Incremental Linear Discriminant Analysis for Classification of Data Streams

This paper presents a constructive method for deriving an updated discriminant eigenspace for classification, when bursts of new classes of data is being added to an initial discriminant eigenspace in the form of random chunks. The proposed Chunk incremental linear discriminant analysis (I-LDA) can effectively evolve a discriminant eigenspace over a fast and large data stream, and extract features with superior discriminability in classification, when compared with other methods.

This paper proposes a new online feature extraction method called Incremental Recursive Fisher Linear Discriminant (IRFLD) whose batch learning algorithm called RFLD has been proposed by Xiang et al. In the conventional Linear Discriminant Analysis (LDA), the number of discriminant vectors is limited to the number of classes minus one due to the rank of the between-class covariance matrix. However, RFLD and the proposed IRFLD can break this limit; that is, an arbitrary number of discriminant vectors can be obtained. In the proposed IRFLD, the Pang et al.'s Incremental Linear Discriminant Analysis (ILDA) is extended such that effective discriminant vectors are recursively searched for the complementary space of a conventional discriminant subspace. In addition, to estimate a suitable number of effective discriminant vectors, the classification accuracy is evaluated with a cross-validation method in an online manner. For this purpose, validation data are obtained by performing the k-means clustering against incoming training data and previous validation data. The performance of IRFLD is evaluated for 16 benchmark data sets. The experimental results show that the final classification accuracies of IRFLD are always better than those of ILDA. We also reveal that this performance improvement is attained by adding discriminant vectors in a complementary LDA subspace.

This paper examines the possibilities of using Landsat Thematic Mapper images for updating land-use information on topographic maps. Information obtained from satellite images can be kept up-todate and a large number of classes can be distinguished. However, the quality of the information still leaves much to be desired, with a reliability of no more than 40 - 90 %. By using digitized landuse information from a topographic map as a source of contest information the reliability could be improved considerably. The method permitted the Identification of a large number of additional classes and provided quantitative insight into the dynamics of landscap change. Verification using 1:18,000 scale aerial photographs and field data showed the results to have a reliability of over 95 %. It can be expected that whereever topographic maps permit the extraction of land-use information in a similar way as described in this paper, remote sensing information will meet operational accuracy requirements for many fields of application e.g. physical planning, map udating, land-use planning etc. Paper presented at the IGARSS'88 conference Remote Sensing - moving towards the 21st century in Edinburgh, Scotland, 12-16 September 1988

The label tree-based classification is one of the most popular approaches for reducing the testing complexity to sublinear with the large number of classes. One of the popular approaches to generate the label tree is to apply recursively a spectral clustering algorithm to an affinity matrix for partition set of class labels into subsets, each subset corresponds to a child node of the tree. To obtain the affinity matrix from confusion matrix, a set of N binary one-versus-all classifiers is trained and applied on validation set, where N is number of classes. However, these approaches are not reliable when there are a large number of classes because it is too costly to train these classifiers. Furthermore, the affinity matrix could not reflect the real similarity among classes due to the classification accuracy can be low. In addition, the resulting label tree may not be balanced due to the objective function of spectral clustering penalizes unbalanced partitions. In this paper, to achieve better similarity measurement between classes and without using one-versus-all classifiers, we adopt the sum match kernel to get similarity matrix. Moreover, we propose a heuristic for learning balanced tree structure by adjusting the number of class labels in clusters after the spectral clustering is done. The experimental results on benchmark datasets SUN-397 and Caltech-256 show that the performance of the proposed approach outperforms significantly the other approaches.

Conventional application of convolutional neural networks (CNNs) for image classification and recognition is based on the assumption that all target classes are equal (i.e. no hierarchy) and exclusive of one another (i.e. no overlap). CNN-based image classifiers built on this assumption, therefore, cannot take into account an innate hierarchy among target classes (e.g. cats and dogs in animal image classification) or additional information that can be easily derived from the data (e.g. numbers larger than five in the recognition of handwritten digits), thereby resulting in scalability issues when the number of target classes is large. Combining two related but slightly different ideas of hierarchical classification and logical learning by auxiliary inputs, we propose a new learning framework called hierarchical auxiliary learning, which not only address the scalability issues with a large number of classes but also could further reduce the classification/recognition errors with a reasonable number of classes. In the hierarchical auxiliary learning, target classes are semantically or non-semantically grouped into superclasses, which turns the original problem of mapping between an image and its target class into a new problem of mapping between a pair of an image and its superclass and the target class. To take the advantage of a superclass as a hint during the learning phase, we introduce an auxiliary block into a neural network, which generates auxiliary scores used as additional information for final classification/recognition; in this paper, we add the auxiliary block between the last residual block and the fully-connected output layer of the ResNet. Experimental results show that the proposed hierarchical auxiliary learning reduces classification errors up to 0.56, 1.6 and 3.56 percent with MNIST, SVHN and CIFAR-10 datasets, respectively.

