Interactive Knowledge-Based Kernel PCA

Abstract

Abstract. Data understanding is an iterative process in which domain experts combine their knowledge with the data at hand to explore and confirm hypotheses. One important set of tools for exploring hypotheses about data are visualizations. Often, however, traditional, unsupervised dimensionality reduction algorithms are used for visualization. These tools allow for interaction, i.e., exploring different visualizations, only by means of manipulating some technical parameters of the algorithm. Therefore, instead of being able to intuitively interact with the visualization, domain experts have to learn and argue about these technical parameters. In this paper we propose a knowledge-based kernel PCA approach that allows for intuitive interaction with data visualizations. Each embedding direction is given by a non-convex quadratic optimization problem over an ellipsoid and has a globally optimal solution in the kernel feature space. A solution can be found in polynomial time using the algorithm presented in this paper. To facilitate direct feedback, i.e., updating the whole embedding with a sufficiently high frame-rate during interaction, we reduce the computational complexity further by incremental up-and down-dating. Our empirical evaluation demonstrates the flexibility and utility of this approach.

Informed Machine Learning - A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems

“…Expert Knowledge. Examples of knowledge that fall into this category include knowledge about topics in text documents [149], agent behaviors [144], [153], [154], [155], [156], and data patterns and hierarchies [148], [149], [151], [152], [157]. Knowledge is often provided in form of relevance or preference feedback and humans in the loop are not required to provide an explanation for their decision.…”

“…Algebraic Equations [44] [38], [39], [42], [45] [11], [12], [36], [37], [41], [43] [11], [46] Logic Rules kernel PCA embeddings [152] or to drag similar data points closer in order to learn distance functions [148]. In object recognition, users can provide corrective feedback via brush strokes [147] and for classifying plants as healthy or diseased, correctly identified instances where the interpretation is not in line with human explanations can be altered by a human expert [157].…”

Machine learning provides an accurate prognostication model for refractory overactive bladder treatment response and is noninferior to human experts

“…Unlike many out‐of‐the‐box neural network training approaches (Adam, Stochastic Gradient, l‐BFGS, RMSProp), the novel interpolation technique we employed here is guaranteed to both yield a training error of zero, and result in a network which is optimal under the (pseudo‐Riemannian) metric induced by the resulting reproducing kernel Hilbert (Krein) space 12,13 . Because of this, our method comes with a guarantee of generalization (in an RKHS sense) after a finite number of samples.…”

“…To predict responsivity in patients, a novel reproducing kernel Krein space (RKKS), interpolation technique was employed 12 . Specifically, the softplus function K ( x, y ) = log (1 + e x*y ) was used, generating a RKKS.…”

Relational Similarity Machines

“…Existing work has focused mainly on traditional machine learning problems that are limited to independent and identically distributed (IID) data [15]. In addition, Oglic et al propose interactive kernel PCA [37]. Kapoor et al [19] use a humanassisted optimization strategy in the design of multi-class classifiers for iid data.…”