Regularizing Image Reconstruction for Gradient-Domain Rendering with Feature Patches

We present a novel algorithm to reconstruct high-quality images from sampled pixels and gradients in gradient-domain rendering. Our approach extends screened Poisson reconstruction by adding additional regularization constraints. Our key idea is to exploit local patches in feature images, which contain per-pixels normals, textures, position, etc., to formulate these constraints. We describe a GPU implementation of our approach that runs on the order of seconds on megapixel images. We demonstrate a significant improvement in image quality over screened Poisson reconstruction under the L1 norm. Because we adapt the regularization constraints to the noise level in the input, our algorithm is consistent and converges to the ground truth.

An empirical evaluation of the Random Forests classifier models for variable selection in a large-scale lung cancer case-control study

Random Forests™ is reported to be one of the most accurate classification algorithms in complex data analysis. It shows excellent performance even when most predictors are noisy and the number of variables is much larger than the number of observations. In this thesis Random Forests was applied to a large-scale lung cancer case-control study. A novel way of automatically selecting prognostic factors was proposed. Also, synthetic positive control was used to validate Random Forests method. Throughout this study we showed that Random Forests can deal with large number of weak input variables without overfitting. It can account for non-additive interactions between these input variables. Random Forests can also be used for variable selection without being adversely affected by collinearities. ^ Random Forests can deal with the large-scale data sets without rigorous data preprocessing. It has robust variable importance ranking measure. Proposed is a novel variable selection method in context of Random Forests that uses the data noise level as the cut-off value to determine the subset of the important predictors. This new approach enhanced the ability of the Random Forests algorithm to automatically identify important predictors for complex data. The cut-off value can also be adjusted based on the results of the synthetic positive control experiments. ^ When the data set had high variables to observations ratio, Random Forests complemented the established logistic regression. This study suggested that Random Forests is recommended for such high dimensionality data. One can use Random Forests to select the important variables and then use logistic regression or Random Forests itself to estimate the effect size of the predictors and to classify new observations. ^ We also found that the mean decrease of accuracy is a more reliable variable ranking measurement than mean decrease of Gini. ^

Radiomics of NSCLC: Quantitative CT Image Feature Characterization and Tumor Shrinkage Prediction

Radiomics is the high-throughput extraction and analysis of quantitative image features. For non-small cell lung cancer (NSCLC) patients, radiomics can be applied to standard of care computed tomography (CT) images to improve tumor diagnosis, staging, and response assessment. The first objective of this work was to show that CT image features extracted from pre-treatment NSCLC tumors could be used to predict tumor shrinkage in response to therapy. This is important since tumor shrinkage is an important cancer treatment endpoint that is correlated with probability of disease progression and overall survival. Accurate prediction of tumor shrinkage could also lead to individually customized treatment plans. To accomplish this objective, 64 stage NSCLC patients with similar treatments were all imaged using the same CT scanner and protocol. Quantitative image features were extracted and principal component regression with simulated annealing subset selection was used to predict shrinkage. Cross validation and permutation tests were used to validate the results. The optimal model gave a strong correlation between the observed and predicted shrinkages with . The second objective of this work was to identify sets of NSCLC CT image features that are reproducible, non-redundant, and informative across multiple machines. Feature sets with these qualities are needed for NSCLC radiomics models to be robust to machine variation and spurious correlation. To accomplish this objective, test-retest CT image pairs were obtained from 56 NSCLC patients imaged on three CT machines from two institutions. For each machine, quantitative image features with concordance correlation coefficient values greater than 0.90 were considered reproducible. Multi-machine reproducible feature sets were created by taking the intersection of individual machine reproducible feature sets. Redundant features were removed through hierarchical clustering. The findings showed that image feature reproducibility and redundancy depended on both the CT machine and the CT image type (average cine 4D-CT imaging vs. end-exhale cine 4D-CT imaging vs. helical inspiratory breath-hold 3D CT). For each image type, a set of cross-machine reproducible, non-redundant, and informative image features was identified. Compared to end-exhale 4D-CT and breath-hold 3D-CT, average 4D-CT derived image features showed superior multi-machine reproducibility and are the best candidates for clinical correlation.

