Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in data analysis.

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It is proposed in this paper that many geometrical optical illusions, as well as illusory patterns due to motion signals in line drawings, are due to the statistics of visual computations. The interpretation of image patterns is preceded by a step where image features such as lines, intersections of lines, or local image movement must be derived. However, there are many sources of noise or uncertainty in the formation and processing of images, and they cause problems in the estimation of these features; in particular, they cause bias. As a result, the locations of features are perceived erroneously and the appearance of the patterns is altered. The bias occurs with any visual processing of line features; under average conditions it is not large enough to be noticeable, but illusory patterns are such that the bias is highly pronounced. Thus, the broader message of this paper is that there is a general uncertainty principle which governs the workings of vision systems, and optical illusions are an artifact of this principle.

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This paper analyses the uncertainty in the estimation of shape from different cues, specifically motion, stereo, and texture. It is shown that there are computational limitations of a statistical nature that previously have not been recognized. Because there is noise in all the input parameters, we cannot avoid bias. The analysis of shape from multiple views rests on a new constraint which relates image lines and rotation to shape. Because the human visual system has to cope with bias as well, it makes errors. This explains the underestimation of slant found in computational and psychophysical experiments, and demonstrated here for an illusory display. We discuss properties of the best known estimators with regard to the problem, as well as possible avenues for visual systems to deal with the bias. Finally, we show experiments that confirm the theoretical analysis. 1.

Abstract — Recently several papers studied resampling approaches to determine the number of clusters in prototype-based clustering. The core idea underlying these approaches is that with the right choice for the number of clusters basically the same cluster structures should be obtained from subsamples of the given data set, while a wrong choice should produce considerably varying cluster structures. In this paper we investigate whether these approaches can be transferred to fuzzy clustering. It turns out that they are applicable to fuzzy clustering as well, but that not all relative cluster evaluation measures that work for crisp clustering can also be used for fuzzy clustering. I.

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Abstract. Resampling methods are among the best approaches to determine the number of clusters in prototype-based clustering. The core idea is that with the right choice for the number of clusters basically the same cluster structures should be obtained from subsamples of the given data set, while a wrong choice should produce considerably varying cluster structures. In this paper I give a brief overview how such resampling approaches can be transferred to fuzzy and probabilistic clustering. 1

[Submitted draft. See www.cs.helsinki.fi/patrik.hoyer / for latest version and citation info.] Estimation of linear, non-gaussian causal models in the presence of confounding latent variables