From visual data exploration to visual data mining: a survey <s> BASIC CONCEPTS AND TERMINOLOGY <s> A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in k-d space, using k feature-extraction functions, provided by a domain expert [25]. Thus, we can subsequently use highly fine-tuned spatial access methods (SAMs), to answer several types of queries, including the 'Query By Example' type (which translates to a range query); the 'all pairs' query (which translates to a spatial join [8]); the nearest-neighbor or best-match query, etc.However, designing feature extraction functions can be hard. It is relatively easier for a domain expert to assess the similarity/distance of two objects. Given only the distance information though, it is not obvious how to map objects into points.This is exactly the topic of this paper. We describe a fast algorithm to map objects into points in some k-dimensional space (k is user-defined), such that the dis-similarities are preserved. There are two benefits from this mapping: (a) efficient retrieval, in conjunction with a SAM, as discussed before and (b) visualization and data-mining: the objects can now be plotted as points in 2-d or 3-d space, revealing potential clusters, correlations among attributes and other regularities that data-mining is looking for.We introduce an older method from pattern recognition, namely, Multi-Dimensional Scaling (MDS) [51]; although unsuitable for indexing, we use it as yardstick for our method. Then, we propose a much faster algorithm to solve the problem in hand, while in addition it allows for indexing. Experiments on real and synthetic data indeed show that the proposed algorithm is significantly faster than MDS, (being linear, as opposed to quadratic, on the database size N), while it manages to preserve distances and the overall structure of the data-set. <s> BIB001 </s> From visual data exploration to visual data mining: a survey <s> BASIC CONCEPTS AND TERMINOLOGY <s> Presents the state of the art in scientific visualization both as an overview for the scientist and as a basic foundation for developers. Topics are: scientific visualization; frameworks and methodologies; and techniques and algorithms. <s> BIB002 </s> From visual data exploration to visual data mining: a survey <s> BASIC CONCEPTS AND TERMINOLOGY <s> A programmable DC power supply including a proportionally controlled transistor connected in series with the load for varying the load current in accordance with the magnitude of a control signal applied to the transistor. A detector coupled across the transistor functions to sense high and low voltage thresholds and thereupon select an incrementally higher or lower voltage for application to the load to assure that the transistor operates continuously in its proportional range, thereby enabling the input signal to maintain control of the load current. <s> BIB003 </s> From visual data exploration to visual data mining: a survey <s> BASIC CONCEPTS AND TERMINOLOGY <s> Knowledge discovery in databases is a rapidly growing field, whose development is driven by strong research interests as well as urgent practical, social, and economical needs. While the last few years knowledge discovery tools have been used mainly in research environments, sophisticated software products are now rapidly emerging. In this paper, we provide an overview of common knowledge discovery tasks and approaches to solve these tasks. We propose a feature classification scheme that can be used to study knowledge and data mining software. This scheme is based on the software's general characteristics, database connectivity, and data mining characteristics. We then apply our feature classification scheme to investigate 43 software products, which are either research prototypes or commercially available. Finally, we specify features that we consider important for knowledge discovery software to possess in order to accommodate its users effectively, as well as issues that are either not addressed or insufficiently solved yet. <s> BIB004
Both scientific visualization and information visualization create graphical models and visual representations from data that support direct user interaction for exploring and acquiring insight into useful information embedded in the underlying data. In scientific visualization, the graphical models are typically constructed from measured or simulated data representing objects or concepts associated with phenomena from the physical world. As such, the data and, hence, its derived visual representations represent objects that exist in a 1D (one-dimensional), 2D, or 3D object space. Eventually, data will also include a temporal dimension and the presence of spatial and temporal dimensions is a determinant factor in deriving visual representations from the data. In information visualization, the graphical models may represent abstract concepts and relationships that do not necessarily have a counterpart in the physical world, e.g., information describing user accesses to pages of an Internet portal or records describing selected properties of different car brands and models. Typically, each data unity describes multiple related attributes (usually more than four) that are not of a spatial or temporal nature. Although spatial and temporal attributes may occur, the data exists in an abstract (conceptual) data space. Raw data come in many formats and, to map a data set into visual formats, it is convenient to transform it into a structured relation or a set of relations (tuples). Card et al. BIB003 define the Table Data Model: A Data Table is a structured data format organized as rows and columns that express relations, in addition to metadata, i.e., descriptive information about such relations, such as the labels for rows and columns. In their arrangement, the rows represent variables (covering the range of values in the tuples) and the columns represent cases (the data records with sets of values for each variable). The opposite arrangement is more common, with the columns representing the data variables and the rows denoting the data