A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map

Signal analysis and feature generation for pattern identification of partial discharges in high-voltage equipment

This paper proposes a method for the identification of different partial discharges (PDs) sources through the analysis of a collection of PD signals acquired with a PD measurement system. This method, robust and sensitive enough to cope with noisy data and external interferences, combines the characterization of each signal from the collection, with a clustering procedure, the CLARA algorithm. Several features are proposed for the characterization of the signals, being the wavelet variances, the frequency estimated with the Prony method, and the energy, the most relevant for the performance of the clustering procedure. The result of the unsupervised classification is a set of clusters each containing those signals which are more similar to each other than to those in other clusters. The analysis of the classification results permits both the identification of different PD sources and the discrimination between original PD signals, reflections, noise and external interferences. The methods and graphical tools detailed in this paper have been coded and published as a contributed package of the R environment under a GNU/GPL license.

Multi-criteria selection of structural adhesives to bond ABS parts obtained by rapid prototyping

One of the most used methods in rapidprototyping is Fused Deposition Modeling (FDM), which provides components with a reasonable strength in plastic materials such as ABS and has a low environmental impact. However, the FDM process exhibits low levels of surface finishing, difficulty in getting complex and/or small geometries and low consistency in “slim” elements of the parts. Furthermore, “cantilever” elements need large material structures to be supported. The solution of these deficiencies requires a comprehensive review of the three-dimensional part design to enhance advantages and performances of FDM and reduce their constraints. As a key feature of this redesign a novel method of construction by assembling parts with structuraladhesive joints is proposed. These adhesive joints should be designed specifically to fit the plastic substrate and the FDM manufacturing technology. To achieve this, the most suitable structuraladhesiveselection is firstly required. Therefore, the present work analyzes five different families of adhesives (cyanoacrylate, polyurethane, epoxy, acrylic and silicone), and, by means of the application of technical multi-criteria decision analysis based on the analytic hierarchy process (AHP), to select the structuraladhesive that better conjugates mechanical benefits and adaptation to the FDM manufacturing process

A simple genetic algorithm for calibration of stochastic rock discontinuity networks

Este artículo propone un método para llevar a cabo la calibración de las familias de discontinuidades en macizos rocosos. We present a novel approach for calibration of stochastic discontinuity network parameters based on genetic algorithms (GAs). To validate the approach, examples of application of the method to cases with known parameters of the original Poisson discontinuity network are presented. Parameters of the model are encoded as chromosomes using a binary representation, and such chromosomes evolve as successive generations of a randomly generated initial population, subjected to GA operations of selection, crossover and mutation. Such back-calculated parameters are employed to make assessments about the inference capabilities of the model using different objective functions with different probabilities of crossover and mutation. Results show that the predictive capabilities of GAs significantly depend on the type of objective function considered; and they also show that the calibration capabilities of the genetic algorithm can be acceptable for practical engineering applications, since in most cases they can be expected to provide parameter estimates with relatively small errors for those parameters of the network (such as intensity and mean size of discontinuities) that have the strongest influence on many engineering applications.

Regularized logistic regression and multi-objective variable selection for classifying MEG data

This paper addresses the question of maximizing classifier accuracy for classifying task-related mental activity from Magnetoencelophalography (MEG) data. We propose the use of different sources of information and introduce an automatic channel selection procedure. To determine an informative set of channels, our approach combines a variety of machine learning algorithms: feature subset selection methods, classifiers based on regularized logistic regression, information fusion, and multiobjective optimization based on probabilistic modeling of the search space. The experimental results show that our proposal is able to improve classification accuracy compared to approaches whose classifiers use only one type of MEG information or for which the set of channels is fixed a priori.

A new feature extraction method for signal classification applied to cat spinal cord signals

In the spinal cord of the anesthetized cat, spontaneous cord dorsum potentials (CDPs) appear synchronously along the lumbo-sacral segments. These CDPs have different shapes and magnitudes. Previous work has indicated that some CDPs appear to be specially associated with the activation of spinal pathways that lead to primary afferent depolarization and presynaptic inhibition. Visual detection and classification of these CDPs provides relevant information on the functional organization of the neural networks involved in the control of sensory information and allows the characterization of the changes produced by acute nerve and spinal lesions. We now present a novel feature extraction approach for signal classification, applied to CDP detection. The method is based on an intuitive procedure. We first remove by convolution the noise from the CDPs recorded in each given spinal segment. Then, we assign a coefficient for each main local maximum of the signal using its amplitude and distance to the most important maximum of the signal. These coefficients will be the input for the subsequent classification algorithm. In particular, we employ gradient boosting classification trees. This combination of approaches allows a faster and more accurate discrimination of CDPs than is obtained by other methods.

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods.

