Singular Value Decomposition Analysis Research Articles

SVD perspectives for augmenting DeepONet flexibility and interpretability

Deep operator networks (DeepONets) are powerful and flexible architectures that are attracting attention in multiple fields due to their utility for fast and accurate emulation of complex dynamics. As their remarkable generalization capabilities are primarily enabled by their projection-based attribute, in this paper, we investigate connections with low-rank techniques derived from the singular value decomposition (SVD). We demonstrate that some of the concepts behind proper orthogonal decomposition (POD)-neural networks can improve DeepONet’s design and training phases. These ideas lead us to a methodology extension that we name SVD-DeepONet. Moreover, through multiple SVD analyses of scenario- and time-aggregated snapshots matrices, we find that DeepONet inherits from its projection-based attribute strong inefficiencies in representing dynamics characterized by symmetries. Inspired by the work on shifted-POD, we develop flexDeepONet, an architecture enhancement that relies on a pre-transformation network for generating a moving reference frame and isolating the rigid components of the dynamics. In this way, the physics can be represented on a latent space free from rotations, translations, and stretches, and an accurate projection can be performed to a low-dimensional basis. In addition to improving DeepONet’s flexibility and interpretability, the proposed perspectives increase its generalization capabilities and computational efficiencies. For instance, we show flexDeepONet can accurately surrogate the dynamics of 19 thermodynamic variables in a combustion chemistry application by relying on 95% fewer trainable parameters than that of the ‘vanilla’ architecture. As stressed in the paper, we argue that DeepONet and SVD-based methods can reciprocally benefit from each other. In particular, the flexibility of the former in leveraging multiple data sources and multifidelity knowledge in the form of both unstructured data and physics-informed constraints has the potential to greatly extend the applicability of methodologies such as POD and principal component analysis (PCA).

Influence of sea surface wave-dependent roughness on summer precipitation over the Southeastern United States

To study the influence of ocean surface roughness on summer precipitation over the southeastern United States, we perform singular value decomposition (SVD) analysis between the mean summer precipitations and the significant wave height from 1979 to 2017 over the Gulf of Mexico (GOM). The first dominant mode shows that the swell energy in the northern GOM is larger than that in the southern GOM, especially over the region adjacent to the southeastern United States (SE-US). Meanwhile, the precipitation in the SE-US is much heavier than the other regions. Composite analysis shows that when the first pattern takes place, the wind speed is small near the region of the SE-US, swell dominates. There is a cyclonic wind anomaly at 850 hPa over the SE-US, which results in strong upward motion, therefore heavy rainfall in this region. To further study the effect of the swell on the precipitation in the SE-US, we also design two numerical experiments using the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modelling System. In the control (CTL) experiment, the popular Charnock aerodynamical roughness length parameterization is adopted. In the other experiment, a wave-dependent roughness scheme is used. The precipitation in the SE-US is better simulated in the wave-dependent roughness experiment than in the CTL experiment. In summer, the 10-m wind speed is weak in the northeastern Gulf of Mexico, and that means the swell is dominant in this region. The wave-dependent surface roughness strengthens the wind, which means that the momentum is transferred from the wave to the atmosphere under swell dominant conditions. The increase of the shear term and the cyclonic wind anomaly in the lower layers of the atmosphere leads to a stronger upward motion which drives heavier rainfall in the SE-US.

Local Linearity Analysis of Deep Learning CT Denoising Algorithms.

The rapid development of deep-learning methods in medical imaging has called for an analysis method suitable for non-linear and data-dependent algorithms. In this work, we investigate a local linearity analysis where a complex neural network can be represented as piecewise linear systems. We recognize that a large number of neural networks consists of alternating linear layers and rectified linear unit (ReLU) activations, and are therefore strictly piecewise linear. We investigated the extent of these locally linear regions by gradually adding perturbations to an operating point. For this work, we explored perturbations based on image features of interest, including lesion contrast, background, and additive noise. We then developed strategies to extend these strictly locally linear regions to include neighboring linear regions with similar gradients. Using these approximately linear regions, we applied singular value decomposition (SVD) analysis to each local linear system to investigate and explain the overall nonlinear and data-dependent behaviors of neural networks. The analysis was applied to an example CT denoising algorithm trained on thorax CT scans. We observed that the strictly local linear regions are highly sensitive to small signal perturbations. Over a range of lesion contrast from 0.007 to 0.04 mm-1, there is a total of 33992 linear regions. The Jacobians are also shift-variant. However, the Jacobians of neighboring linear regions are very similar. By combining linear regions with similar Jacobians, we narrowed down the number of approximately linear regions to four over lesion contrast from 0.001 to 0.08 mm-1. The SVD analysis to different linear regions revealed denoising behavior that is highly dependent on the background intensity. Analysis further identified greater amount of noise reduction in uniform regions compared to lesion edges. In summary, the local linearity analysis framework we proposed has the potential for us to better characterize and interpret the non-linear and data-dependent behaviors of neural networks.