records. The ordering of rows and columns in the Data Table may or may not be relevant and this very general definition rules out structured or hierarchical data. Hoffman  uses the term " Table Visualizations" to denote visualizations of data sets expressed as Data Tables. Strictly speaking, the term "dimensions" should be used to refer to the independent variables represented in the tuples, whereas "variates" refer to the dependent variables (see Wong and Bergeron BIB002 for a good discussion on terminology). Usually, in a DM or visual exploration task, one does not know in advance which are the dependent/ independent variables and it is common to refer to data variables generally as data "dimensions" or "attributes," the latter being more common in the DM literature. In this paper, we use the terms "data item" to denote a tuple describing a relationship among multiple variables (i.e., a case, or data record) and "attribute," rather than dimension, to denote the variables (either dependent or independent). "Attribute value" refers to the information content associated with a particular attribute of a particular data item and "attribute range" refers to the range of values assumed by a particular attribute in a data set. An n-dimensional visualization is one capable of visually depicting n attributes of a table data set. It is not always precisely clear what characterizes a "high-dimensional" data set. The conceptual boundary between low and high-dimensional data is around three to four data attributes. For a lot of people, moving beyond 3D or 4D makes the set significantly more complex. Certainly, most people are overwhelmed by 5D. Again, as general guidelines for characterizing dimensionality one could probably use "low" for up to four, "medium" for five to nine, "high" for 10 or more, although this is an arbitrary choice. It is more important to observe the significant differences in human perceptual capabilities between low (no more than 4D) and higher. For most human beings, there is no real difference between dealing with 5D and 50D data sets: Both are beyond their ability to comprehend, as geometric projections in more than 4D are ineffective to convey information to them. Similarly, the terms "large," "very large," and "massive" are used to qualify data sets in a somewhat loose manner, as the concept of large varies with the increase in computer power. As general guidelines, we can currently think of a "large" data set as one containing over 100,000 data items, whereas a data set with more than 1,000,000 is definitely more than just "large" and one with hundreds of millions items can easily be classified as "massive." As DM is usually targeted at massive data sets, interaction between both fields has made clear the need of interactive visualization techniques better equipped for handling such large data sets. Most visual techniques discussed in Section 3 map each data item into a corresponding graphical element, which may be a pixel, a line, an icon, or other graphical marker. The implication is that they do not scale well when handling millions of data items, which is just one of the reasons for the lack in the capability of current visual data exploration tools in handling databases of such an order of magnitude. DM methods have different goals and several methods may have to be applied successively to achieve a desired result. Most DM tasks, targeted at either insight or prediction, fall into one of the following categories BIB004 : data processing, prediction, regression, classification, clustering, identifying meaningful associations between data attributes, model visualization, and exploratory data analysis. Data processing is generally required as a starting point of a KDD/DM/Data Exploration project as analysts may have to select, filter, aggregate, sample, clean, and/or transform data. Dimension reduction may be necessary to produce a k-dimensional data set from a given n-dimensional one, where usually n is very large and k should be much smaller than n. Some common techniques are Principal Component Analysis  , Factor Analysis  , Multidimensional Scaling  , and FastMap BIB001 . Subsetting techniques may use sampling to determine a representative subset of the original data set or querying to assist in determining an a priori fixed subset of the data for further processing. Segmentation techniques produce multiple subsets of data items based upon attribute values or attribute ranges of the original data, whereas aggregation techniques produce a set of aggregate values based upon, e.g., attribute values and topological properties of the original data. Model Visualization and Exploratory Data Analysis (EDA) are the DM tasks in which visualization has played a major role up to now. Model visualization is the process of using visual techniques to make the discovered knowledge understandable and interpretable by humans. Techniques range from simple scatter plots and histograms to sophisticated multidimensional visualizations and animations. EDA is the interactive exploration of (usually) graphical representations of a data set without heavy dependence on preconceived assumptions and models, thus attempting to identify interesting and previously unknown patterns. Visual Data Exploration techniques are designed to take advantage of the powerful visual capabilities of human beings and can support users in formulating hypotheses about the data that may be useful in further stages of the mining process. Different visualization techniques can also support DM tasks of cluster and outlier detection, important feature detection, classification, and rule or pattern detection. A key distinction is that visual data exploration is a completely human guided process, whereas DM algorithms can automatically analyze a data set searching for useful information and statistically valid patterns. The degree of automation of DM algorithms actually varies considerably as different levels of human guidance and interaction are usually required, but still the algorithm, not the user, is the one that is to look for patterns.