Collaborative data stream mining in ubiquitous environments using dynamic classifier selection

In ubiquitous data stream mining applications, different devices often aim to learn concepts that are similar to some extent. In these applications, such as spam filtering or news recommendation, the data stream underlying concept (e.g., interesting mail/news) is likely to change over time. Therefore, the resultant model must be continuously adapted to such changes. This paper presents a novel Collaborative Data Stream Mining (Coll-Stream) approach that explores the similarities in the knowledge available from other devices to improve local classification accuracy. Coll-Stream integrates the community knowledge using an ensemble method where the classifiers are selected and weighted based on their local accuracy for different partitions of the feature space. We evaluate Coll-Stream classification accuracy in situations with concept drift, noise, partition granularity and concept similarity in relation to the local underlying concept. The experimental results show that Coll-Stream resultant model achieves stability and accuracy in a variety of situations using both synthetic and real world datasets.

Multi-dimensional classification using Bayesian networks for stationary and evolving streaming data

Hoy en día, con la evolución continua y rápida de las tecnologías de la información y los dispositivos de computación, se recogen y almacenan continuamente grandes volúmenes de datos en distintos dominios y a través de diversas aplicaciones del mundo real. La extracción de conocimiento útil de una cantidad tan enorme de datos no se puede realizar habitualmente de forma manual, y requiere el uso de técnicas adecuadas de aprendizaje automático y de minería de datos. La clasificación es una de las técnicas más importantes que ha sido aplicada con éxito a varias áreas. En general, la clasificación se compone de dos pasos principales: en primer lugar, aprender un modelo de clasificación o clasificador a partir de un conjunto de datos de entrenamiento, y en segundo lugar, clasificar las nuevas instancias de datos utilizando el clasificador aprendido. La clasificación es supervisada cuando todas las etiquetas están presentes en los datos de entrenamiento (es decir, datos completamente etiquetados), semi-supervisada cuando sólo algunas etiquetas son conocidas (es decir, datos parcialmente etiquetados), y no supervisada cuando todas las etiquetas están ausentes en los datos de entrenamiento (es decir, datos no etiquetados). Además, aparte de esta taxonomía, el problema de clasificación se puede categorizar en unidimensional o multidimensional en función del número de variables clase, una o más, respectivamente; o también puede ser categorizado en estacionario o cambiante con el tiempo en función de las características de los datos y de la tasa de cambio subyacente. A lo largo de esta tesis, tratamos el problema de clasificación desde tres perspectivas diferentes, a saber, clasificación supervisada multidimensional estacionaria, clasificación semisupervisada unidimensional cambiante con el tiempo, y clasificación supervisada multidimensional cambiante con el tiempo. Para llevar a cabo esta tarea, hemos usado básicamente los clasificadores Bayesianos como modelos. La primera contribución, dirigiéndose al problema de clasificación supervisada multidimensional estacionaria, se compone de dos nuevos métodos de aprendizaje de clasificadores Bayesianos multidimensionales a partir de datos estacionarios. Los métodos se proponen desde dos puntos de vista diferentes. El primer método, denominado CB-MBC, se basa en una estrategia de envoltura de selección de variables que es voraz y hacia delante, mientras que el segundo, denominado MB-MBC, es una estrategia de filtrado de variables con una aproximación basada en restricciones y en el manto de Markov. Ambos métodos han sido aplicados a dos problemas reales importantes, a saber, la predicción de los inhibidores de la transcriptasa inversa y de la proteasa para el problema de infección por el virus de la inmunodeficiencia humana tipo 1 (HIV-1), y la predicción del European Quality of Life-5 Dimensions (EQ-5D) a partir de los cuestionarios de la enfermedad de Parkinson con 39 ítems (PDQ-39). El estudio experimental incluye comparaciones de CB-MBC y MB-MBC con los métodos del estado del arte de la clasificación multidimensional, así como con métodos comúnmente utilizados para resolver el problema de predicción de la enfermedad de Parkinson, a saber, la regresión logística multinomial, mínimos cuadrados ordinarios, y mínimas desviaciones absolutas censuradas. En ambas aplicaciones, los resultados han sido prometedores con respecto a la precisión de la clasificación, así como en relación al análisis de las estructuras gráficas que identifican interacciones conocidas y novedosas entre las variables. La segunda contribución, referida al problema de clasificación semi-supervisada unidimensional cambiante con el tiempo, consiste en un método nuevo (CPL-DS) para clasificar flujos de datos parcialmente etiquetados. Los flujos de datos difieren de los conjuntos de datos estacionarios en su proceso de generación muy rápido y en su aspecto de cambio de concepto. Es decir, los conceptos aprendidos y/o la distribución subyacente están probablemente cambiando y evolucionando en el tiempo, lo que hace que el modelo de clasificación actual sea obsoleto y deba ser actualizado. CPL-DS utiliza la divergencia de Kullback-Leibler y el método de bootstrapping para cuantificar y detectar tres tipos posibles de cambio: en las predictoras, en la a posteriori de la clase o en ambas. Después, si se detecta cualquier cambio, un nuevo modelo de clasificación se aprende usando el algoritmo EM; si no, el modelo de clasificación actual se mantiene sin modificaciones. CPL-DS es general, ya que puede ser aplicado a varios modelos de clasificación. Usando dos modelos diferentes, el clasificador naive Bayes y la regresión logística, CPL-DS se ha probado con flujos de datos sintéticos y también se ha aplicado al problema real de la detección de código malware, en el cual los nuevos ficheros recibidos deben ser