Matching and Inference for Multiple Correlated Data Sets

Given multiple correlated data sets, an important question is how to make use of them to benefit later statistical inference. This is a realistic setting in the modern world as more and more related data sets are collected, say images and their descriptions, articles in multiple languages, actors in multiple social networks; and real data are often multivariate or high-dimensional such that dimension reduction is necessary before any inference. In this dissertation, I consider three dimension reduction and matching methods, namely principal component analysis followed by Procrustes matching, canonical correlation analysis, and nonlinear matching using shortest-path distance and joint neighborhood. I investigate their theoretical properties and their impact on later inference using the Procrustes fitting error, classification error, and hypothesis testing respectively. The main conclusion of this dissertation is that given a particular inference task for multiple correlated data sets, we may significantly improve the inference performance by joint matching and projection, compared to separate projection or omitting modalities. Numerical experiments are provided to illustrate the theorems and the methodology using simulated data and real data

Indexing and Retrieval of 3D Articulated Geometry Models

In this PhD research study, we focus on building a content-based search engine for 3D articulated geometry models. 3D models are essential components in nowadays graphic applications, and are widely used in the game, animation and movies production industry. With the increasing number of these models, a search engine not only provides an entrance to explore such a huge dataset, it also facilitates sharing and reusing among different users. In general, it reduces production costs and time to develop these 3D models. Though a lot of retrieval systems have been proposed in recent years, search engines for 3D articulated geometry models are still in their infancies. Among all the works that we have surveyed, reliability and efficiency are the two main issues that hinder the popularity of such systems. In this research, we have focused our attention mainly to address these two issues. We have discovered that most existing works design features and matching algorithms in order to reflect the intrinsic properties of these 3D models. For instance, to handle 3D articulated geometry models, it is common to extract skeletons and use graph matching algorithms to compute the similarity. However, since this kind of feature representation is complex, it leads to high complexity of the matching algorithms. As an example, sub-graph isomorphism can be NP-hard for model graph matching. Our solution is based on the understanding that skeletal matching seeks correspondences between the two comparing models. If we can define descriptive features, the correspondence problem can be solved by bag-based matching where fast algorithms are available. In the first part of the research, we propose a feature extraction algorithm to extract such descriptive features. We then convert the skeletal matching problems into bag-based matching. We further define metric similarity measure so as to support fast search. We demonstrate the advantages of this idea in our experiments. The improvement on precision is 12\% better at high recall. The indexing search of 3D model is 24 times faster than the state of the art if only the first relevant result is returned. However, improving the quality of descriptive features pays the price of high dimensionality. Curse of dimensionality is a notorious problem on large multimedia databases. The computation time scales exponentially as the dimension increases, and indexing techniques may not be useful in such situation. In the second part of the research, we focus ourselves on developing an embedding retrieval framework to solve the high dimensionality problem. We first argue that our proposed matching method projects 3D models on manifolds. We then use manifold learning technique to reduce dimensionality and maximize intra-class distances. We further propose a numerical method to sub-sample and fast search databases. To preserve retrieval accuracy using fewer landmark objects, we propose an alignment method which is also beneficial to existing works for fast search. The advantages of the retrieval framework are demonstrated in our experiments that it alleviates the problem of curse of dimensionality. It also improves the efficiency (3.4 times faster) and accuracy (30\% more accurate) of our matching algorithm proposed above. In the third part of the research, we also study a closely related area, 3D motions. 3D motions are captured by sticking sensor on human beings. These captured data are real human motions that are used to animate 3D articulated geometry models. Creating realistic 3D motions is an expensive and tedious task. Although 3D motions are very different from 3D articulated geometry models, we observe that existing works also suffer from the problem of temporal structure matching. This also leads to low efficiency in the matching algorithms. We apply the same idea of bag-based matching into the work of 3D motions. From our experiments, the proposed method has a 13\% improvement on precision at high recall and is 12 times faster than existing works. As a summary, we have developed algorithms for 3D articulated geometry models and 3D motions, covering feature extraction, feature matching, indexing and fast search methods. Through various experiments, our idea of converting restricted matching to bag-based matching improves matching efficiency and reliability. These have been shown in both 3D articulated geometry models and 3D motions. We have also connected 3D matching to the area of manifold learning. The embedding retrieval framework not only improves efficiency and accuracy, but has also opened a new area of research

