There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Part I. Experimental Studies: 2. Experiment in psychology 3. Experiments on perceiving III Experiments on imaging 4-8. Experiments on remembering: (a) The method of description (b) The method of repeated reproduction (c) The method of picture writing (d) The method of serial reproduction (e) The method of serial reproduction picture material 9. Perceiving, recognizing, remembering 10. A theory of remembering 11. Images and their functions 12. Meaning Part II. Remembering as a Study in Social Psychology: 13. Social psychology 14. Social psychology and the matter of recall 15. Social psychology and the manner of recall 16. Conventionalism 17. The notion of a collective unconscious 18. The basis of social recall 19. A summary and some conclusions.

Remembering. A Study in Experimental and Social Psychology, Cambridge (University Press) 1964.

This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse' framework that we call cluster ensembles. The cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information. In addition to a direct maximization approach, we propose three effective and efficient techniques for obtaining high-quality combiners (consensus functions). The first combiner induces a similarity measure from the partitionings and then reclusters the objects. The second combiner is based on hypergraph partitioning. The third one collapses groups of clusters into meta-clusters which then compete for each object to determine the combined clustering. Due to the low computational costs of our techniques, it is quite feasible to use a supra-consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation. We evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios: (i) where the original clusters were formed based on non-identical sets of features, (ii) where the original clustering algorithms worked on non-identical sets of objects, and (iii) where a common data-set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution. Promising results are obtained in all three situations for synthetic as well as real data-sets.

/pdf/cluster-ensembles-a-knowledge-reuse-framework-for-combining-3qjcysq4q0.pdf

Cluster ensembles --- a knowledge reuse framework for combining multiple partitions

Kraken is an ultrafast and highly accurate program for assigning taxonomic labels to metagenomic DNA sequences. Previous programs designed for this task have been relatively slow and computationally expensive, forcing researchers to use faster abundance estimation programs, which only classify small subsets of metagenomic data. Using exact alignment of k-mers, Kraken achieves classification accuracy comparable to the fastest BLAST program. In its fastest mode, Kraken classifies 100 base pair reads at a rate of over 4.1 million reads per minute, 909 times faster than Megablast and 11 times faster than the abundance estimation program MetaPhlAn. Kraken is available at http://ccb.jhu.edu/software/kraken/.

/pdf/kraken-ultrafast-metagenomic-sequence-classification-using-uhl9fkaqpz.pdf

Kraken: ultrafast metagenomic sequence classification using exact alignments

In matters of great importance that have financial, medical, social, or other implications, we often seek a second opinion before making a decision, sometimes a third, and sometimes many more. In doing so, we weigh the individual opinions, and combine them through some thought process to reach a final decision that is presumably the most informed one. The process of consulting "several experts" before making a final decision is perhaps second nature to us; yet, the extensive benefits of such a process in automated decision making applications have only recently been discovered by computational intelligence community. Also known under various other names, such as multiple classifier systems, committee of classifiers, or mixture of experts, ensemble based systems have shown to produce favorable results compared to those of single-expert systems for a broad range of applications and under a variety of scenarios. Design, implementation and application of such systems are the main topics of this article. Specifically, this paper reviews conditions under which ensemble based systems may be more beneficial than their single classifier counterparts, algorithms for generating individual components of the ensemble systems, and various procedures through which the individual classifiers can be combined. We discuss popular ensemble based algorithms, such as bagging, boosting, AdaBoost, stacked generalization, and hierarchical mixture of experts; as well as commonly used combination rules, including algebraic combination of outputs, voting based techniques, behavior knowledge space, and decision templates. Finally, we look at current and future research directions for novel applications of ensemble systems. Such applications include incremental learning, data fusion, feature selection, learning with missing features, confidence estimation, and error correcting output codes; all areas in which ensemble systems have shown great promise