continuamente clasificados en malware o goodware. Los resultados experimentales muestran que nuestro método es efectivo para la detección de diferentes tipos de cambio a partir de los flujos de datos parcialmente etiquetados y también tiene una buena precisión de la clasificación. Finalmente, la tercera contribución, sobre el problema de clasificación supervisada multidimensional cambiante con el tiempo, consiste en dos métodos adaptativos, a saber, Locally Adpative-MB-MBC (LA-MB-MBC) y Globally Adpative-MB-MBC (GA-MB-MBC). Ambos métodos monitorizan el cambio de concepto a lo largo del tiempo utilizando la log-verosimilitud media como métrica y el test de Page-Hinkley. Luego, si se detecta un cambio de concepto, LA-MB-MBC adapta el actual clasificador Bayesiano multidimensional localmente alrededor de cada nodo cambiado, mientras que GA-MB-MBC aprende un nuevo clasificador Bayesiano multidimensional. El estudio experimental realizado usando flujos de datos sintéticos multidimensionales indica los méritos de los métodos adaptativos propuestos. ABSTRACT Nowadays, with the ongoing and rapid evolution of information technology and computing devices, large volumes of data are continuously collected and stored in different domains and through various real-world applications. Extracting useful knowledge from such a huge amount of data usually cannot be performed manually, and requires the use of adequate machine learning and data mining techniques. Classification is one of the most important techniques that has been successfully applied to several areas. Roughly speaking, classification consists of two main steps: first, learn a classification model or classifier from an available training data, and secondly, classify the new incoming unseen data instances using the learned classifier. Classification is supervised when the whole class values are present in the training data (i.e., fully labeled data), semi-supervised when only some class values are known (i.e., partially labeled data), and unsupervised when the whole class values are missing in the training data (i.e., unlabeled data). In addition, besides this taxonomy, the classification problem can be categorized into uni-dimensional or multi-dimensional depending on the number of class variables, one or more, respectively; or can be also categorized into stationary or streaming depending on the characteristics of the data and the rate of change underlying it. Through this thesis, we deal with the classification problem under three different settings, namely, supervised multi-dimensional stationary classification, semi-supervised unidimensional streaming classification, and supervised multi-dimensional streaming classification. To accomplish this task, we basically used Bayesian network classifiers as models. The first contribution, addressing the supervised multi-dimensional stationary classification problem, consists of two new methods for learning multi-dimensional Bayesian network classifiers from stationary data. They are proposed from two different points of view. The first method, named CB-MBC, is based on a wrapper greedy forward selection approach, while the second one, named MB-MBC, is a filter constraint-based approach based on Markov blankets. Both methods are applied to two important real-world problems, namely, the prediction of the human immunodeficiency virus type 1 (HIV-1) reverse transcriptase and protease inhibitors, and the prediction of the European Quality of Life-5 Dimensions (EQ-5D) from 39-item Parkinson’s Disease Questionnaire (PDQ-39). The experimental study includes comparisons of CB-MBC and MB-MBC against state-of-the-art multi-dimensional classification methods, as well as against commonly used methods for solving the Parkinson’s disease prediction problem, namely, multinomial logistic regression, ordinary least squares, and censored least absolute deviations. For both considered case studies, results are promising in terms of classification accuracy as well as regarding the analysis of the learned MBC graphical structures identifying known and novel interactions among variables. The second contribution, addressing the semi-supervised uni-dimensional streaming classification problem, consists of a novel method (CPL-DS) for classifying partially labeled data streams. Data streams differ from the stationary data sets by their highly rapid generation process and their concept-drifting aspect. That is, the learned concepts and/or the underlying distribution are likely changing and evolving over time, which makes the current classification model out-of-date requiring to be updated. CPL-DS uses the Kullback-Leibler divergence and bootstrapping method to quantify and detect three possible kinds of drift: feature, conditional or dual. Then, if any occurs, a new classification model is learned using the expectation-maximization algorithm; otherwise, the current classification model is kept unchanged. CPL-DS is general as it can be applied to several classification models. Using two different models, namely, naive Bayes classifier and logistic regression, CPL-DS is tested with synthetic data streams and applied to the real-world problem of malware detection, where the new received files should be continuously classified into malware or goodware. Experimental results show that our approach is effective for detecting different kinds of drift from partially labeled data streams, as well as having a good classification performance. Finally, the third contribution, addressing the supervised multi-dimensional streaming classification problem, consists of two adaptive methods, namely, Locally Adaptive-MB-MBC (LA-MB-MBC) and Globally Adaptive-MB-MBC (GA-MB-MBC). Both methods monitor the concept drift over time using the average log-likelihood score and the Page-Hinkley test. Then, if a drift is detected, LA-MB-MBC adapts the current multi-dimensional Bayesian network classifier locally around each changed node, whereas GA-MB-MBC learns a new multi-dimensional Bayesian network classifier from scratch. Experimental study carried out using synthetic multi-dimensional data streams shows the merits of both proposed adaptive methods.

