ethos framework to compare statistics of the Lyman-α forest in cold dark matter (CDM) with an alternative model in which the DM couples strongly with a relativistic species in the early universe. These models are characterized by a cut-off in the linear power spectrum, followed by a series of ‘dark acoustic oscillations’ (DAOs) on sub-dwarf scales. While the primordial cut-off delays the formation of the first galaxies, structure builds up more rapidly in the interacting DM model compared to CDM. We show that although DAOs are quickly washed away in the non-linear clustering of DM at z ≲ 10, their signature can be imprinted prominently in the Lyman-α flux power spectrum at z > 5. On scales larger than the cut-off (k ∼ 0.08 s km−1 for the specific model considered here), the relative difference to CDM is reminiscent of a warm dark matter (WDM) model with a similar initial cut-off; however, the redshift evolution on smaller scales is distinctly different. The appearance and disappearance of DAOs in the Lyman-α flux spectrum provides a powerful way to distinguish interacting DM models from WDM and, indeed, variations in the thermal history of the IGM that may also induce a small-scale cut-off.

The Association of Paternal IQ With Autism Spectrum Disorders and Its Comorbidities: A Population-Based Cohort Study

Original case descriptions of autism noted that parents of the affected children tended to be highly educated and intelligent, a characterization that has endured publicly. Recent genetic studies indicate that risk for autism spectrum disorders (ASD) is associated with high intelligence. We examined the association between paternal intelligence and ASD, considering co-occurring intellectual disability (ID) and attention-deficit/hyperactivity disorder (ADHD). We used a register-based cohort study design including 360,151 individuals with fathers conscripted to the Swedish military, resident in Stockholm, Sweden, born from 1984 to 2008, and followed until December 31, 2011, for diagnosis of ASD, ADHD, and/or ID. Risk of neurodevelopmental disorders relative to paternal IQ (rated on a 9-point scale) was assessed using a score of 5 (average intelligence) as the referent in models accounting for potentially nonlinear relationships and clustering of siblings. We observed an association between high paternal IQ and offspring risk of ASD without ID/ADHD in models adjusted for individual and family characteristics (ORIQ=9 1.32, 95% CI 1.15-1.52), an association that appeared to be driven largely by the fathers' score on the technical comprehension portion of the test (ORTechnical IQ= 9 1.53, 95% CI 1.31-1.78). Conversely, low paternal IQ was associated with ASD+ID (ORIQ= 11.78, 95% CI 1.27-2.49) and ASD+ADHD (ORIQ= 11.40, 95% CI 1.16-1.70); low paternal IQ was strongly associated with ID (ORIQ= 1 4.46, 95% CI 3.62-5.49) and present also for ADHD (ORIQ= 11.56, 95% CI 1.42-1.72)] without co-occurring ASD or ID. The relationship between paternal IQ and offspring risk of ASD was nonmonotonic and varied by the presence of co-occurring disorders, probably reflecting phenotypic diversity among affected individuals.

Combined classification and source apportionment analysis for trace elements in western Philippine Sea sediments

Trace elements have been widely used for classification (of variables and of samples) and source apportionment studies, but the comparison and combination of the two is uncommon in previous works. In this paper, the grouping of trace elements, clustering of samples, and source identification were merged for an integrated understanding of the origin and distribution of trace elements in western Philippine Sea sediments. The grouping and clustering studies were implemented by a nonlinear clustering method called a self-organizing map (SOM), and the source identification was accomplished by a nontraditional factor analysis method called positive matrix factorization (PMF). Through visualization and clustering techniques, the SOM simultaneously classified a database of 26 trace elements into four groups of trace elements and five clusters of samples. Each sample cluster occupies a certain geographic area and is characterized by high concentrations of trace elements that are classified within one or two groups. Five potential sources were identified by PMF, representing the land mass of Taiwan Island, anthropogenic emissions from Taiwan, nutrient exportation from the South China Sea, mineral attachment in the deep ocean, and biogenetic components and riverine inputs from the Luzon Islands. The spatial distributions of the sample clusters are comparable to the ranges of high contributions from the five sources distinguished by PMF. This conclusion was further supported by displaying the PMF outputs on the SOM plane. Furthermore, a corresponding relationship was observed between every factor profile and every trace element group. Our work tests the consistency of the classification (of the trace elements and of the samples) and source identification and improves the application of multiperspective methodology in environmental studies.