Principal component analysis for complex geometry modal identification

Recent advances to resonant ultrasound spectroscopy (RUS) to include finite element methods (FERUS) have expanded its application to more complex geometries. When measuring a sample of complex geometry, it is often challenging to retrieve all modal information from a single point, this is due to the complexity of the mode shapes and likeliness of landing on a node location. To capture all the modal information, many measurement points are used to superimpose into a final resonant spectrum, and these measurements points are often based on intuition or experience. The work presented in this abstract proposes a simple method of finding crucial measurement locations on a complex sample using singular value decomposition (SVD) and principal component analysis (PCA). Applying SVD to a group of forward calculated eigenvectors, a set of measurement locations can then be extracted from the high amplitude locations identified from the subset of eigen images. This method of PCA for mode identification has been shown to accurately identify essential measurement locations.

Spatiotemporal organisation of protein processing in the kidney

The kidney regulates plasma protein levels by eliminating them from the circulation. Proteins filtered by glomeruli are endocytosed and degraded in the proximal tubule and defects in this process result in tubular proteinuria, an important clinical biomarker. However, the spatiotemporal organization of renal protein metabolism in vivo was previously unclear. Here, using functional probes and intravital microscopy, we track the fate of filtered proteins in real time in living mice, and map specialized processing to tubular structures with singular value decomposition analysis and three-dimensional electron microscopy. We reveal that degradation of proteins requires sequential, coordinated activity of distinct tubular sub-segments, each adapted to specific tasks. Moreover, we leverage this approach to pinpoint the nature of endo-lysosomal disorders in disease models, and show that compensatory uptake in later regions of the proximal tubule limits urinary protein loss. This means that measurement of proteinuria likely underestimates severity of endocytotic defects in patients.

Singular value decomposition of protein sequences as a method to visualize sequence and residue space.

Singular value decomposition (SVD) of multiple sequence alignments (MSAs) is an important and rigorous method to identify subgroups of sequences within the MSA, and to extract consensus and covariance sequence features that define the alignment and distinguish the subgroups. This information can be correlated to structure, function, stability, and taxonomy. However, the mathematics of SVD is unfamiliar to many in the field of protein science. Here, we attempt to present an intuitive yet comprehensive description of SVD analysis of MSAs. We begin by describing the underlying mathematics of SVD in a way that is both rigorous and accessible. Next, we use SVD to analyze sequences generated with a simplified model in which the extent of sequence conservation and covariance between different positions is controlled, to show how conservation and covariance produce features in the decomposed coordinate system. We then use SVD to analyze alignments of two protein families, the homeodomain and the Ras superfamilies. Both families show clear evidence of sequence clustering when projected into singular value space. We use k-means clustering to group MSA sequences into specific clusters, show how the residues that distinguish these clusters can be identified, and show how these clusters can be related to taxonomy and function. We end by providing a description a set of Python scripts that can be used for SVD analysis of MSAs, displaying results, and identifying and analyzing sequence clusters. These scripts are freely available on GitHub.

Spatiotemporal Variation of Actual Evapotranspiration and Its Relationship with Precipitation in Northern China under Global Warming

The analysis of actual evapotranspiration (ETa) changes is of great significance for the utilization and allocation of water resources. In this study, ETa variability in northern China (aridity index < 0.65) is investigated based on the average of seven datasets (GLEAM, GLASS, a complementary relationship-based dataset, CRA-40, MERRA2, JRA-55, and ERA5-Land). The results show that ETa increases significantly from 1982 to 2017. Limited by water supply, ETa is significantly correlated with precipitation (R = 0.682), whereas the increase in precipitation is insignificant (p = 0.151). Spatially, the long-term trend of ETa is also not completely consistent with that of precipitation. According to a singular value decomposition (SVD) analysis, the trend of ETa is mainly related to the first four leading SVD modes. Homogeneous correlation patterns indicate that more precipitation generally leads to high ETa; however, this relationship is modulated by other factors. Overall, positive potential evapotranspiration anomalies convert more surface water into ETa, resulting in a higher increase in ETa than in precipitation. Specifically, ETa in the northern Tibetan Plateau is associated with meltwater generated by rising temperatures, and ETa in the Badain Jaran Desert is highly dependent on the wet-day frequency. Under global warming, the inconsistency between ETa and precipitation changes has a great impact on water resources in northern China.