Neuroanatomic-based detection algorithm for automatic labeling of brain structures in brain injury

The number and grade of injured neuroanatomic structures and the type of injury determine the degree of impairment after a brain injury event and the recovery options of the patient. However, the body of knowledge and clinical intervention guides are basically focused on functional disorder and they still do not take into account the location of injuries. The prognostic value of location information is not known in detail either. This paper proposes a feature-based detection algorithm, named Neuroanatomic-Based Detection Algorithm (NBDA), based on SURF (Speeded Up Robust Feature) to label anatomical brain structures on cortical and sub-cortical areas. Themain goal is to register injured neuroanatomic structures to generate a database containing patient?s structural impairment profile. This kind of information permits to establish a relation with functional disorders and the prognostic evolution during neurorehabilitation procedures.

A multi-resource load balancing algorithm for cloud cache systems

With the advent of cloud computing model, distributed caches have become the cornerstone for building scalable applications. Popular systems like Facebook [1] or Twitter use Memcached [5], a highly scalable distributed object cache, to speed up applications by avoiding database accesses. Distributed object caches assign objects to cache instances based on a hashing function, and objects are not moved from a cache instance to another unless more instances are added to the cache and objects are redistributed. This may lead to situations where some cache instances are overloaded when some of the objects they store are frequently accessed, while other cache instances are less frequently used. In this paper we propose a multi-resource load balancing algorithm for distributed cache systems. The algorithm aims at balancing both CPU and Memory resources among cache instances by redistributing stored data. Considering the possible conflict of balancing multiple resources at the same time, we give CPU and Memory resources weighted priorities based on the runtime load distributions. A scarcer resource is given a higher weight than a less scarce resource when load balancing. The system imbalance degree is evaluated based on monitoring information, and the utility load of a node, a unit for resource consumption. Besides, since continuous rebalance of the system may affect the QoS of applications utilizing the cache system, our data selection policy ensures that each data migration minimizes the system imbalance degree and hence, the total reconfiguration cost can be minimized. An extensive simulation is conducted to compare our policy with other policies. Our policy shows a significant improvement in time efficiency and decrease in reconfiguration cost.

Consideration of Multi-Phase Criterion in the Differential Protection Algorithm for High-Impedance Grounded Synchronous Generators

The generator differential protection is one of the most important electrical protections of synchronous generator stator windings. Its operation principle is based on the comparison of the input current and output current at each phase winding. Unwanted trip commands are usually caused by CT saturation, wrong CT selection, or the fact that they may come from different manufacturers. In generators grounded through high impedance, only phase-to-phase or three-phase faults can be detected by the differential protection. This kind of fault causes differential current to flow in, at least, two phases of the winding. Several cases of unwanted trip commands caused by the appearance of differential current in only one phase of the generator have been reported. In this paper multi-phase criterion is proposed for generator differential protection algorithm when applied to high impedance grounded generators.