The full-sky angular bispectrum in redshift space

We compute the redshift-dependent angular bispectrum of galaxy number counts at tree-level, including nonlinear clustering bias and estimating numerically for the first time the effect of redshift space distortions (RSD). We show that for narrow redshift bins the amplitude of nonlinear RSD is comparable with the matter density perturbations. While our numerical results only include terms relevant on sub-horizon scales, the formalism can readily be extended to the full tree-level bispectrum. Our approach does not rely on the flat-sky approximation and it can be easily generalized to different sources by including the appropriate bias expansion. We test the accuracy of Limber approximation for different z-bins. We highlight the subtle but relevant differences in the angular bispectrum of galaxy number counts with respect to CMB, due to the different scale dependence of perturbations. Our formalism can also be directly applied to the angular HI intensity mapping bispectrum.

Optical evidence of magnetic field-induced ferrofluid aggregation: Comparison of cobalt ferrite, magnetite, and magnesium ferrite

Light-transmitting measurements of white light and a consequentially chosen laser beam of 655 nm propagating through citrate- and oleate-coated CoFe2O4, FeFe2O4, and MgFe2O4 nanoparticles under the influence of an external magnetic field were presented. New experimental settings were developed for the optical study of ferrites’ behavior in ferrofluid with the applied magnetic field strength within the 30–400 mT range. A magnetic field-induced change of light transmittance occurred and a precipitation of all studied samples was obtained. Optical investigations of ferrofluid suspensions revealed that, contrary to the linear aggregates of colloidal CoFe2O4 and FeFe2O4, spheroidal aggregates were formed in the case of MgFe2O4. In all three cases, the surface modification resulted in decreased dipole–dipole interactions between ferrite cores, and thus, less precipitates were noticed. All oleate-coated nanoparticles have demonstrated weaker magnetic responses compared to the citrate-encapsulated samples. The aggregation of nanoparticles potentially increases cytotoxicity. Regarding non-linear clustering of MgFe2O4 suspensions, it can be concluded that its excretion from the organism may likely be easier and faster when used in diagnosis and/or therapy. Therefore, more attention should be paid to the lowly toxic MgFe2O4 regarding its medical application.

The Aemulus Project. III. Emulation of the Galaxy Correlation Function

Abstract Using the N-body simulations of the Aemulus Project, we construct an emulator for the nonlinear clustering of galaxies in real and redshift space. We construct our model of galaxy bias using the halo occupation framework, accounting for possible velocity bias. The model includes 15 parameters, including both cosmological and galaxy bias parameters. We demonstrate that our emulator achieves ∼1% precision at the scales of interest, 0.1 h −1 Mpc < r < 10 h −1 Mpc, and recovers the true cosmology when tested against independent simulations. Our primary parameters of interest are related to the growth rate of structure, f, and its degenerate combination, fσ 8. Using this emulator, we show that the constraining power on these parameters monotonically increases as smaller scales are included in the analysis, all the way down to 0.1 h −1 Mpc. For a BOSS-like survey, the constraints on fσ 8 from r < 30 h −1 Mpc scales alone are nearly a factor of two tighter than those from the fiducial BOSS analysis of redshift-space clustering using perturbation theory at larger scales. The combination of real- and redshift-space clustering allows us to break the degeneracy between f and σ 8, yielding an 11% constraint on f alone for a BOSS-like analysis. The current Aemulus simulations limit this model to surveys of massive galaxies. Future simulations will allow this framework to be extended to all galaxy target types, including emission-line galaxies.

