We propose a new matrix learning scheme to extend relevance learning vector quantization (RLVQ), an efficient prototype-based classification algorithm, towards a general adaptive metric. By introducing a full matrix of relevance factors in the distance measure, correlations between different features and their importance for the classification scheme can be taken into account and automated, general metric adaptation takes place during training. In comparison to the weighted Euclidean metric used in RLVQ and its variations, a full matrix is more powerful to represent the internal structure of the data appropriately. Large margin generalization bounds can be transfered to this case leading to bounds which are independent of the input dimensionality. This also holds for local metrics attached to each prototype which corresponds to piecewise quadratic decision boundaries. The algorithm is tested in comparison to alternative LVQ schemes using an artificial data set, a benchmark multi-class problem from the UCI repository, and a problem from bioinformatics, the recognition of splice sites for C. elegans.

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Recently, incremental and on-line learning gained more attention especially in the context of big data and learning from data streams, conflicting with the traditional assumption of complete data availability. Even though a variety of different methods are available, it often remains unclear which of them is suitable for a specific task and how they perform in comparison to each other. We analyze the key properties of eight popular incremental methods representing different algorithm classes. Thereby, we evaluate them with regards to their on-line classification error as well as to their behavior in the limit. Further, we discuss the often neglected issue of hyperparameter optimization specifically for each method and test how robustly it can be done based on a small set of examples. Our extensive evaluation on data sets with different characteristics gives an overview of the performance with respect to accuracy, convergence speed as well as model complexity, facilitating the choice of the best method for a given application.

Abstract-Data Mining in non-stationary data streams is gaining more attention recently, especially in the context of Internet of Things and Big Data. It is a highly challenging task, since the fundamentally different types of possibly occurring drift undermine classical assumptions such as data independence or stationary distributions. Available algorithms are either struggling with certain forms of drift or require a priori knowledge in terms of a task specific setting. We propose the Self Adjusting Memory (SAM) model for the k Nearest Neighbor (kNN) algorithm since kNN constitutes a proven classifier within the streaming setting. SAM-kNN can deal with heterogeneous concept drift, i.e different drift types and rates, using biologically inspired memory models and their coordination. It can be easily applied in practice since an optimization of the meta parameters is not necessary. The basic idea is to construct dedicated models for the current and former concepts and apply them according to the demands of the given situation. An extensive evaluation on various benchmarks, consisting of artificial streams with known drift characteristics as well as real world datasets is conducted. Thereby, we explicitly add new benchmarks enabling a precise performance evaluation on multiple types of drift. The highly competitive results throughout all experiments underline the robustness of SAM-kNN as well as its capability to handle heterogeneous concept drift.

Novel non-parametric dimensionality reduction techniques such as t-distributed stochastic neighbor embedding (t-SNE) lead to a powerful and flexible visualization of high-dimensional data. One drawback of non-parametric techniques is their lack of an explicit out-of-sample extension. In this contribution, we propose an efficient extension of t-SNE to a parametric framework, kernel t-SNE, which preserves the flexibility of basic t-SNE, but enables explicit out-of-sample extensions. We test the ability of kernel t-SNE in comparison to standard t-SNE for benchmark data sets, in particular addressing the generalization ability of the mapping for novel data. In the context of large data sets, this procedure enables us to train a mapping for a fixed size subset only, mapping all data afterwards in linear time. We demonstrate that this technique yields satisfactory results also for large data sets provided missing information due to the small size of the subset is accounted for by auxiliary information such as class labels, which can be integrated into kernel t-SNE based on the Fisher information.