Class visualization of high-dimensional data with applications

Summarizing Finite Mixture Model with Overlapping Quantification

Finite mixture models are widely used for modeling and clustering data. When they are used for clustering, they are often interpreted by regarding each component as one cluster. However, this assumption may be invalid when the components overlap. It leads to the issue of analyzing such overlaps to correctly understand the models. The primary purpose of this paper is to establish a theoretical framework for interpreting the overlapping mixture models by estimating how they overlap, using measures of information such as entropy and mutual information. This is achieved by merging components to regard multiple components as one cluster and summarizing the merging results. First, we propose three conditions that any merging criterion should satisfy. Then, we investigate whether several existing merging criteria satisfy the conditions and modify them to fulfill more conditions. Second, we propose a novel concept named clustering summarization to evaluate the merging results. In it, we can quantify how overlapped and biased the clusters are, using mutual information-based criteria. Using artificial and real datasets, we empirically demonstrate that our methods of modifying criteria and summarizing results are effective for understanding the cluster structures. We therefore give a new view of interpretability/explainability for model-based clustering.

Explainers: expert explorations with crafted projections

This paper introduces an approach to exploration and discovery in high-dimensional data that incorporates a user's knowledge and questions to craft sets of projection functions meaningful to them. Unlike most prior work that defines projections based on their statistical properties, our approach creates projection functions that align with user-specified annotations. Therefore, the resulting derived dimensions represent concepts defined by the user's examples. These especially crafted projection functions, or explainers, can help find and explain relationships between the data variables and user-designated concepts. They can organize the data according to these concepts. Sets of explainers can provide multiple perspectives on the data. Our approach considers tradeoffs in choosing these projection functions, including their simplicity, expressive power, alignment with prior knowledge, and diversity. We provide techniques for creating collections of explainers. The methods, based on machine learning optimization frameworks, allow exploring the tradeoffs. We demonstrate our approach on model problems and applications in text analysis.

Perception of average value in multiclass scatterplots

The visual system can make highly efficient aggregate judgements about a set of objects, with speed roughly independent of the number of objects considered. While there is a rich literature on these mechanisms and their ramifications for visual summarization tasks, this prior work rarely considers more complex tasks requiring multiple judgements over long periods of time, and has not considered certain critical aggregation types, such as the localization of the mean value of a set of points. In this paper, we explore these questions using a common visualization task as a case study: relative mean value judgements within multi-class scatterplots. We describe how the perception literature provides a set of expected constraints on the task, and evaluate these predictions with a large-scale perceptual study with crowd-sourced participants. Judgements are no harder when each set contains more points, redundant and conflicting encodings, as well as additional sets, do not strongly affect performance, and judgements are harder when using less salient encodings. These results have concrete ramifications for the design of scatterplots.

Graph embedding to improve supervised classification and novel class detection: application to prostate cancer

Recently there has been a great deal of interest in algorithms for constructing low-dimensional feature-space embeddings of high dimensional data sets in order to visualize inter- and intra-class relationships. In this paper we present a novel application of graph embedding in improving the accuracy of supervised classification schemes, especially in cases where object class labels cannot be reliably ascertained. By refining the initial training set of class labels we seek to improve the prior class distributions and thus classification accuracy. We also present a novel way of visualizing the class embeddings which makes it easy to appreciate inter-class relationships and to infer the presence of new classes which were not part of the original classification. We demonstrate the utility of the method in detecting prostatic adenocarcinoma from high-resolution MRI.