Ensemble based systems in decision making

Future Directions -- Semi-supervised Multiple Classifier Systems: Background and Research Directions -- Boosting -- Boosting GMM and Its Two Applications -- Boosting Soft-Margin SVM with Feature Selection for Pedestrian Detection -- Observations on Boosting Feature Selection -- Boosting Multiple Classifiers Constructed by Hybrid Discriminant Analysis -- Combination Methods -- Decoding Rules for Error Correcting Output Code Ensembles -- A Probability Model for Combining Ranks -- EER of Fixed and Trainable Fusion Classifiers: A Theoretical Study with Application to Biometric Authentication Tasks -- Mixture of Gaussian Processes for Combining Multiple Modalities -- Dynamic Classifier Integration Method -- Recursive ECOC for Microarray Data Classification -- Using Dempster-Shafer Theory in MCF Systems to Reject Samples -- Multiple Classifier Fusion Performance in Networked Stochastic Vector Quantisers -- On Deriving the Second-Stage Training Set for Trainable Combiners -- Using Independence Assumption to Improve Multimodal Biometric Fusion -- Design Methods -- Half-Against-Half Multi-class Support Vector Machines -- Combining Feature Subsets in Feature Selection -- ACE: Adaptive Classifiers-Ensemble System for Concept-Drifting Environments -- Using Decision Tree Models and Diversity Measures in the Selection of Ensemble Classification Models -- Ensembles of Classifiers from Spatially Disjoint Data -- Optimising Two-Stage Recognition Systems -- Design of Multiple Classifier Systems for Time Series Data -- Ensemble Learning with Biased Classifiers: The Triskel Algorithm -- Cluster-Based Cumulative Ensembles -- Ensemble of SVMs for Incremental Learning -- Performance Analysis -- Design of a New Classifier Simulator -- Evaluation of Diversity Measures for Binary Classifier Ensembles -- Which Is the Best Multiclass SVM Method? An Empirical Study -- Over-Fitting in Ensembles of Neural Network Classifiers Within ECOC Frameworks -- Between Two Extremes: Examining Decompositions of the Ensemble Objective Function -- Data Partitioning Evaluation Measures for Classifier Ensembles -- Dynamics of Variance Reduction in Bagging and Other Techniques Based on Randomisation -- Ensemble Confidence Estimates Posterior Probability -- Applications -- Using Domain Knowledge in the Random Subspace Method: Application to the Classification of Biomedical Spectra -- An Abnormal ECG Beat Detection Approach for Long-Term Monitoring of Heart Patients Based on Hybrid Kernel Machine Ensemble -- Speaker Verification Using Adapted User-Dependent Multilevel Fusion -- Multi-modal Person Recognition for Vehicular Applications -- Using an Ensemble of Classifiers to Audit a Production Classifier -- Analysis and Modelling of Diversity Contribution to Ensemble-Based Texture Recognition Performance -- Combining Audio-Based and Video-Based Shot Classification Systems for News Videos Segmentation -- Designing Multiple Classifier Systems for Face Recognition -- Exploiting Class Hierarchies for Knowledge Transfer in Hyperspectral Data.

Multiple Classifier Systems

We introduce Learn++, an algorithm for incremental training of neural network (NN) pattern classifiers. The proposed algorithm enables supervised NN paradigms, such as the multilayer perceptron (MLP), to accommodate new data, including examples that correspond to previously unseen classes. Furthermore, the algorithm does not require access to previously used data during subsequent incremental learning sessions, yet at the same time, it does not forget previously acquired knowledge. Learn++ utilizes ensemble of classifiers by generating multiple hypotheses using training data sampled according to carefully tailored distributions. The outputs of the resulting classifiers are combined using a weighted majority voting procedure. We present simulation results on several benchmark datasets as well as a real-world classification task. Initial results indicate that the proposed algorithm works rather well in practice. A theoretical upper bound on the error of the classifiers constructed by Learn++ is also provided.

/pdf/learn-an-incremental-learning-algorithm-for-supervised-3mjnxl7p3a.pdf

Learn++: an incremental learning algorithm for supervised neural networks

We introduce an ensemble of classifiers-based approach for incremental learning of concept drift, characterized by nonstationary environments (NSEs), where the underlying data distributions change over time. The proposed algorithm, named Learn++.NSE, learns from consecutive batches of data without making any assumptions on the nature or rate of drift; it can learn from such environments that experience constant or variable rate of drift, addition or deletion of concept classes, as well as cyclical drift. The algorithm learns incrementally, as other members of the Learn++ family of algorithms, that is, without requiring access to previously seen data. Learn++.NSE trains one new classifier for each batch of data it receives, and combines these classifiers using a dynamically weighted majority voting. The novelty of the approach is in determining the voting weights, based on each classifier's time-adjusted accuracy on current and past environments. This approach allows the algorithm to recognize, and act accordingly, to the changes in underlying data distributions, as well as to a possible reoccurrence of an earlier distribution. We evaluate the algorithm on several synthetic datasets designed to simulate a variety of nonstationary environments, as well as a real-world weather prediction dataset. Comparisons with several other approaches are also included. Results indicate that Learn++.NSE can track the changing environments very closely, regardless of the type of concept drift. To allow future use, comparison and benchmarking by interested researchers, we also release our data used in this paper.

/pdf/incremental-learning-of-concept-drift-in-nonstationary-39gk79d4v5.pdf

Incremental Learning of Concept Drift in Nonstationary Environments

The prevalence of mobile phones, the internet-of-things technology, and networks of sensors has led to an enormous and ever increasing amount of data that are now more commonly available in a streaming fashion [1]-[5]. Often, it is assumed - either implicitly or explicitly - that the process generating such a stream of data is stationary, that is, the data are drawn from a fixed, albeit unknown probability distribution. In many real-world scenarios, however, such an assumption is simply not true, and the underlying process generating the data stream is characterized by an intrinsic nonstationary (or evolving or drifting) phenomenon. The nonstationarity can be due, for example, to seasonality or periodicity effects, changes in the users' habits or preferences, hardware or software faults affecting a cyber-physical system, thermal drifts or aging effects in sensors. In such nonstationary environments, where the probabilistic properties of the data change over time, a non-adaptive model trained under the false stationarity assumption is bound to become obsolete in time, and perform sub-optimally at best, or fail catastrophically at worst.

/pdf/learning-in-nonstationary-environments-a-survey-4qv18ybr8l.pdf

Robi Polikar

Papers

Ensemble based systems in decision making

Multiple Classifier Systems

Learn++: an incremental learning algorithm for supervised neural networks

Incremental Learning of Concept Drift in Nonstationary Environments

Learning in Nonstationary Environments: A Survey