Adaptive constrained clustering with application to dynamic image database categorization and visualization.

The advent of larger storage spaces, affordable digital capturing devices, and an ever growing online community dedicated to sharing images has created a great need for efficient analysis methods. In fact, analyzing images for the purpose of automatic categorization and retrieval is quickly becoming an overwhelming task even for the casual user. Initially, systems designed for these applications relied on contextual information associated with images. However, it was realized that this approach does not scale to very large data sets and can be subjective. Then researchers proposed methods relying on the content of the images. This approach has also proved to be limited due to the semantic gap between the low-level representation of the image and the high-level user perception. In this dissertation, we introduce a novel clustering technique that is designed to combine multiple forms of information in order to overcome the disadvantages observed while using a single information domain. Our proposed approach, called Adaptive Constrained Clustering (ACC), is a robust, dynamic, and semi-supervised algorithm. It is based on minimizing a single objective function incorporating the abilities to: (i) use multiple feature subsets while learning cluster independent feature relevance weights; (ii) search for the optimal number of clusters; and (iii) incorporate partial supervision in the form of pairwise constraints. The content of the images is used to extract the features used in the clustering process. The context information is used in constructing a set of appropriate constraints. These constraints are used as partial supervision information to guide the clustering process. The ACC algorithm is dynamic in the sense that the number of categories are allowed to expand and contract depending on the distribution of the data and the available set of constraints. We show that the proposed ACC algorithm is able to partition a given data set into meaningful clusters using an adaptive, soft constraint satisfaction methodology for the purpose of automatically categorizing and summarizing an image database. We show that the ACC algorithm has the ability to incorporate various types of contextual information. This contextual information includes: spatial information provided by geo-referenced images that include GPS coordinates pinpointing their location, temporal information provided by each image\u27s time stamp indicating the capture time, and textual information provided by a set of keywords describing the semantics of the associated images

Unsupervised and semi-supervised fuzzy clustering with multiple kernels.

For real-world clustering tasks, the input data is typically not easily separable due to the highly complex data structure or when clusters vary in size, density and shape. Recently, kernel-based clustering has been proposed to perform clustering in a higher-dimensional feature space spanned by embedding maps and corresponding kernel functions. Although good results were obtained using the Gaussian kernel function, its performance depends on the selection of the scaling parameter among an extensive range of possibilities. This step is often heavily influenced by prior knowledge about the data and by the patterns we expect to discover. Unfortunately, it is often unclear which kernels are more suitable for a particular task. The problem is aggravated for many real-world clustering applications, in which the distributions of the different clusters in the feature space exhibit large variations. Thus, in the absence of a priori knowledge, a single kernel selected from a predefined group is sometimes insufficient to represent the data. One way to learn optimal scaling parameters is through an exhaustive search of one optimal scaling parameter for each cluster. However, this approach is not practical since it is computationally expensive, especially when the data includes a large number of clusters and when the dynamic range of possible values of the scaling parameters is large. Moreover, the evaluation of the resulting partition in order to select the optimal parameters is not an easy task. To overcome the above drawbacks, we introduce two novel fuzzy clustering techniques that use Multiple Kernel Learning to provide an elegant solution for parameter selection. The Fuzzy C-Means with Multiple Kernels algorithm (FCMK) simultaneously finds the optimal partition and the cluster-dependent kernel combination weights that reflect the intrinsic structure of the data. The Relational Fuzzy Clustering with Multiple Kernels (RFCMK) learns the kernel combination weights by optimizing the relational dissimilarities. Consequently, the learned kernel combination weights reflect the relative density, size, and position of each cluster with respect to the other clusters. We also extended FCMK and RFCMK to the semi-supervised paradigms. We show that the incorporation of prior knowledge in the unsupervised clustering task in the form of a small set of constraints on which instances should or should not reside in the same cluster, guides the unsupervised approaches to a better partitioning of the data and avoid local minima, especially for high dimensional real world data. All of the proposed algorithms are optimized iteratively by dynamically updating the partition and the kernel combination weights in each iteration. This makes these algorithms simple and fast. Moreover, our algorithms are formulated to work on both vector and relational data. This makes them applicable to data where objects cannot be represented by vectors or when clusters of similar objects cannot be represented efficiently by a single prototype. We also introduced two relational fuzzy clustering with multiple kernel algorithms for large data to deal with the scalability issue of RFCMK. The random sample and extend RFCMK (rseRFCMK) computes cluster prototypes from a smaller sample of randomly selected objects, and then extends the partition to the remainder of the data. The single pass RFCMK (spRFCMK) sequentially loads manageable sized chunks, clustering the chunks in a single pass, and then combining the results from each chunk. Our extensive experiments show that RFCMK and SS-RFCMK outperform existing algorithms. In particular, we show that when data include clusters with various intrinsic structures and densities, learning kernel weights that vary over clusters is crucial in obtaining a good partition

Unsupervised and semi-supervised clustering with learnable cluster dependent kernels.