Nonlinear Subspace Clustering via Adaptive Graph Regularized Autoencoder

Most existing subspace clustering methods focus on learning a meaningful (e.g., sparse or low-rank) representation of the data. However, they have the following two problems which greatly limit the performance: 1) They neglect the intrinsic local geometrical structures within the data to result in locality preserving property be missing. 2) They neglect the feature learning of the raw data which is usually so complex that the learned representation coefficient is not an optimal graph for clustering. This paper addresses the above problems and proposes a novel nonlinear subspace clustering model via adaptive graph regularized autoencoder (NSC-AGA). This model unifies feature learning, locality preserving, and representation matrix learning into a framework, and a new adaptive graph regularizer is introduced, which takes the representation coefficient matrix as a learnable similarity graph imposed on the Euclidean distance matrix of the deep features. Two matrices interact with each other to make the representation coefficient matrix reflect both the global linear correlation and the local geometric distance relationship. A number of experimental results on the five public image database demonstrate that the proposed NSC-AGA model achieves superior clustering performance compared with the state-of-the-art methods.

Evaluation of the Performance and Efficiency of the Automated Linguistic Features for Author Identification in Short Text Messages Using Different Variable Selection Techniques

The aim of this paper was to evaluate the efficiency of automated linguistic features to test its capacity or discriminating power as style markers for author identification in short text messages of the Facebook genre. The corpus used to evaluate the automated linguistics features was compiled from 221 Facebook texts (each text is about 2 to 3 lines/35-40 words) written in English, which were written in the same genre and topic and posted in the same year group, totaling 7530 words. To compose the dataset for linguistic features performance or evaluation, frequency values were collected from 16 linguistic feature types involving parts of speech, function words, word bigrams, character tri grams, average sentence length in terms of words, average sentence length in terms of characters, Yule’s K measure, Simpson’s D measure, average words length, FW/CW ratio, average characters, content specific key words, type/token ratio, total number of short words less than four characters, contractions, and total number of characters in words which were selected from five corpora, totalling 328 test features. The evaluation of the 16 linguistic feature types differ from those of other analyses because the study used different variable selection methods including feature type frequency, variance, term frequency/ inverse document frequency (TF.IDF), signal-noise ratio, and Poisson term distribution. The relationships between known and anonymous text messages were examined using hierarchical linear and non-hierarchical nonlinear clustering methods, taking into accounts the nonlinear patterns among the data. There were similarities between the anonymous text messages and the authors of the non-anonymous text messages in terms function word and parts of speech usages based on TF.IDF technique and the efficiency of function word usages (=60%) and the efficiency of parts of speech frequencies (=50%). There were no similarities between the anonymous text messages and the authors of the non-anonymous text messages in terms of the other features using feature type frequency and variance techniques in this test and the efficiency of these features in the corpus (< 40%). There was a positive effect on identification performance using parts of speech and function word frequency usages and applying TF.IDF technique as the length of text messages increased (N≥ 100). Through this way, the performance and efficiency of syntactic features and function word usages to identify anonymous authors or text messages is improved by increasing the length of the text messages using TF.IDF variable selection technique, but decreased as feature type frequency and variance techniques in the selection process apply.

Predicting the sufficient-statistics power spectrum for galaxy surveys: a recipe for P A*(k).

Future galaxy surveys hope to realize significantly tighter constraints on various cosmological parameters. The higher number densities achieved by these surveys will allow them to probe the smaller scales affected by non-linear clustering. However, in these regimes, the standard power spectrum can extract only a portion of such surveys' cosmological information. In contrast, the alternate statistic A* has the potential to double these surveys' information return, provided one can predict the A* power spectrum for a given cosmology. Thus, in this work we provide a prescription for this power spectrum P A* (k), finding that the prescription is typically accurate to about 5 per cent for near-concordance cosmologies. This prescription will thus allow us to multiply the information gained from surveys such as Euclid and WFIRST.