Graph Construction for Manifold Discovery

Manifold learning is a class of machine learning methods that exploits the observation that high-dimensional data tend to lie on a smooth lower-dimensional manifold. Manifold discovery is the essential first component of manifold learning methods, in which the manifold structure is inferred from available data. This task is typically posed as a graph construction problem: selecting a set of vertices and edges that most closely approximates the true underlying manifold. The quality of this learned graph is critical to the overall accuracy of the manifold learning method. Thus, it is essential to develop accurate, efficient, and reliable algorithms for constructing manifold approximation graphs. To aid in this investigation of graph construction methods, we propose new methods for evaluating graph quality. These quality measures act as a proxy for ground-truth manifold approximation error and are applicable even when prior information about the dataset is limited. We then develop an incremental update scheme for some quality measures, demonstrating their usefulness for efficient parameter tuning. We then propose two novel methods for graph construction, the Manifold Spanning Graph and the Mutual Neighbors Graph algorithms. Each method leverages assumptions about the structure of both the input data and the subsequent manifold learning task. The algorithms are experimentally validated against state of the art graph construction techniques on a multi-disciplinary set of application domains, including image classification, directional audio prediction, and spectroscopic analysis. The final contribution of the thesis is a method for aligning sequential datasets while still respecting each set’s internal manifold structure. The use of high quality manifold approximation graphs enables accurate alignments with few ground-truth correspondences

Puolivalvottu WLAN-radiokarttojen oppiminen

In this thesis a manifold learning method is applied to the problem of WLAN positioning and automatic radio map creation. Due to the nature of WLAN signal strength measurements, a signal map created from raw measurements results in non-linear distance relations between measurement points. These signal strength vectors reside in a high-dimensioned coordinate system. With the help of the so called Isomap-algorithm the dimensionality of this map can be reduced, and thus more easily processed. By embedding position-labeled strategic key points, we can automatically adjust the mapping to match the surveyed environment. The environment is thus learned in a semi-supervised way; gathering training points and embedding them in a two-dimensional manifold gives us a rough mapping of the measured environment. After a calibration phase, where the labeled key points in the training data are used to associate coordinates in the manifold representation with geographical locations, we can perform positioning using the adjusted map. This can be achieved through a traditional supervised learning process, which in our case is a simple nearest neighbors matching of a sampled signal strength vector. We deployed this system in two locations in the Kumpula campus in Helsinki, Finland. Results indicate that positioning based on the learned radio map can achieve good accuracy, especially in hallways or other areas in the environment where the WLAN signal is constrained by obstacles such as walls.Työssä sovelletaan monisto-oppimismenetelmää WLAN-paikannuksen ja automaattisen radiokartan luonnin ongelmaan. WLAN-signaalivoimakkuuksien mittausten luonteen takia käsittelemättömät mittaukset aiheuttavat epälineaarisia suhteita radiokartan mittauspisteiden välille. Nämä signaalivoimakkuusvektorit sijaitsevat avaruudessa jolla on korkea ulottuvuus. Niin kutsutun Isomap-algoritmin avulla kartan ulottuvuuksia voidaan karsia, jolloin sitä on helpompi työstää. Upottamalla karttaan merkittyjä avainpisteitä, se voidaan automaattisesti säätää vastaamaan mitattua ympäristöä. Ympäristö siis opitaan puolivalvotusti; keräämällä harjoituspisteitä ja upottamalla ne kaksiulotteiseen monistoon saadaan karkea kartta ympäristöstä. Kalibrointivaiheen jälkeen, jossa merkittyjä avainpisteitä käytetään yhdistämään moniston koordinaatit maantieteellisiin kohteisiin, voidaan suorittaa paikannusta säädetyn kartan avulla. Tämä voidaan tehdä perinteisen valvotun oppimisen avulla, joka tässä tapauksessa on yksinkertainen lähimmän naapurin löytäminen mitatulle signaalivoimakkuusvektorille. Järjestelmää kokeiltiin kahdessa paikassa Kumpulan kampuksessa Helsingissä. Tulokset viittaavat siihen että opitun radiokartan avulla paikannus voi saavuttaa hyvän tarkkuuden, etenkin käytävissä ja muissa tiloissa jossa esteet kuten seinät rajoittavat WLAN-signaalia

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them