A dynamic detection method for polygonal wear of railway wheel based on parametric power spectral estimation

Severe wheel polygon will cause the strong repeated wheel-rail excitation, accelerating the failure of vehicle key components. Nevertheless, the traditional spectral estimation methods are not ideal for dealing with these wheel fault signals, making the characteristic frequencies caused by wheel polygon hardly detected. This paper proposes a dynamic detection method for wheel polygon based on parametric power spectral estimation for the first time. Firstly, according to the dynamic characteristics of the wheel polygon, the harmonic frequency recovery model is established. Secondly, the order of the harmonic frequency recovery model is determined based on singular value decomposition and normalised error analysis. Then, the total least square method is used to calculate the parameters of the harmonic recovery model. Finally, the power spectrum of the fault signal is evaluated according to the Cadzow estimation theory. The simulation signal and the measured axle-box vertical vibration acceleration signal of a metro vehicle are taken as case studies to verify the feasibility and effectiveness of the proposed method thoroughly. The results show the proposed method can avoid the inherent defects of traditional detection and analysis methods, weaken the influence of background noise, and is highly advantageous in detecting the initial stage of wheel polygonal wear.

Gas puff imaging system for edge plasma fluctuation measurements in large helical device.

A gas puff imaging system has been developed to measure edge fluctuations in large helical device. The optical system splits the image of the plasma into four wavelengths, Hα/Dα (656nm), HeI (1s2p-1s3d; 587.6; 1s2p-1s3d, 667.8; and 1s2p-1s3s, 706.5nm), enabling simultaneous measurement of the spatial distribution of line ratios of He I. The image of the plasma is amplified with an image intensifier and recorded with a fast-framing camera. The measurement area has a diameter of 20cm just outside of the last closed flux surface. The spatial resolution of the optical system is about 3mm, and the frame rate is 100kHz for acquisition of the four wavelength images. Signal-to-noise ratio is evaluated for the system, and further improvement is discussed. Clear images are obtained for all wavelengths and a slightly different pattern is recognized, depending on the wavelength. A singular value decomposition analysis can decompose the image clearly to one perpendicular and parallel to the magnetic field lines.

Causes of decadal distributions of Indian summer monsoon rainfall during the last 1500 years

AbstractUnderstanding the distribution of Indian summer monsoon rainfall (ISMR) and the relationships with external forcing factors (EXFs) and internal climate variability (ICV) is crucial for improving the prediction accuracy of ISMR. Here, we explore and quantify the influence of EXFs and ICV on the distribution of ISMR at decadal timescales over the past 1500 years using the Community Earth System Model (CESM). We identified the major ICV and EXF modes of ISMR distributions in simulations from 501 to 1850 ad and 1851 to 2000 ad. The results show that ICV plays a dominant role in decadal ISMR changes during the pre‐industrial and the current periods. Simulations show east–west contrasts over the Indian subcontinent, with a center of rainfall variability in the high‐latitude regions around 28°N. The EXF mode, calculated from the leading mode of the singular value decomposition analysis, exhibits a nearly uniform increase (or decrease) in the distribution of ISMR over the study region. From 501 to 1850 ad, the signals of greenhouse gases (GHGs), and land use and land cover (LULC) in the ISMR at the decadal timescale are weak and difficult to isolate from the ICV. Our numerical analyses show that natural forcing was a dominant contribution (~64.1%) to the forced ISMR distribution. From 1851 to 2000 ad, natural forcing, GHGs and LULC all contributed to the forced ISMR distribution. GHGs represent a key external forcing factor affecting the distribution of ISMR and could explain 22.3% of the total variance. LULC and natural forcing factors contribute 17.5 and 16.4% to the total variance, respectively. Our results contribute to a better understanding of the mechanisms controlling decadal variability of the Indian summer monsoon.