Euler Clustering on Large-Scale Dataset

Our concern is nonlinear clustering on large-scale dataset. While existing popular kernels (RBF, Polynomials, Spatial Pyramid, etc.) are popularly used for implicitly mapping data into a high-dimensional or infinite dimensional space in order to generalise linear clustering methods, using these kernels cannot make kernel clustering approaches directly applicable for large scale dataset, since large scale kernel matrix or similarity matrix consumes a lot of memory (e.g., 7,450 GB memory over 1 million samples of data). To solve this problem, we introduce an Euler clustering approach. Euler clustering employs Euler kernels in order to intrinsically map the input data onto a complex space of the same dimension as the input or twice, so that Euler clustering can get rid of kernel trick and does not need to rely on any approximation or random sampling on kernel function/matrix, whilst performing a more robust nonlinear clustering against noise and outliers. Moreover, since the original Euler kernel cannot generate a non-negative similarity matrix and thus is inapplicable to spectral clustering, we introduce a positive Euler kernel, and more importantly we have proved when it can generate a non-negative similarity matrix. We apply Euler kernel and the proposed positive Euler kernel to kernel k-means and spectral clustering so as to develop Euler k-means and Euler spectral clustering, respectively. An efficient Stiefel-manifold-based gradient method and an equivalent weighted positive Euler k-means are derived for fast computation of Euler spectral clustering and further alleviating the impact of discretization of the cluster membership indicators in Euler spectral clustering. The results show that the proposed Euler clustering approach achieves overall better clustering performance compared to using popular Mercer kernels and approximation models, whilst keeping the computational complexity of the same magnitude as the most popular linear clustering method k-means.

Density distribution of the cosmological matter field

The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering, massive production of mock galaxy catalogs, and testing predictions of cosmological models. Here we make a comprehensive analysis of the dark matter PDF using a suite of 7000 N-body simulations that covers a wide range of numerical and cosmological parameters. We find that the PDF has a simple shape: it declines with density as a power-law P~rho**(-2), which is exponentially suppressed on both small and large densities. The proposed double-exponential approximation provides an accurate fit to all our N-body results for small filtering scales R< 5Mpc/h with rms density fluctuations sigma>1. In combination with the spherical infall model that works well for small fluctuations sigma<1, the PDF is now approximated with just few percent errors over the range of twelve orders of magnitude -- a remarkable example of precision cosmology. We find that at 5-10% level the PDF explicitly depends on redshift (at fixed sigma) and on cosmological density parameter Omega_m. We test different existing analytical approximations and find that the often used log-normal approximation is always 3-5 times less accurate than either the double-exponential approximation or the spherical infall model.

Evaluation of the Performance and Efficiency of the Automated Linguistic Features for Author Identification in Short Text Messages Using Different Variable Selection Techniques

The aim of this paper was to evaluate the efficiency of automated linguistic features to test its capacity or discriminating power as style markers for author identification in short text messages of the Facebook genre. The corpus used to evaluate the automated linguistics features was compiled from 221 Facebook texts (each text is about 2 to 3 lines/35-40 words) written in English, which were written in the same genre and topic and posted in the same year group, totaling 7530 words. To compose the dataset for linguistic features performance or evaluation, frequency values were collected from 16 linguistic feature types involving parts of speech, function words, word bigrams, character tri grams, average sentence length in terms of words, average sentence length in terms of characters, Yule’s K measure, Simpson’s D measure, average words length, FW/CW ratio, average characters, content specific key words, type/token ratio, total number of short words less than four characters, contractions, and total number of characters in words which were selected from five corpora, totaling 328 test features. The evaluation of the 16 linguistic feature types differ from those of other analyses because the study used different variable selection methods including feature type frequency, variance, term frequency/ inverse document frequency (TF.IDF), signal-noise ratio, and Poisson term distribution. The relationships between known and anonymous text messages were examined using hierarchical linear and non-hierarchical nonlinear clustering methods, taking into accounts the nonlinear patterns among the data. There were similarities between the anonymous text messages and the authors of the non-anonymous text messages in terms function word and parts of speech usages based on TF.IDF technique and the efficiency of function word usages (=60%) and the efficiency of parts of speech frequencies (=50%). There were no similarities between the anonymous text messages and the authors of the non-anonymous text messages in terms of the other features using feature type frequency and variance techniques in this test and the efficiency of these features in the corpus (< 40%). There was a positive effect on identification performance using parts of speech and function word frequency usages and applying TF.IDF technique as the length of text messages increased (N≥ 100). Through this way, the performance and efficiency of syntactic features and function word usages to identify anonymous authors or text messages is improved by increasing the length of the text messages using TF.IDF variable selection technique, but decreased as feature type frequency and variance techniques in the selection process apply.

