Variational Bayesian Independent Component Analysis Research Articles

On the Initial Phase of the Ongoing Unrest at Campi Flegrei and Its Relation with Subsidence at Vesuvio (Italy)

The densely inhabited area of Naples (Italy), between the Campi Flegrei and Vesuvio volcanoes, is one of the most hazardous regions in the world. After two decades of sustained subsidence, Campi Flegrei has been experiencing an accelerating uplift since 2005. The uplift is currently associated with unusual seismicity and increased degassing. To try to identify the cause of the shift from subsidence to uplift and explore any connection between Campi Flegrei and Vesuvio, we analysed the ground displacement time series of the two volcanoes from 1993 to 2010, obtained from ERS/ENVISAT Synthetic Aperture Radar imagery. To distinguish between the various sources of deformation, we used simple scatter plots and a blind source separation technique called variational Bayesian independent component analysis (vbICA). We obtained consistent results using both approaches. Specifically, with vbICA, we identified two significant independent components (ICs). IC1 describes the subsidence that occurred at Campi Flegrei prior to 2000, including the mini-uplifts of 2000 and 2005, and part of the post-2005 uplift. The expansion and contraction of two volumes beneath Campi Flegrei satisfy IC1: a sill-shaped volume at a depth of approximately 3 km and a small volume at a depth of 1–2 km, respectively. The two sources of deformation reproduce the large-scale deformation in the Campi Flegrei area and the local deformation in the Solfatara area, respectively. In the Campi Flegrei area, IC2 exhibits primarily uplift, which is concentrated in the eastern part of the caldera. The deformation pattern is complex and difficult to interpret. If we model it using simple spheroidal deformation sources, the pattern suggests that two volumes at depths of approximately 9 and 8 km are experiencing opposite activity, namely contraction (beneath the southwestern part of the caldera) and expansion (beneath the central part of the caldera). In the Vesuvio area, IC2 is consistent with the deformation induced by the contraction of a volume at a depth of around 9 km. The contraction beneath Vesuvio is smaller in magnitude than the expansion/contraction beneath Campi Flegrei. The correlation observed after 2002 between uplift at Campi Flegrei and subsidence at Vesuvio suggests the transfer of magma and/or magmatic fluids between the two plumbing systems at 8–9 km depth. This implies that part of the ongoing unrest at Campi Flegrei may have been promoted by mass transfer from below Vesuvio.

Interplay Between Seismic and Aseismic Deformation on the Central Range Fault During the 2013 Mw 6.3 Ruisui Earthquake (Taiwan)

AbstractThe 2013 Ruisui earthquake represents the first unequivocal evidence of the activity of the Central Range fault (CRF) in central Longitudinal Valley, Taiwan. Using a joint Bayesian finite‐fault source inversion of Global Navigation Satellite System and strain time series, we infer that coseismic rupture occurred between 4 and 19 km depth with maximum slip of 0.5 m located near the hypocenter. We then apply a variational Bayesian independent component analysis approach to displacement signals to infer a 3‐months long afterslip located in the near‐source region. This observation represents the first evidence of aseismic slip on the CRF. Combining geodetic and seismological analysis with simulations based on rate‐and‐state friction mechanics, we analyze the interplay between seismic and aseismic deformation during the earthquake sequence. We observe that afterslip is the dominant postseismic deformation mechanism, with >95% of the moment being released aseismically in the postseismic phase and also likely represents the driving force controlling aftershock productivity. Finally, we infer the presence of a shallow velocity strengthening zone (∼0–4 km depth) associated with spatially heterogeneous slip during the postseismic phase with maximum slip of 0.18 m located above the zone of maximum coseismic deformation.

Characterizing hydrological droughts within three watersheds in Yunnan, China from GNSS-inferred terrestrial water storage changes constrained by GRACE data