A new scheme for extracting fault features of rolling element bearings

PurposeThe purpose of this paper is to propose a new fault feature extraction scheme for the rolling element bearing.Design/methodology/approachThe generalized Stockwell transform (GST) and the singular value ratio spectrum (SVRS) methods are combined. A time-frequency distribution measurement criterion named the energy concentration measurement (ECM) is initially used to determine the parameter of the optimal GST method. Then, the optimal GST is applied to conduct a time-frequency transformation for a raw signal. Subsequently, the two-dimensional time-frequency matrix is obtained. Finally, the improved singular value decomposition (SVD) analysis is used to conduct a noise reduction of the time-frequency matrix. The SVRS is proposed to select the effective singular values. Furthermore, the time-domain feature of the impact signal is obtained by taking the inverse GST transform.FindingsThe simulated and experimental signals are used to verify the superiority of the proposed method over conventional methods. The obtained results show that the proposed method can effectively extract fault features of the rolling element bearing.Research limitations/implicationsThis paper mainly discusses the application of GST and SVRS methods to analyze the weak fault feature extraction problem. The next research direction is to explore the application of the Hilbert Huang transform (HHT) and variational modal decomposition (VMD) in the impact feature extraction of rolling bearing.Originality/valueIn the present study, a new SVRS method is proposed to select the number of effective singular values. This paper proposed an effective way to obtain the fault feature in monitoring of rotating machinery.

Caught in the act: Monitoring O[sbnd]O bond cleavage in Acylperoxoferric cytochrome P450cam to form compound I in real time

While monitoring the reaction of ferric cytochrome P450cam (Cyp101) with substituted peroxybenzoic acids using rapid-scanning, stopped-flow (RSSF) spectroscopy, an intermediate appears en route to formation of the high-valent moiety known as Compound I [Fe(IV)=O/porphyrin radical cation] that is thought to be the key catalytic species for O-atom transfer to substrate. We have previously suggested (Spolitak, T., Dawson, J.H., Ballou, D.P., J. Biol. Chem.2005, 280, 20,300–20,309) that this species is an acylperoxo-ferric heme adduct that subsequently undergoes OO bond cleavage to generate Compound I. Singular value decomposition analysis of the RSSF data for formation of this intermediate shows that the energy of its Soret absorption peak is sensitive to the electron donor properties of the aryl substituents on the peracid. A linear Hammett correlation plot is seen for the energy of the Soret absorption peak vs. the Hammett σ constant. This correlation requires that the aryl substituents remain as part of the ligand bound to the heme iron, providing direct evidence that the adduct is indeed a ferric acylperoxo derivative. Linear Hammett correlation plots are also seen for both the rate of formation of the intermediate as well as for its conversion to Compound I. It is proposed that the electron donating/withdrawing properties of the aryl-bound substituents affect the electrophilic nature for binding substrate, changing the observed rate of formation for the acylperoxo intermediate, as well as the propensity and stability of the substituted benzoic acid to serve as the leaving group during OO bond cleavage yielding Compound I.

Derivation of the Gait Deviation Index for Spinal Cord Injury.

The Gait Deviation Index (GDI) is a dimensionless multivariate measure of overall gait pathology represented as a single score that indicates the gait deviation from a normal gait average. It is calculated using kinematic data recorded during a three-dimensional gait analysis and an orthonormal vectorial basis with 15 gait features that was originally obtained using singular value decomposition and feature analysis on a dataset of children with cerebral palsy. Ever since, it has been used as an outcome measure to study gait in several conditions, including spinal cord injury (SCI). Nevertheless, the validity of implementing the GDI in a population with SCI has not been studied yet. We investigate the application of these mathematical methods to derive a similar metric but with a dataset of adults with SCI (SCI-GDI). The new SCI-GDI is compared with the original GDI to evaluate their differences and assess the need for a specific GDI for SCI and with the WISCI II to evaluate its sensibility. Our findings show that a 21-feature basis is necessary to account for most of the variance in gait patterns in the SCI population and to provide high-quality reconstructions of the gait curves included in the dataset and in foreign data. Furthermore, using only the first 15 features of our SCI basis, the fidelity of the reconstructions obtained in our population is higher than that when using the basis of the original GDI. The results showed that the SCI-GDI discriminates most levels of the WISCI II scale, except for levels 12 and 18. Statistically significant differences were found between both indexes within each WISCI II level except for 12, 20, and the control group (p < 0.05). In all levels, the average GDI value was greater than the average SCI-GDI value, but the difference between both indexes is larger in data with greater impairment and it reduces progressively toward a normal gait pattern. In conclusion, the implementation of the original GDI in SCI may lead to overestimation of gait function, and our new SCI-GDI is more sensitive to larger gait impairment than the GDI. Further validation of the SCI-GDI with other scales validated in SCI is needed.

