Kanri Distance (KDC)
Kanri’s proprietary combination of patented statistical and process methods provides a uniquely powerful and insightful ability to evaluate large data sets with multiple variables. While many tools evaluate patterns and dynamics for large data, only the Kanri Distance Calculator allows users to understand where they stand with respect to a desired target state and the specific contribution of each variable toward the overall distance from the target state. The Kanri model not only calculates the relationship of variables within the overall data set, but more importantly mathematically teases out the interaction between each of them. This combination of relational insights fuels Kanri’s breakthrough distance calculator. It answers the question “In a world of exponentially expanding data how do I find the variables that will solve my problem and it helps quickly to reach that conclusion.” But the Kanri model does not stop there. Kanri tells you exactly, formulaically how much each variable contributes. The Kanri Distance Calculator opens a new world of solution development possibilities that can apply the power of massive data sets to an individual…or to an individualized objective. …

Probably Approximately Correct Learning (PAC Learning,WARL)
In computational learning theory, probably approximately correct learning (PAC learning) is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions. The goal is that, with high probability (the “probably” part), the selected function will have low generalization error (the “approximately correct” part). The learner must be able to learn the concept given any arbitrary approximation ratio, probability of success, or distribution of the samples. The model was later extended to treat noise (misclassified samples). An important innovation of the PAC framework is the introduction of computational complexity theory concepts to machine learning. In particular, the learner is expected to find efficient functions (time and space requirements bounded to a polynomial of the example size), and the learner itself must implement an efficient procedure (requiring an example count bounded to a polynomial of the concept size, modified by the approximation and likelihood bounds). …

Local Projections
In this paper, we propose a novel approach for outlier detection, called local projections, which is based on concepts of Local Outlier Factor (LOF) (Breunig et al., 2000) and RobPCA (Hubert et al., 2005). By using aspects of both methods, our algorithm is robust towards noise variables and is capable of performing outlier detection in multi-group situations. We are further not reliant on a specific underlying data distribution. For each observation of a dataset, we identify a local group of dense nearby observations, which we call a core, based on a modification of the k-nearest neighbours algorithm. By projecting the dataset onto the space spanned by those observations, two aspects are revealed. First, we can analyze the distance from an observation to the center of the core within the projection space in order to provide a measure of quality of description of the observation by the projection. Second, we consider the distance of the observation to the projection space in order to assess the suitability of the core for describing the outlyingness of the observation. These novel interpretations lead to a univariate measure of outlyingness based on aggregations over all local projections, which outperforms LOF and RobPCA as well as other popular methods like PCOut (Filzmoser et al., 2008) and subspace-based outlier detection (Kriegel et al., 2009) in our simulation setups. Experiments in the context of real-word applications employing datasets of various dimensionality demonstrate the advantages of local projections. …