Algorithms for Multi-Sample Cluster Analysis

In this study, we develop algorithms to solve the Multi-Sample Cluster Analysis (MSCA) problem. This problem arises when we have multiple samples and we need to find the statistical model that best fits the cluster structure of these samples. One important area among others in which our algorithms can be used is international market segmentation. In this area, samples about customers’preferences and characteristics are collected from di¤erent regions in the market. The goal in this case is to join the regions with similar customers’characteristics in clusters (segments). We develop branch and bound algorithms and a genetic algorithm. In these algorithms, any of the available information criteria (AIC, CAIC, SBC, and ICOMP) can be used as the objective function to be optimized. Our algorithms use the Clique Partitioning Problem (CPP) formulation. They are the first algorithms to use information criteria with the CPP formulation. When the branch and bound algorithms are allowed to run to completion, they converge to the optimal MSCA alternative. These methods also proved to find good solutions when they were stopped short of convergence. In particular, we develop a branching strategy which uses a look-ahead technique. We refer to this strategy as the complete adaptive branching strategy. This strategy makes the branch and bound algorithm quickly search for the optimal solution in multiple branches of the enumeration tree before using a depth- first branching strategy. In computational tests, this method’s performance was superior to other branching methods as well as to the genetic algorithm

A Method for Comparing Multivariate Time Series with Different Dimensions

In many situations it is desirable to compare dynamical systems based on their behavior. Similarity of behavior often implies similarity of internal mechanisms or dependency on common extrinsic factors. While there are widely used methods for comparing univariate time series, most dynamical systems are characterized by multivariate time series. Yet, comparison of multivariate time series has been limited to cases where they share a common dimensionality. A semi-metric is a distance function that has the properties of non-negativity, symmetry and reflexivity, but not sub-additivity. Here we develop a semi-metric – SMETS – that can be used for comparing groups of time series that may have different dimensions. To demonstrate its utility, the method is applied to dynamic models of biochemical networks and to portfolios of shares. The former is an example of a case where the dependencies between system variables are known, while in the latter the system is treated (and behaves) as a black box

Grouping Uncertain Oriented Projective Geometric Entities with Application to Automatic Building Reconstruction

The fully automatic reconstruction of 3d scenes from a set of 2d images has always been a key issue in photogrammetry and computer vision and has not been solved satisfactory so far. Most of the current approaches match features between the images based on radiometric cues followed by a reconstruction using the image geometry. The motivation for this work is the conjecture that in the presence of highly redundant data it should be possible to recover the scene structure by grouping together geometric primitives in a bottom-up manner. Oriented projective geometry will be used throughout this work, which allows to represent geometric primitives, such as points, lines and planes in 2d and 3d space as well as projective cameras, together with their uncertainty. The first major contribution of the work is the use of uncertain oriented projective geometry, rather than uncertain projective geometry, that enables the representation of more complex compound entities, such as line segments and polygons in 2d and 3d space as well as 2d edgels and 3d facets. Within the uncertain oriented projective framework a procedure is developed, which allows to test pairwise relations between the various uncertain oriented projective entities. Again, the novelty lies in the possibility to check relations between the novel compound entities. The second major contribution of the work is the development of a data structure, specifically designed to enable performing the tests between large numbers of entities in an efficient manner. Being able to efficiently test relations between the geometric entities, a framework for grouping those entities together is developed. Various different grouping methods are discussed. The third major contribution of this work is the development of a novel grouping method that by analyzing the entropy change incurred by incrementally adding observations into an estimation is able to balance efficiency against robustness in order to achieve better grouping results. Finally the applicability of the proposed representations, tests and grouping methods for the task of purely geometry based building reconstruction from oriented aerial images is demonstrated. It will be shown that in the presence of highly redundant datasets it is possible to achieve reasonable reconstruction results by grouping together geometric primitives.Gruppierung unsicherer orientierter projektiver geometrischer Elemente mit Anwendung in der automatischen Gebäuderekonstruktion Die vollautomatische Rekonstruktion von 3D Szenen aus einer Menge von 2D Bildern war immer ein Hauptanliegen in der Photogrammetrie und Computer Vision und wurde bisher noch nicht zufriedenstellend gelöst. Die meisten aktuellen Ansätze ordnen Merkmale zwischen den Bildern basierend auf radiometrischen Eigenschaften zu. Daran schließt sich dann eine Rekonstruktion auf der Basis der Bildgeometrie an. Die Motivation für diese Arbeit ist die These, dass es möglich sein sollte, die Struktur einer Szene durch Gruppierung geometrischer Primitive zu rekonstruieren, falls die Eingabedaten genügend redundant sind. Orientierte projektive Geometrie wird in dieser Arbeit zur Repräsentation geometrischer Primitive, wie Punkten, Linien und Ebenen in 2D und 3D sowie projektiver Kameras, zusammen mit ihrer Unsicherheit verwendet.Der erste Hauptbeitrag dieser Arbeit ist die Verwendung unsicherer orientierter projektiver Geometrie, anstatt von unsicherer projektiver Geometrie, welche die Repräsentation von komplexeren zusammengesetzten Objekten, wie Liniensegmenten und Polygonen in 2D und 3D sowie 2D Edgels und 3D Facetten, ermöglicht. Innerhalb dieser unsicheren orientierten projektiven Repräsentation wird ein Verfahren zum testen paarweiser Relationen zwischen den verschiedenen unsicheren orientierten projektiven geometrischen Elementen entwickelt. Dabei liegt die Neuheit wieder in der Möglichkeit, Relationen zwischen den neuen zusammengesetzten Elementen zu prüfen. Der zweite Hauptbeitrag dieser Arbeit ist die Entwicklung einer Datenstruktur, welche speziell auf die effiziente Prüfung von solchen Relationen zwischen vielen Elementen ausgelegt ist. Die Möglichkeit zur effizienten Prüfung von Relationen zwischen den geometrischen Elementen erlaubt nun die Entwicklung eines Systems zur Gruppierung dieser Elemente. Verschiedene Gruppierungsmethoden werden vorgestellt. Der dritte Hauptbeitrag dieser Arbeit ist die Entwicklung einer neuen Gruppierungsmethode, die durch die Analyse der änderung der Entropie beim Hinzufügen von Beobachtungen in die Schätzung Effizienz und Robustheit gegeneinander ausbalanciert und dadurch bessere Gruppierungsergebnisse erzielt. Zum Schluss wird die Anwendbarkeit der vorgeschlagenen Repräsentationen, Tests und Gruppierungsmethoden für die ausschließlich geometriebasierte Gebäuderekonstruktion aus orientierten Luftbildern demonstriert. Es wird gezeigt, dass unter der Annahme von hoch redundanten Datensätzen vernünftige Rekonstruktionsergebnisse durch Gruppierung von geometrischen Primitiven erzielbar sind