Hidden Complexity in the Mechanism of the Autoreduction of Myoglobin Compound II.

The non-native oxidation of horse heart myoglobin with hydrogen peroxide produces compound II which autoreduces by utilizing an internal oxidation site. Here, we utilize full UV–visible time-dependent kinetics with global kinetic singular value decomposition analysis to explore the mechanism and uncover more detail about the high-valent heme spectral features. By varying the hydrogen peroxide and myoglobin concentration, we were able to uncover more detailed spectra of myoglobin compound II and the autoreduction rate under several different pH conditions. The compound II spectra demonstrate pH-dependent features with an inflection point around pH 5.7 ± 0.1. The rate of autoreduction of compound II, k2, increases with lower pH with a half-power proton dependence and no indication of a pKa > 3.9 ± 0.2, indicating that the autoreduction is still dependent on the protonation of the ferryl oxo species. The k2 also demonstrates both hydrogen peroxide and myoglobin dependency. At myoglobin concentrations greater than 6.6 μM, the k2 is myoglobin-independent, but for lower concentrations, a pH-sensitive concentration dependence is seen.

Ultrafast vibrational dynamics of the free OD at the air/water interface: Negligible isotopic dilution effect but large isotope substitution effect.

Vibrational relaxation dynamics of the OH stretch of water at the air/water interface has been a subject of intensive research, facilitated by recent developments in ultrafast interface-selective nonlinear spectroscopy. However, a reliable determination of the vibrational relaxation dynamics in the OD stretch region at the air/D2O interface has not been yet achieved. Here, we report a study of the vibrational relaxation of the free OD carried out by time-resolved heterodyne-detected vibrational sum frequency generation spectroscopy. The results obtained with the aid of singular value decomposition analysis indicate that the vibrational relaxation (T1) time of the free OD at the air/D2O interface and air/isotopically diluted water (HOD-H2O) interfaces show no detectable isotopic dilution effect within the experimental error, as in the case of the free OH in the OH stretch region. Thus, it is concluded that the relaxation of the excited free OH/OD predominantly proceeds with their reorientation, negating a major contribution of the intramolecular energy transfer. It is also shown that the T1 time of the free OD is substantially longer than that of the free OH, further supporting the reorientation relaxation mechanism. The large difference in the T1 time between the free OD and the free OH (factor of ∼2) may indicate the nuclear quantum effect on the diffusive reorientation of the free OD/OH because this difference is significantly larger than the value expected for a classical rotational motion.

Spatio-Temporal Characterization with Wavelet Coherence: Anexus between Environment and Pandemic

Identifying spatio-temporal synchrony in a complex, interacting and oscillatory coupled-system is a challenge. In particular, the characterization of statistical relationships between environmental or biophysical variables with the multivariate data of pandemic is a difficult process because of the intrinsic variability and non-stationary nature of the time-series in space and time. This paper presents a methodology to address these issues by examining the bivariate relationship between Covid-19 and temperature time-series in the time-localized frequency domain by using Singular Value Decomposition (SVD) and continuous cross-wavelet analysis. First, the dominant spatio-temporal trends are derived by using the eigen decomposition of SVD. The Covid-19 incidence data and the temperature data of the corresponding period are transformed into significant eigen-state vectors for each spatial unit. The Morlet Wavelet transformation is performed to analyse and compare the frequency structure of the dominant trends derived by the SVD. The result provides cross-wavelet transform and wavelet coherence measures in the ranges of time period for the corresponding spatial units. Additionally, wavelet power spectrum and paired wavelet coherence statistics and phase difference are estimated. The result suggests statistically significant coherency at various frequencies providing insight into spatio-temporal dynamics. Moreover, it provides information about the complex conjugate dynamic relationships in terms phases and phase differences.