In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the nonasymptotic bounds for misclassification excess risk of the resulting classifier. We establish also their tightness by deriving the corresponding minimax lower bounds. In particular, we show that there exist two regimes corresponding to small and large number of classes. The bounds can be reduced under the additional low noise condition. To find a penalized maximum likelihood solution with a complexity penalty requires, however, a combinatorial search over all possible models. To design a feature selection procedure computationally feasible for high-dimensional data, we propose multinomial logistic group Lasso and Slope classifiers and show that they also achieve the minimax order.

The state-of-the-art object detection and image classification methods can perform impressively on more than 9k classes. In contrast, the number of classes in semantic segmentation datasets is relatively limited. This is not surprising when the restrictions caused by the lack of labeled data and high computation demand for segmentation are considered. In this paper, we propose a novel training methodology to train and scale the existing semantic segmentation models for a large number of semantic classes without increasing the memory overhead. In our embedding-based scalable segmentation approach, we reduce the space complexity of the segmentation model’s output from O(C) to O(1), propose an approximation method for ground-truth class probability, and use it to compute cross-entropy loss. The proposed approach is general and can be adopted by any state-of-the-art segmentation model to gracefully scale it for any number of semantic classes with only one GPU. Our approach achieves similar, and in some cases, even better mIoU for Cityscapes, Pascal VOC, ADE20k, COCO-Stuff10k datasets when adopted to DeeplabV3+ model with different backbones. We demonstrate a clear benefit of our approach on a dataset with 1284 classes, bootstrapped from LVIS and COCO annotations, with almost three times better mIoU than the DeeplabV3+. Our source code is available at: https://github.com/shipra25jain/ESSNet.

A learning-based classification problem with a large number of classes is considered. The error-correcting-output-codes (ЕСОС) scheme is optimized. An initial binary matrix is formed at random so that the number of its rows is equal to the number of classes and each column corresponds to the union of several classes in two macroclasses. In the ЕСОС approach, a binary classification problem is solved for every object to be recognized and for every union. The object is assigned to the class with the nearest code row. A generalization of the ЕСОС approach is presented in which a discrete optimization problem is solved to find optimal unions, probabilities of correct classification are used in dichotomy problems, and the degree of dichotomy informativeness is taken into account. If the solution algorithms for the dichotomy problems are correct, the recognition algorithm for the original problem is correct as well.

Machine learning based algorithms, such as a decision tree (DT) classifier, have been applied to automated process monitoring and fault identification in manufacturing processes, however the current DT-based process control models employ a single DT classifier for both mean shift detection and fault identification. As many manufacturing processes use automated data collection for multiple process parameters, a DT classifier would have to handle a large number of classes. Previous research shows that a large number of classes can degrade the accuracy of a DT multiclass classifier. In this study we propose a new process monitoring model using multiple DT classifiers with each handling a small number of classes. Moreover, we not only detect mean shifts but also identify process variability levels that may cause out-of-control signals. Experimental results show that our proposed model achieves satisfactory performance in process monitoring and fault identification with various parameter settings. It achieves better ARL performance compared with the baseline method based on a single DT classifier.

Visual thalamic neurons were stained in a Golgilike fashion following cortical injections of horseradish peroxidase (HRP). Such staining allows neurons to be classified on the basis of their dendritic morphology, and it enables the direct relation of morphologically identified neurons with their respective cortical projection target to be visualized. All classes of neurons categorized on the basis of Golgi material (Guillery, '66) were identified in the dorsal part of the lateral geniculate body (LGBd): class 1 and class 2 neurons in the laminae A, A1, and C; class 3 neurons in laminae A and A1; class 4 cells in the C‐laminae. Three subtypes of class 4 neurons were differentiated: round cells, spindle cells, and fusiform cells. The round subtype is similar in dendritic morphology to the class 3 neurons, but its soma is larger (mean soma diameter 17 μm compared with 13 μm). Other types of neurons were identified in the laminae A, A1, and C, having morphological characteristics intermediate between class 1 and class 2, and between class 2 and class 3.Class 1 neurons, class 2 neurons, and flat neurons were identified in the medial interlaminar nucleus (MIN). The flat type is similar in morphology to the fusiform type in the C‐laminae; however, its soma is larger (mean soma diameter 23 μm compared with 19 μm), and its dendrites are free of appendages.In the extrageniculate nuclei three types of neurons were found: class 2 neurons in the pulvinar, medium‐sized cells—probably class 5—in the pulvinar and in the nucleus lateralis posterior, and neurons with an isodendritic branching pattern in the intralaminar nuclei.The cortical projections of the various thalamic cell classes were analyzed by injection of HRP into acallosal parts, or callosal parts of area 17 or area 18. Area 17 receives input from a large number of class 2 neurons and from a moderate number of class 1 neurons in the LGBd. In contrast, area 18 receives a dominant input from class 1 neurons and only weak input from class 2 neurons (up to 10% of the population of projection cells in the individual cases).Class 3 neurons in the A‐laminae and class 4 neurons in the C‐laminae project to either cortical area. Class 2 neurons in MIN project only to callosal parts of area 18, whereas class 2 neurons in pulvinar project in addition to acallosal parts of area 18. The significant change in the relative number of class 1 and class 2 neurons in the LGBd occurs gradually across the callosal zone from area 17 to area 18; it is not strictly related to the 17/18 border as defined by cytoarchitectonic or physiological criteria. The class 1/class 2 relation in the projection to area 18 is independent of eccentricity in the A‐laminae. An increase in the frequency of occurrence with eccentricity is noted, however, for class 4 neurons in the C‐laminae and for flat neurons in MIN. The correlation between neuronal function and morphology is discussed. It is concluded that, in addition to strong input with y‐characteristics, area 18 receives significant inputs with non‐y properties. latter inputs arise mainly from the laminae of the LGBd and from extra‐geniculate nuclei, but also may be seen to originate from MIN and the A‐laminae of the LGBd.