SUMMARY The spatiotemporal evolution of drought is often modulated by climate and watershed characteristics. While numerous drought studies using space geodesy have been conducted in Yunnan, the scarcity and limited sensitivity of observation instruments have hindered the development of watershed-scale drought analyses. This study aims to accurately characterize hydrological droughts within three watersheds in Yunnan from 2011 January to 2021 May by a Global Navigation Satellite System (GNSS) inversion constrained by Gravity Recovery and Climate Experiment (GRACE) data. Initially, we employed Variational Bayesian Independent Component Analysis to reconstruct the 3-D crustal deformations at 43 GNSS stations resulting from hydrological loadings. We then computed the time-series of vertical displacements caused by GRACE Mascon water products. Subsequently, utilizing the method of least squares, we derived the scaling factors between the vertical crustal displacements (VCD) obtained from GNSS observations and the synthetic displacements derived from GRACE data. By combing scaling-factor-adjusted VCDs derived from GRACE with the GNSS data, we have obtained accurate estimates of water storage for three Yunnan watersheds. Finally, we identified drought events characterized by abnormal decreases in water storage and used climatological methods to quantitatively describe the severity, extent and recovery of these drought extremes. Additionally, we evaluated the influence of various earth elastic structures on the scaling factors, and demonstrated their advantageous contribution to aligning GNSS and GRACE observations. In conclusion, our study introduces a novel approach to integrate GNSS and GRACE retrievals, allowing for accurate characterization of droughts in data-scarce regions, which cannot be achieved by GNSS or GRACE individually. Moreover, our results underscore the potential benefits of watershed-scale drought monitoring and analysis for effective water resource management.

Searching for Transient Slow Slips Along the San Andreas Fault Near Parkfield Using Independent Component Analysis

AbstractThe Parkfield segment of the San Andreas Fault (SAF) sits at the transition between the locked Cholame segment to the South and the SAF creeping segment to the North. The Parkfield segment hosts regular 6 earthquakes followed by postseismic deformation. Recent studies based on geodetic data have highlighted spatial and temporal variations of aseismic slip rate in addition to postseismic slip along this section of the fault. We combine Global Navigation Satellite Systems (GNSS) and seismicity data over the 2006–2018 period to detail a comprehensive picture of transient slip events. We produce a catalog of relocated seismicity and repeating earthquakes. We use a variational Bayesian independent component analysis decomposition on GNSS data to separate geodetic deformation due to non‐tectonic sources from signals of potential tectonic origin. We then reconstruct the temporal evolution of fault slip and detect potential slip transients. Those events, determined as mostly aseismic with the exception of one related to a 4.8 earthquake, occur more frequently during the 2004 6 post‐seismic period than during the subsequent inter‐seismic phase. Our study illustrates the rich dynamics of seismic and aseismic slip during both post‐ and inter‐seismic periods along active faults.

Post-Seismic Deformation Related to the 2016 Central Italy Seismic Sequence From GPS Displacement Time-Series.

The 2016–2017 Central Italy earthquake sequence struck the central Apennines between August 2016 and October 2016 with Mw ∈ [5.9; 6.5], plus four earthquakes occurring in January 2017 with Mw ∈ [5.0; 5.5]. We study Global Positioning System time series including near‐ and far‐field domains. We use a variational Bayesian independent component analysis technique to separate the post‐seismic deformation from signals caused by variation of the water content in aquifers at hundreds of meters of depth and of the soil moisture. For each independent component, realistic uncertainties and a plausible physical explanation are provided. We focus on the study of afterslip on the main structures surrounding the mainshock, highlighting the role played by faults that were not activated during the co‐seismic phase in accommodating the post‐seismic deformation. We report aseismic deformation occurring on the Paganica fault, which hosted the Mw 6.1 2009 L'Aquila earthquake, suggesting that static stress transfer and aseismic slip influence the recurrence time of nearby (∼50 km further south of the mainshocks) segments. A ∼2–3 km thick subhorizontal shear‐zone, clearly illuminated by seismicity, which bounds at depth the west‐dipping normal faults where the mainshocks nucleated, also shows aseismic slip. Since afterslip alone underestimates the displacement in the far‐field domain, we consider the possibility that the shear zone marks the brittle‐ductile transition, assuming the viscoelastic relaxation of the lower crust as a mechanism contributing to the post‐seismic displacement. Our results suggest that multiple deformation processes are active in the first 2 years after the mainshocks.

The 2011-2019 Long Valley Caldera inflation: New insights from separation of superimposed geodetic signals and 3D modeling