An efficient and accurate hybrid method for simulating non-linear neutrino structure

We present an efficient and accurate method for simulating massive neutrinos in cosmological structure formation simulations, together with an easy to use public implementation. Our method builds on our earlier implementation of the linear response approximation (LRA) for neutrinos, coupled with an N-body code for cold dark matter particles. The LRA's good behaviour at early times and in the linear regime is preserved, while better following the non-linear clustering of neutrinos on small scales. Massive neutrinos are split into initially "fast" and "slow" components. The fast component is followed analytically with the LRA all the way to redshift zero. The slow component is evolved with the LRA only down to a switch-on redshift $z_\nu = 1$, below which it is followed with the particle method, in order to fully account for its non-linear evolution. The slow neutrino particles are initialized at $z = 99$ in order to have accurate positions and velocities at the switch-on time, but are not used to compute the potential until $z \leq 1$, thus avoiding the worst effect of particle shot noise. We show that our hybrid method matches (and for small neutrino masses, exceeds) the accuracy of neutrino particle simulations with substantially lower particle load requirements.

Clustering by twin support vector machine and least square twin support vector classifier with uniform output coding

The recently proposed twin support vector clustering (TWSVC) is a powerful clustering method. However, TWSVC may encounter the singularity problem and it is time consuming in the learning stage. In this paper, we introduce some efficient techniques into TWSVC, and propose two clustering models, called twin bounded support vector clustering (TBSVC) and least square twin bounded support vector clustering (LSTBSVC), respectively. TBSVC introduces a maximum margin regularization term into TWSVC, which not only avoids its singularity but also significantly improves the performance. LSTBSVC introduces the least square formation into TBSVC to greatly accelerate its learning speed. Moreover, a uniform output coding for LSTBSVC is introduced to cope with the non-uniformed problem in the learning procedures. In addition, nonlinear clustering is also extended to the above clustering methods by using the kernel trick. Experimental results show the effectiveness and efficiency of our methods.

Detecting global hyperparaboloid correlated clusters: a Hough-transform based multicore algorithm

Correlation clustering detects complex and intricate relationships in high-dimensional data by identifying groups of data points, each characterized by differents correlation among a (sub)set of features. Current correlation clustering methods generally limit themselves to linear correlations only. In this paper, we introduce a method for detecting global non-linear correlated clusters focusing on quadratic relations. We introduce a novel Hough transform for the detection of hyperparaboloids and apply it to the detection of hyperparaboloid correlated clusters in arbitrary high-dimensional data spaces. We further provide a solution for utilizing all available CPU cores on a system. For this we simply split the Hough space among a pre-defined axis into a number of equi-sized partitions. In this paper we show that this most simple way of parallelization already improves the runtime significantly. Non-linear correlation clustering like our method can reveal valuable insights which are not covered by current linear versions. Our empirical results on synthetic and real world data reveal that the proposed method is robust against noise, jitter and irregular densities.