Despite the large number of existing clustering methods, clustering remains a challenging task especially when the structure of the data does not correspond to easily separable categories, and when clusters vary in size, density and shape. Existing kernel based approaches allow to adapt a specific similarity measure in order to make the problem easier. Although good results were obtained using the Gaussian kernel function, its performance depends on the selection of the scaling parameter. Moreover, since one global parameter is used for the entire data set, it may not be possible to find one optimal scaling parameter when there are large variations between the distributions of the different clusters in the feature space. One way to learn optimal scaling parameters is through an exhaustive search of one optimal scaling parameter for each cluster. However, this approach is not practical since it is computationally expensive especially when the data includes a large number of clusters and when the dynamic range of possible values of the scaling parameters is large. Moreover, it is not trivial to evaluate the resulting partition in order to select the optimal parameters. To overcome this limitation, we introduce two new fuzzy relational clustering techniques that learn cluster dependent Gaussian kernels. The first algorithm called clustering and Local Scale Learning algorithm (LSL) minimizes one objective function for both the optimal partition and for cluster dependent scaling parameters that reflect the intra-cluster characteristics of the data. The second algorithm, called Fuzzy clustering with Learnable Cluster dependent Kernels (FLeCK) learns the scaling parameters by optimizing both the intra-cluster and the inter-cluster dissimilarities. Consequently, the learned scale parameters reflect the relative density, size, and position of each cluster with respect to the other clusters. We also introduce semi-supervised versions of LSL and FLeCK. These algorithms generate a fuzzy partition of the data and learn the optimal kernel resolution of each cluster simultaneously. We show that the incorporation of a small set of constraints can guide the clustering process to better learn the scaling parameters and the fuzzy memberships in order to obtain a better partition of the data. In particular, we show that the partial supervision is even more useful on real high dimensional data sets where the algorithms are more susceptible to local minima. All of the proposed algorithms are optimized iteratively by dynamically updating the partition and the scaling parameter in each iteration. This makes these algorithms simple and fast. Moreover, our algorithms are formulated to work on relational data. This makes them applicable to data where objects cannot be represented by vectors or when clusters of similar objects cannot be represented efficiently by a single prototype. Our extensive experiments show that FLeCK and SS-FLeCK outperform existing algorithms. In particular, we show that when data include clusters with various inter-cluster and intra-cluster distances, learning cluster dependent kernel is crucial in obtaining a good partition

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Semi-supervised cross-entropy clustering with information bottleneck constraint

In this paper, we propose a semi-supervised clustering method, CEC-IB, that models data with a set of Gaussian distributions and that retrieves clusters based on a partial labeling provided by the user (partition-level side information). By combining the ideas from cross-entropy clustering (CEC) with those from the information bottleneck method (IB), our method trades between three conflicting goals: the accuracy with which the data set is modeled, the simplicity of the model, and the consistency of the clustering with side information. Experiments demonstrate that CEC-IB has a performance comparable to Gaussian mixture models (GMM) in a classical semi-supervised scenario, but is faster, more robust to noisy labels, automatically determines the optimal number of clusters, and performs well when not all classes are present in the side information. Moreover, in contrast to other semi-supervised models, it can be successfully applied in discovering natural subgroups if the partition-level side information is derived from the top levels of a hierarchical clustering

Bridging the semantic gap in content-based image retrieval.

To manage large image databases, Content-Based Image Retrieval (CBIR) emerged as a new research subject. CBIR involves the development of automated methods to use visual features in searching and retrieving. Unfortunately, the performance of most CBIR systems is inherently constrained by the low-level visual features because they cannot adequately express the user\u27s high-level concepts. This is known as the semantic gap problem. This dissertation introduces a new approach to CBIR that attempts to bridge the semantic gap. Our approach includes four components. The first one learns a multi-modal thesaurus that associates low-level visual profiles with high-level keywords. This is accomplished through image segmentation, feature extraction, and clustering of image regions. The second component uses the thesaurus to annotate images in an unsupervised way. This is accomplished through fuzzy membership functions to label new regions based on their proximity to the profiles in the thesaurus. The third component consists of an efficient and effective method for fusing the retrieval results from the multi-modal features. Our method is based on learning and adapting fuzzy membership functions to the distribution of the features\u27 distances and assigning a degree of worthiness to each feature. The fourth component provides the user with the option to perform hybrid querying and query expansion. This allows the enrichment of a visual query with textual data extracted from the automatically labeled images in the database. The four components are integrated into a complete CBIR system that can run in three different and complementary modes. The first mode allows the user to query using an example image. The second mode allows the user to specify positive and/or negative sample regions that should or should not be included in the retrieved images. The third mode uses a Graphical Text Interface to allow the user to browse the database interactively using a combination of low-level features and high-level concepts. The proposed system and ail of its components and modes are implemented and validated using a large data collection for accuracy, performance, and improvement over traditional CBIR techniques