Increasingly accurate, and spatio-temporally dense, measurements of Earth surface movements enable us to identify multiple deformation patterns and highlight the need to properly characterize the related source processes. This is particularly important in tectonically active areas, where deformation measurement is crucial for monitoring ongoing processes and assessing future hazard. Long Valley Caldera, California, USA, is a volcanic area where frequent episodes of unrest involve inflation and increased seismicity. Ground- and satellite-based instruments show that volcanic inflation renewed in 2011, and is continuing as of early 2021. Additionally, Long Valley Caldera is affected by the large, but spatially and temporally variable, amounts of precipitation falling on the adjacent Sierra Nevada Range.The density and long duration of deformation measurements at Long Valley Caldera provide an excellent collection of data to decompose time-series and separate multiple superimposed deformation sources. We analyze Global Navigation Satellite System (GNSS) time-series and apply variational Bayesian Independent Component Analysis (vbICA) decomposition method to isolate inflation-related signals from other processes. We show that hydrological forcing causes significant horizontal and vertical deformation at different temporal (seasonal and multiyear) and spatial (few to hundreds of km) scales that cannot be ignored while analyzing and modeling the tectonic signal. Focusing on the last inflation episode, we then improve on prior simplistic models of the inflation reservoir by including heterogeneous subsurface material properties and topography. Our results suggest the persistence and stability of the reservoir (prolate ellipsoid at about 8 km beneath the resurgent dome) and indicate a 40-50% reduction of the inflation rate after about 3 years from the inflation onset. The onset of the reduced inflation rate corresponded in time with the occurrence of a strong seismic swarm in the Caldera, but also to the temporal variation of climatic conditions in the area.

Variational Bayesian Independent Component Analysis for InSAR Displacement Time‐Series With Application to Central California, USA

AbstractThe exploitation of ever increasing Interferometric Synthetic Aperture Radar (InSAR) data sets to monitor the Earth's surface deformation is an important goal of today's geodesy. In this study our observations consist of deformations along the Line‐Of‐Sight direction of the satellite. Our observations are the result of the combination of a multitude of sources (either volcano‐tectonic or nontectonic deformation). In most cases, we are facing a Blind source separation (BSS) problem. Natural approaches to tackle BSS problems are multivariate statistical techniques that attempt to decompose the data set into a limited number of statistically independent sources, under the assumption that the different physical mechanisms contributing to the observations have independent footprints in space and/or time. We show the capabilities of a variational Bayesian independent component analysis (vbICA) algorithm in dealing with synthetic InSAR time series and compare it to the commonly used FastICA algorithm. We explore the effectiveness of the spatial and temporal mode decompositions. We apply vbICA on data relative to the San Joaquin Valley and the Central San Andreas fault (CSAF), California, spanning the time range 2015/03/01–2019/07/14. The proposed approach likely isolates the contribution of shallow and deep aquifers to the surface deformation as well as the elastic and inelastic deformation. We present a 1‐dimensional compaction estimation of the elastic and inelastic storage coefficients adopting a formalism that takes into account the last century water level history. Concerning the CSAF, the algorithm helps separating tectonic loading from seasonal behavior concentrated in the Quaternary sediments of the Salinas Valley.

Postseismic Deformation Following the 2015 Mw7.8 Gorkha (Nepal) Earthquake: New GPS Data, Kinematic and Dynamic Models, and the Roles of Afterslip and Viscoelastic Relaxation

AbstractWe report Global Positioning System (GPS) measurements of postseismic deformation following the 2015 Mw7.8 Gorkha (Nepal) earthquake, including previously unpublished data from 13 continuous GPS stations installed in southern Tibet shortly after the earthquake. We use variational Bayesian Independent Component Analysis (vbICA) to extract the signal of postseismic deformation from the GPS time series, revealing a broad displacement field extending >150 km northward from the rupture. Kinematic inversions and dynamic forward models show that these displacements could have been produced solely by afterslip on the Main Himalayan Thrust (MHT) but would require a broad distribution of afterslip extending similarly far north. This would require the constitutive parameter (a − b)σ to decrease northward on the MHT to ≤0.05 MPa (an extreme sensitivity of creep rate to stress change) and seems unlikely in light of the low interseismic coupling and high midcrustal temperatures beneath southern Tibet. We conclude that the northward reach of postseismic deformation more likely results from distributed viscoelastic relaxation, possibly in a midcrustal shear zone extending northward from the seismogenic MHT. Assuming a shear zone 5–20 km thick, we estimate an effective shear‐zone viscosity of ~3·1016–3·1017 Pa·s over the first 1.12 postseismic years. Near‐field deformation can be more plausibly explained by afterslip itself and implies (a − b)σ ~ 0.5–1 MPa, consistent with other afterslip studies. This near‐field afterslip by itself would have re‐increased the Coulomb stress by ≥0.05 MPa over >30% of the Gorkha rupture zone in the first postseismic year, and deformation further north would have compounded this reloading.