Organising a photograph collection based on human appearance

This thesis describes a complete framework for organising digital photographs in an unsupervised manner, based on the appearance of people captured in the photographs. Organising a collection of photographs manually, especially providing the identities of people captured in photographs, is a time consuming task. Unsupervised grouping of images containing similar persons makes annotating names easier (as a group of images can be named at once) and enables quick search based on query by example. The full process of unsupervised clustering is discussed in this thesis. Methods for locating facial components are discussed and a technique based on colour image segmentation is proposed and tested. Additionally a method based on the Principal Component Analysis template is tested, too. These provide eye locations required for acquiring a normalised facial image. This image is then preprocessed by a histogram equalisation and feathering, and the features of MPEG-7 face recognition descriptor are extracted. A distance measure proposed in the MPEG-7 standard is used as a similarity measure. Three approaches to grouping that use only face recognition features for clustering are analysed. These are modified k-means, single-link and a method based on a nearest neighbour classifier. The nearest neighbour-based technique is chosen for further experiments with fusing information from several sources. These sources are context-based such as events (party, trip, holidays), the ownership of photographs, and content-based such as information about the colour and texture of the bodies of humans appearing in photographs. Two techniques are proposed for fusing event and ownership (user) information with the face recognition features: a Transferable Belief Model (TBM) and three level clustering. The three level clustering is carried out at “event” level, “user” level and “collection” level. The latter technique proves to be most efficient. For combining body information with the face recognition features, three probabilistic fusion methods are tested. These are the average sum, the generalised product and the maximum rule. Combinations are tested within events and within user collections. This work concludes with a brief discussion on extraction of key images for a representation of each cluster

3DMiner: Discovering Shapes from Large-Scale Unannotated Image Datasets

We present 3DMiner -- a pipeline for mining 3D shapes from challenging large-scale unannotated image datasets. Unlike other unsupervised 3D reconstruction methods, we assume that, within a large-enough dataset, there must exist images of objects with similar shapes but varying backgrounds, textures, and viewpoints. Our approach leverages the recent advances in learning self-supervised image representations to cluster images with geometrically similar shapes and find common image correspondences between them. We then exploit these correspondences to obtain rough camera estimates as initialization for bundle-adjustment. Finally, for every image cluster, we apply a progressive bundle-adjusting reconstruction method to learn a neural occupancy field representing the underlying shape. We show that this procedure is robust to several types of errors introduced in previous steps (e.g., wrong camera poses, images containing dissimilar shapes, etc.), allowing us to obtain shape and pose annotations for images in-the-wild. When using images from Pix3D chairs, our method is capable of producing significantly better results than state-of-the-art unsupervised 3D reconstruction techniques, both quantitatively and qualitatively. Furthermore, we show how 3DMiner can be applied to in-the-wild data by reconstructing shapes present in images from the LAION-5B dataset. Project Page: https://ttchengab.github.io/3dminerOfficialComment: In ICCV 202