Consensus embedding for multiple networks: Computation and applications

AbstractMachine learning applications on large-scale network-structured data commonly encode network information in the form of node embeddings. Network embedding algorithms map the nodes into a low-dimensional space such that the nodes that are “similar” with respect to network topology are also close to each other in the embedding space. Real-world networks often have multiple versions or can be “multiplex” with multiple types of edges with different semantics. For such networks, computation ofConsensus Embeddings based on the node embeddings of individual versions can be useful for various reasons, including privacy, efficiency, and effectiveness of analyses. Here, we systematically investigate the performance of three dimensionality reduction methods in computing consensus embeddings on networks with multiple versions: singular value decomposition, variational auto-encoders, and canonical correlation analysis (CCA). Our results show that (i) CCA outperforms other dimensionality reduction methods in computing concensus embeddings, (ii) in the context of link prediction, consensus embeddings can be used to make predictions with accuracy close to that provided by embeddings of integrated networks, and (iii) consensus embeddings can be used to improve the efficiency of combinatorial link prediction queries on multiple networks by multiple orders of magnitude.

CalFitter 2.0: Leveraging the power of singular value decomposition to analyse protein thermostability.

The importance of the quantitative description of protein unfolding and aggregation for the rational design of stability or understanding the molecular basis of protein misfolding diseases is well established. Protein thermostability is typically assessed by calorimetric or spectroscopic techniques that monitor different complementary signals during unfolding. The CalFitter webserver has already proved integral to deriving invaluable energy parameters by global data analysis. Here, we introduce CalFitter 2.0, which newly incorporates singular value decomposition (SVD) of multi-wavelength spectral datasets into the global fitting pipeline. Processed time- or temperature-evolved SVD components can now be fitted together with other experimental data types. Moreover, deconvoluted basis spectra provide spectral fingerprints of relevant macrostates populated during unfolding, which greatly enriches the information gains of the CalFitter output. The SVD analysis is fully automated in a highly interactive module, providing access to the results to users without any prior knowledge of the underlying mathematics. Additionally, a novel data uploading wizard has been implemented to facilitate rapid and easy uploading of multiple datasets. Together, the newly introduced changes significantly improve the user experience, making this software a unique, robust, and interactive platform for the analysis of protein thermal denaturation data. The webserver is freely accessible at https://loschmidt.chemi.muni.cz/calfitter.

Informative singular value decomposition and its application in fault detection of planetary gearbox

The fault features of planetary gearboxes are modulated complexly and are submerged by other signal components, for its vibration signal has the characteristics of multi-source and multi transmission path. A fault detection method of planetary gearboxes based on informative singular value decomposition and envelope spectrum analysis (ISVD-ESA) is proposed in this paper. In this method, the advantage of blind source separation of singular value decomposition (SVD) method is combined with the ability of negentropy and cyclic autocorrelation (CA) in non-Gaussian characteristics recognition. The fast SVD is firstly performed to decompose the vibration signal into a series of singular value decomposition component signals (SVCSs). Secondly, the detector of negentropy combined with CA is applied to estimate the fault informativeness of each SVCS. The SVCSs are amplified by the fault informativeness and reconstructed to the out signal of ISVD. Finally, the fault features can be extracted by the ESA from the output signal of ISVD. The performance of the proposed method is verified by simulation and experimental studies. Results show that the proposed ISVD-ESA strategy can enhance the weak features of multi-modulation and accurately extract the faults of tooth tip pitting and misalignment of sun gear of the planetary gearbox.

The impact of El Niño southern oscillation and Indian Ocean Dipole on the burned area in Indonesia

Land and forest fire have been identified as one of the main problems contributing to forest biodiversity and Global Warming and well known as the phenomenon affected by El Niño Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD). The total burned area becomes higher when either El Niño or positive IOD occur. This research aims to analyze and quantify the direct correlation of the Niño 3.4 and difference between west and east pole of IOD sea surface temperature anomaly (SSTA) to the burned area in Indonesia and the impact of ENSO and IOD of each category on the burned area. The correlation between spatial location with Niño 3.4 and difference IOD SST's will be analyzed using a heterogeneous correlation map. Meanwhile, the quantitative impact will be calculated based on the singular value decomposition analysis result to each year categories. The most significant impact of El Niño has occurred on Merauke following Kalimantan shows the strongest correlation between burned area and Niño 3.4 SST. However, the significant increase of burned area only occurred during very strong El Niño. Both areas can have double amount of burned area during peak fire in very strong El Niño. Moderate El Niño have the most diverse impact with the stronger one occurs on Kalimantan and Merauke. Weak El Niño can have a significant impact if occurred simultaneously with positive IOD. Even more, it can surpass the effect of a single Moderate El Niño. Meanwhile, the strongest IOD impact happened in the southern part of Sumatra.