Identification and Extraction of Seasonal Geodetic Signals Due to Surface Load Variations

AbstractDeformation of the Earth's surface associated with redistributions of continental water mass explains, to first order, the seasonal signals observed in geodetic position time series. Discriminating these seasonal signals from other sources of deformation in geodetic measurements is essential to isolate tectonic signals and to monitor spatio‐temporal variations in continental water storage. We propose a new methodology to identify and extract these seasonal signals. The approach uses a variational Bayesian Independent Component Analysis (vbICA) to extract the seasonal signals and a gravity‐based deformation model to identify which of these signals are caused by surface loading. We test the procedure on two study areas, the Arabian Peninsula and the Nepal Himalaya, and find that the technique successfully extracts the seasonal signals with one or two independent components, depending on whether the load is stationary or moving. The approach is robust to spatial heterogeneities inherent to geodetic measurements and can help extract systematic errors in geodetic products (e.g., draconitic errors). We also discuss how to handle the degree‐1 deformation field present in the geodetic data set but not captured by the gravity‐based model.

Interseismic Coupling and Slow Slip Events on the Cascadia Megathrust

In this study, we model geodetic strain accumulation along the Cascadia subduction zone between 2007.0 and 2017.632 using position time series from 352 continuous GPS stations. First, we use the secular linear motion to determine interseismic locking along the megathrust. We determine two end member models, assuming that the megathrust is either a priori locked or creeping, which differ essentially along the trench where the inversion is poorly constrained by the data. In either case, significant locking of the megathrust updip of the coastline is needed. The downdip limit of the locked portion lies ∼ 20–80 km updip from the coast assuming a locked a priori, but very close to the coast for a creeping a priori. Second, we use a variational Bayesian Independent Component Analysis (vbICA) decomposition to model geodetic strain time variations, an approach which is effective to separate the geodetic strain signal due to non-tectonic and tectonic sources. The Slow Slip Events (SSEs) kinematics is retrieved by linearly inverting for slip on the megathrust the Independent Components related to these transient phenomena. The procedure allows the detection and modelling of 64 SSEs which spatially and temporally match with the tremors activity. SEEs and tremors occur well inland from the coastline and follow closely the estimated location of the mantle wedge corner. The transition zone, between the locked portion of the megathrust and the zone of tremors, is creeping rather steadily at the long-term slip rate and probably buffers the effect of SSEs on the megathrust seismogenic portion.

Poroelasticity and Fluid Flow Modeling for the 2012 Emilia-Romagna Earthquakes: Hints from GPS and InSAR Data

The Emilia-Romagna seismic sequence in May 2012 was characterized by two mainshocks which were close in time and space. Several authors already modeled the geodetic data in terms of the mechanical interaction of the events in the seismic sequence. Liquefaction has been extensively observed, suggesting an important role of fluids in the sequence. In this work, we focus on the poroelastic effects induced by the two mainshocks. In particular, the target of this work is to model the influence of fluids and pore-pressure changes on surface displacements and on the Coulomb failure function (CFF). The fluid flow and poroelastic modeling was performed in a 3D half-space whose elastic and hydraulic parameters are depth dependent, in accordance with the geology of the Emilia-Romagna subsoil. The model provides both the poroelastic displacements and the pore-pressure changes induced coseismically by the two mainshocks at subsequent periods and their evolution over time. Modeling results are then compared with postseismic InSAR and GPS displacement time series: the InSAR data consist of two SBAS series presented in previous works, while the GPS signal was detected adopting a variational Bayesian independent component analysis (vbICA) method. Thanks to the vbICA, we are able to separate the contribution of afterslip and poroelasticity on the horizontal surface displacements recorded by the GPS stations. The poroelastic GPS component is then compared to the modeled displacements and shown to be mainly due to drainage of the shallowest layers. Our results offer an estimation of the poroelastic effect magnitude that is small but not negligible and mostly confined in the near field of the two mainshocks. We also show that accounting for a 3D fault representation with a nonuniform slip distribution and the elastic-hydraulic layering of the half-space has an important role in the simulation results.

Unsupervised Gaussian Mixture-Model With Expectation Maximization for Detecting Glaucomatous Progression in Standard Automated Perimetry Visual Fields.

