Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the points are not fixed. Other times, dimensional reduction techniques are employed to summarize the whole dataset in one image, but individual dimensions are lost in this view. In this paper, we present a means of augmenting a dimensional reduction plot with isocontours to reintroduce the original dimensions. By applying this to each dimension in the original data, we create multiple views where the points are consistent, which facilitates their comparison. Our approach employs a combination of a novel, graph-based projection technique with a GPU accelerated implementation of moving least squares to interpolate space between the points. We also present evaluations of this approach both with a case study and with a user study.
Self Organizing Maps (SOMs) have also been used to great effect for multidimensional data, where the points are organized in a space filling manner, and can then be colored according to the component planes @cite_31 . However, as with simply coloring the points in a projection based method, the human eye is not precise enough to discern point values on color alone.
@cite_31
2088709281 2165948731 2021175324 1990086701
The self-organizing map SOM is an efficient tool for visualization of multidimensional numerical data. In this paper, an overview and categorization of both old and new methods for the visualization of SOM is presented. The purpose is to give an idea of what kind of information can be acquired from different presentations and how the SOM can best be utilized in exploratory data visualization. Most of the presented methods can also be applied in the more general case of first making a vector quantization e.g. k-means and then a vector projection e.g. Sammon's mapping. Kohonen's self-organizing map (SOM) is a popular neural network architecture for solving problems in the field of explorative data analysis, clustering, and data visualization. One of the major drawbacks of the SOM algorithm is the difficulty for nonexpert users to interpret the information contained in a trained SOM. In this paper, this problem is addressed by introducing an enhanced version of the Clusot algorithm. This algorithm consists of two main steps: 1) the computation of the Clusot surface utilizing the information contained in a trained SOM and 2) the automatic detection of clusters in this surface. In the Clusot surface, clusters present in the underlying SOM are indicated by the local maxima of the surface. For SOMs with 2-D topology, the Clusot surface can, therefore, be considered as a convenient visualization technique. Yet, the presented approach is not restricted to a certain type of 2-D SOM topology and it is also applicable for SOMs having an n-dimensional grid topology. A new self-organizing map (SOM) architecture called the ASSOM (adaptive-subspace SOM) is shown to create sets of translation-invariant filters when randomly displaced or moving input patterns are used as training data. No analytical functional forms for these filters are thereby postulated. Different kinds of filters are formed by the ASSOM when pictures are rotated during learning, or when they are zoomed. The ASSOM can thus act as a learning feature-extraction stage for pattern recognizers, being able to adapt to many sensory environments and to many different transformation groups of patterns. Visual-interactive cluster analysis provides valuable tools for effectively analyzing large and complex data sets. Due to desirable properties and an inherent predisposition for visualization, the Kohonen Feature Map (or self-organizing map, or SOM) algorithm is among the most popular and widely used visual clustering techniques. However, the unsupervised nature of the algorithm may be disadvantageous in certain applications. Depending on initialization and data characteristics, cluster maps (cluster layouts) may emerge that do not comply with user preferences, expectations, or the application context. Considering SOM-based analysis of trajectory data, we propose a comprehensive visual-interactive monitoring and control framework extending the basic SOM algorithm. The framework implements the general Visual Analytics idea to effectively combine automatic data analysis with human expert supervision. It provides simple, yet effective facilities for visually monitoring and interactively controlling the trajectory clustering process at arbitrary levels of detail. The approach allows the user to leverage existing domain knowledge and user preferences, arriving at improved cluster maps. We apply the framework on a trajectory clustering problem, demonstrating its potential in combining both unsupervised (machine) and supervised (human expert) processing, in producing appropriate cluster results.