## Section: Scientific Foundations

### Data Reduction Techniques

With the explosion of the quantities of data to be analyzed, it is desirable to sacrifice the accuracy of the answers for response time. Particularly in the early, more exploratory, stages of data analysis, interactive response times are critical, while tolerance for approximation errors is quite high. In this context, data reduction is important to control the desired trade-off between answer accuracy and response time.

Data reduction is closely associated with aggregation. While histograms form the baseline approach and have been extensively used for query optimizers, a wealth of techniques have been proposed. In particular, cluster-based reduction of data, where each data item is identified by means of its cluster representative, leads to classical tree indexes, where data is partitioned recursively into buckets. The clusters may be data-driven, or independent from the data. With minimal augmentation, it becomes possible to answer queries approximately based upon an examination of only the top levels of an index tree. If these top levels are cached in memory, as is typically the case, then one can view these top levels of the tree as a reduced form of data suitable for approximate query answering.

To deal with large amounts of data, or high-dimensional data, much work has also been devoted to reducing the dimension of representations, by identifying lower dimension manifolds on which data essentially lies. Single-value decomposition or discrete wavelet transformations are two examples of such transform-based techniques. Among data reduction techniques, one may further distinguish parametric techniques (e.g. linear regression), that assume a model for the data, from non-parametric techniques. While the former offer generally more compression, automatically selecting the form of the model remains a difficult issue.

An important use of data reduction is for retrieval within collections of multimedia material, such as image, audio or video. For the purpose of comparing queries to target documents or for building an index, these documents are represented by features, i.e. multivariate attributes. These features may be used directly (e.g. nearest neighbourhood search among feature vectors, for image matching) or, often, through probabilistic models of their distribution, thereby capturing the variability of a given class. The design of these features requires a specific expertise for each media, to ensure a good trade-off between concision, ability to discriminate and invariance to certain imaging or acoustic conditions. This is typically handled by media-specific research communities.

Nearest neighbour queries are appropriate for multimedia information retrieval. Efficient multimedia feature vectors often span high dimensional spaces, where indexing structures classically used in database management systems (tree-based and hashing-based) are not effective, due to the dimensionality curse. Parallel databases may contribute to maintaining reasonnable query processing time, but require the definition of data distribution strategies. Such strategies are one of the focuses of our work.

Among models, parametric probabilistic models build a very rich, well-founded and well-documented toolbox for representing the data distributions in a concise way, in association to statistical estimation techniques for determining the form of the model and values of its parameters.
Together, they provide a strong share of existing solutions to multimedia data analysis problems (learning and recognition). Relating this to database summaries, seeking simple forms to *describe* the data (structure for efficient retrieval) and forms that *explain* the data (structure for understanding, where parametric forms introduce the necessary inductive biais) are often very close goals, hence a growing number of techniques common to the database and machine learning communities. Among probabilistic models, generative mixture models consider the data to be a combination of several populations, whether this correspond to true variety of natures or whether is a only a modelling tool. Mixtures have wide modelling ability, like non-parametric methods, but retain the parsimony of parametric approaches. Hence, they have been much studied, extended and applied, in the contexts of both supervised and unsupervised learning. In the case of probabilistic models, Bayesian estimation supplies a principled solution to the abovementionned model selection. This long remained either computation-intensive or very approximative, but nowadays, besides increasing computing power available, a corpus of efficient approximate inference mechanisms has been built, for a growing variety of graphical model structures. There remain questions which are receiving growing attention : how can such models be efficiently learned from dynamic distributed data sources ? How can a large set of probabilistic models be indexed ?

Among the broad range of reduction techniques, the database summarization paradigm has become an ubiquitous requirement for a variety of application environments, including corporate data warehouses,network-traffic monitoring and large socio-economic or demographic surveys. Besides, downsizing massive data sets allows to address some critical issues such as individual data obfuscation, optimization of the usage of system resources like storage space and network bandwidth, as well as effective approximate answers to queries. Depending on the application environment and the preferred goal of the approach, we distinguish three families of approaches concerned with database summarization. The first one focuses on aggregate computation and it is supported by statistical databases, OLAP cubes and multdimensional databases.The second class of approaches extends the previous one in that it tries to produce more compact representations of aggregates. The main challenge for such methods is to keep expressiveness of the provided access methods (aggregate queries) to the items without any need to uncompress the structure. Quotient cubes and linguistic summaries are two major contributions in that direction. The third family of approaches deals with intentional characterization of groups of individuals based on usual mining algorithms. Those categories are obviously not sharp and there are many orthogonal criteria that encompass such a classification. For instance, some of them share the same theoretical background (Zadeh's fuzzy set theory) and they use fuzzy partitions and linguistic variables to support a robust summarization process.

This database research field raises new challenges, in particular, to push more semantics into summaries while still remaining efficient in the context of database systems. Update of such metadata is also of major concern. Furthermore, traditional problems of data management such as query evaluation or data integration have to be revisited from the point of view of database summaries.