PurposeTo validate Gaussian mixture-model with expectation maximization (GEM) and variational Bayesian independent component analysis mixture-models (VIM) for detecting glaucomatous progression along visual field (VF) defect patterns (GEM–progression of patterns (POP) and VIM-POP). To compare GEM-POP and VIM-POP with other methods.MethodsGEM and VIM models separated cross-sectional abnormal VFs from 859 eyes and normal VFs from 1117 eyes into abnormal and normal clusters. Clusters were decomposed into independent axes. The confidence limit (CL) of stability was established for each axis with a set of 84 stable eyes. Sensitivity for detecting progression was assessed in a sample of 83 eyes with known progressive glaucomatous optic neuropathy (PGON). Eyes were classified as progressed if any defect pattern progressed beyond the CL of stability. Performance of GEM-POP and VIM-POP was compared to point-wise linear regression (PLR), permutation analysis of PLR (PoPLR), and linear regression (LR) of mean deviation (MD), and visual field index (VFI).ResultsSensitivity and specificity for detecting glaucomatous VFs were 89.9% and 93.8%, respectively, for GEM and 93.0% and 97.0%, respectively, for VIM. Receiver operating characteristic (ROC) curve areas for classifying progressed eyes were 0.82 for VIM-POP, 0.86 for GEM-POP, 0.81 for PoPLR, 0.69 for LR of MD, and 0.76 for LR of VFI.ConclusionsGEM-POP was significantly more sensitive to PGON than PoPLR and linear regression of MD and VFI in our sample, while providing localized progression information.Translational RelevanceDetection of glaucomatous progression can be improved by assessing longitudinal changes in localized patterns of glaucomatous defect identified by unsupervised machine learning.

Noisy Blind Signal-jamming Separation Algorithm Based on VBICA

Aiming at the blind signal-jamming separation (BSJS) in wireless communication environment, we propose a noisy BSJS based on Variational Bayesian Independent Component Analysis algorithm to separat...

A Multispectral Remote Sensing Data Spectral Unmixing Algorithm Based on Variational Bayesian ICA

Mixed pixel is a key issue in medium to coarse resolution remote sensing image, and it seriously restricts the remote sensing classification. This paper presents an Independent component analysis (ICA) algorithm based on the variational Bayesian (VB) methods, named VBICA, for spectral unmixing in multispectral remote sensing image. The model assumes that the mixed pixels to be separated are given as linear mixtures. The matrixes of linear mixtures are assumed to be unknown. In the Bayesian framework, the endmember and abundance have finally been achieved with Bayesian inference and approximate variational algorithm. The proposed method is evaluated and tested on a numerical simulative image from the noise resistance, area size, pixel purity, estimated number of endmembers and real multispectral remote sensing image of 100 × 100 pixels. Experimental results on simulated image demonstrated that compared to the Fast ICA algorithm, the proposed algorithm can give more accurate results, and the validity of the proposed algorithm is verified by the real multispectral remote sensing image of the similarity on spectral curves, average similarity and ground objects distribution maps.

Variational Bayesian independent component analysis for spectral unmixing in remote sensing image

Spectral unmixing is a key technology of optical remote sensing image analysis; it not only influences the accuracy of the extraction of land cover information and automatic classification of topographical objects, but also greatly hinders the development of quantitative remote sensing. Independent component analysis (ICA) is a statistical method which is recently developed to extract the independent linear components, and which can realize the extraction of endmembers as well as fractional abundances with little a priori knowledge. However, ICA still cannot process the correlations among the various components. To overcome this problem, variational Bayesian independent component analysis (VBICA) has been proposed to process optical remote sensing images. In the Bayesian framework, the separation of independent components of remote sensing image has finally been achieved with conditional independence standards of Bayesian network and approximate variational algorithm. In the simulative image and real AVIRIS hyperspectral remote sensing image, the VBICA algorithm demonstrates its better performance. The experiment’s results indicate that the proposed VBICA algorithm is feasible, which has obvious advantages and a good application prospect. The reason is that it can effectively overcome the correlations between the various components in remote sensing images and break through the limitations of traditional remote sensing images analysis. Last but not least, the VBICA algorithm is applied in the classification of the TM multispectral remote sensing images. Compared to basic maximum likelihood classification, principal component analysis and FastICA algorithms, VBICA improves the classification accuracy of remote sensing images, and contributes to the further extension of the application of ICA in remote sensing image analysis.