Question classification is an important phase in question answering systems. In this paper, we propose to apply i) hierarchical classifiers, ii) hierarchical classifiers in combination with semi-supervised learning and iii) hierarchy expansion for question classification for improving the precision. When the number of classes is large, the performance of classification algorithms may be affected. In order to improve the performance by reducing the number of classes for each classifier, we propose to use hierarchical classifiers according to the question taxonomy, in which each internal node is attached a classifier. We try to use semi-supervised learning to consume unlabeled questions with expectation to improve the performance of classifiers in the hierarchy. We explored different applications of learning methods in for each classifier of the hierarchy: a) supervised learning for all classifiers at all levels; b) semi-supervised learning for the first-level classifier and supervised learning for other classifiers; c) semi-supervised learning for all classifiers. The experiments show that the first method (a) has better results than those of flat classification; the second method (b) produces better results than those of the first method while the effort to increase the performance of fine classifiers in the last method (c) is not so successful. As another effort, we propose to automatically group question classes by clustering in order to expand a node which has a large number of classes in the question taxonomy. The experiment also shows that the overall precision is improved.

Evaluating the effects of similar-class combination on class integration test order generation

We describe the design and use of linear hyperplanes to partition the feature space of a classifier. The objective of the partitioning is to minimize the average entropy of the class distribution in the final partitions. The hyperplanes are characterized by a vector /spl nu//sub n/ and scalar h/sub n/, which are computed with the objective of maximizing the mutual information associated with the partitioning. We show that the problem of designing the /spl nu//sub n/ can be simplified to an approximately equivalent problem, the solution of which, interestingly enough, turns out to be the linear discriminant of the data. We also describe a decision-tree based technique that partitions the feature space in a hierarchical fashion where each node in the decision tree represents a linear hyperplane that further partitions the feature space into two regions. The end result of the tree-growing process is that the entire feature space is partitioned into nonoverlapping regions where each region is bounded by a number of hyperplanes. As the criterion for the design of the hyperplanes is the minimization of the average class entropy of the regions, each region is characterized by the occurrence of only a small number of classes. The partitioning information provided by the decision-tree can then be used to eliminate a number of classes from being considered, and hence simplifies the job of the classifier. We show the application of the decision-tree as a preprocessor to a classifier in the speech recognition problem. Here the classes are modeled with mixtures of tens to hundreds of thousands of Gaussians, and the use of the partitioning information reduces the computation associated with the classification process by factors larger than 20 with negligible degradation in the word error rate (note, however, that the overall decoding process comprises other steps in addition to the classification-the computational speedup mentioned above does not affect the computation of these other steps). We also compare the performance of this quantization scheme with standard Gaussian clustering schemes and show that the decision-tree based quantization provides better performance in most cases.

Ternary quadratic forms over number fields with small class number

Classification is one of the widely used techniques to quantify and mine the rich information present in hyperspectral imagery. However, the realization of trustworthy classification still continues to be a challenging task. This is due to the presence of various uncertainties, such as incomplete a priori knowledge on the actual number of classes and noise. Especially, mismatching between the number of spectral classes and the number of information classes leads to substantial omission or commission errors in the classification. In this letter, we present a new multiclass classification framework, named supervised cascaded classifier system (SC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S), that addresses the abovementioned problem by providing reliable results. The SC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S method is a two-stage cascaded classification procedure that involves quantifying the uncertainty and then classifying the samples. In the first stage, pixels for which no reliable training samples can be found in the training stage are detected. In the second stage, pixels that are matched with the respective training distribution are classified using a supervised learning algorithm, otherwise labeled as unknown. The proposed SC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S framework has been implemented on eight different classification scenarios with a varying number of unknown classes (UCs) using hyperspectral and multispectral imageries. The performance of the proposed SC <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S method is compared with other widely used classifiers with and without reject-option. The experimental results indicate that our method offers superior classification results even in the case of data sets with a large number of unknown spectral classes.