Unsupervised learning with independent component analysis can identify patterns of glaucomatous visual field defects

The author previously reported the use of clustering by unsupervised learning with machine learning classifiers to segment clusters of patterns in standard automated perimetry (SAP) for glaucoma. In this study, the process of unsupervised learning by independent component analysis decomposed SAP field patterns into axes, and the information represented by these axes was evaluated. SAP fields were obtained with the Humphrey Visual Field Analyzer on 189 normal eyes and 156 eyes with glaucomatous optic neuropathy (GON) determined by masked review with stereoscopic optic disk photos. The variational Bayesian independent component analysis mixture model (vB-ICA-mm) partitioned the SAP fields into the most informative number of clusters. Simultaneously, it learned an optimal number of maximally independent axes for each cluster. The most informative number of clusters was two. The vB-ICA-mm placed 68.6% of the SAP fields from the eyes with GON in a cluster labeled G and 98.4% of the fields from eyes with normal optic disks in a cluster labeled N. Cluster G optimally contained six axes. Post hoc analysis of patterns generated at −1 SC and +2 SB from the cluster G mean on the six axes revealed defects similar to those identified by experts as indicative of glaucoma. SAP fields associated with an axis showed increasing severity as they were located farther in the positive direction from the cluster G mean. The vB-ICA-mm represented the SAP fields with patterns that were meaningful for glaucoma experts. This process also captured severity in the patterns uncovered. These findings should validate vB-ICA-mm as a data mining technique for new and unfamiliar complex tests.—Hans E. Grossniklaus

Using Unsupervised Learning with Independent Component Analysis to Identify Patterns of Glaucomatous Visual Field Defects

Clustering by unsupervised learning with machine learning classifiers was shown to segment clusters of patterns in standard automated perimetry (SAP) for glaucoma in previous publications. In this study, unsupervised learning by independent component analysis decomposed SAP field patterns into axes, and the information represented by these axes was evaluated. SAP fields were used that were obtained with the Humphrey Visual Field Analyzer (Carl Zeiss Meditec, Dublin, CA) from 189 normal eyes and 156 eyes with glaucomatous optic neuropathy (GON) determined by masked review with stereoscopic optic disc photographs. The variational Bayesian independent component analysis mixture model (vB-ICA-mm) partitioned the SAP fields into the most informative number of clusters. Simultaneously, the model learned an optimal number of maximally independent axes for each cluster. The most informative number of clusters in the SAP set was two. vB-ICA-mm placed 68.6% of the eyes with GON in a cluster labeled G and 98.4% of the eyes with normal optic discs in a cluster labeled N. Cluster G optimally contained six axes. Post hoc analysis of patterns generated at -1 SD and +2 SD from the cluster G mean on the six axes revealed defects similar to those identified by experts as indicative of glaucoma. SAP fields associated with an axis showed increasing severity, as they were located farther in the positive direction from the cluster G mean. vB-ICA-mm represented the SAP fields with patterns that were meaningful for glaucoma experts. This process also captured severity in the patterns uncovered. These findings should validate vB-ICA-mm as a data-mining technique for new and unfamiliar complex tests.

Unsupervised Machine Learning with Independent Component Analysis to Identify Areas of Progression in Glaucomatous Visual Fields

To determine whether a variational Bayesian independent component analysis mixture model (vB-ICA-mm), a form of unsupervised machine learning, can be used to identify and quantify areas of progression in standard automated perimetry fields. In an earlier study, it was shown that a model using vB-ICA-mm can separate normal fields from fields with six different patterns of visual field loss related to glaucomatous optic neuropathy (GON) along maximally independent axes. In the present study, an independent group of 191 patient eyes (66 with ocular hypertension (OHT), 12 with suspected glaucoma by field, 61 with suspected glaucoma by disc, and 52 with glaucoma) with five or more standard visual fields under observation for a mean of 6.24 +/- 2.65 years and 8.11 +/- 2.42 visual fields were evaluated with the vB-ICA-mm. In addition, eyes with progressive GON (PGON) were identified (n = 39). Each participant had a series of fields tested, with each field entered independently and placed along the axes of the previously developed model. This allowed change in one pattern of visual field defect (along one axis) to be assessed relative to results other areas of that same field (no change along other axes). Progression was based on a slope falling outside the 5th and the 95th percentile limits of all slopes, with at least two axes not showing such a deviation in a given individual's series of fields. Fields were also scored using Advanced Glaucoma Intervention Study (AGIS) and the Early Manifest Glaucoma Treatment Trial (EMGT) criteria. Thirty-two of 191 eyes progressed on vB-ICA-mm by this definition. Of the 32, 22 had field loss at baseline, 7 had only GON, 3 were OHTs and 12 were from the 39 eyes (31%) with PGON. The vB-ICA-mm identified a higher percentage of progressing eyes in each diagnostic category than did AGIS or and the EMGT. The vB-ICA-mm can quantitatively identify progression in eyes with glaucoma by evaluating change in one or more patterns of the visual field loss while other areas or patterns remain stable. This may enable each eye to contribute to the determination of whether change is caused by true progression or by variability.