Robust, Scalable, and Provable Approaches to High Dimensional Unsupervised Learning

This doctoral thesis focuses on three popular unsupervised learning problems: subspace clustering, robust PCA, and column sampling. For the subspace clustering problem, a new transformative idea is presented. The proposed approach, termed Innovation Pursuit, is a new geometrical solution to the subspace clustering problem whereby subspaces are identified based on their relative novelties. A detailed mathematical analysis is provided establishing sufficient conditions for the proposed method to correctly cluster the data points. The numerical simulations with both real and synthetic data demonstrate that Innovation Pursuit notably outperforms the state-of-the-art subspace clustering algorithms. For the robust PCA problem, we focus on both the outlier detection and the matrix decomposition problems. For the outlier detection problem, we present a new algorithm, termed Coherence Pursuit, in addition to two scalable randomized frameworks for the implementation of outlier detection algorithms. The Coherence Pursuit method is the first provable and non-iterative robust PCA method which is provably robust to both unstructured and structured outliers. Coherence Pursuit is remarkably simple and it notably outperforms the existing methods in dealing with structured outliers. In the proposed randomized designs, we leverage the low dimensional structure of the low rank component to apply the robust PCA algorithm to a random sketch of the data as opposed to the full scale data. Importantly, it is analytically shown that the presented randomized designs can make the computation or sample complexity of the low rank matrix recovery algorithm independent of the size of the data. At the end, we focus on the column sampling problem. A new sampling tool, dubbed Spatial Random Sampling, is presented which performs the random sampling in the spatial domain. The most compelling feature of Spatial Random Sampling is that it is the first unsupervised column sampling method which preserves the spatial distribution of the data

큰 그래프 상에서의 개인화된 페이지 랭크에 대한 빠른 계산 기법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2020. 8. 이상구.Computation of Personalized PageRank (PPR) in graphs is an important function that is widely utilized in myriad application domains such as search, recommendation, and knowledge discovery. Because the computation of PPR is an expensive process, a good number of innovative and efficient algorithms for computing PPR have been developed. However, efficient computation of PPR within very large graphs with over millions of nodes is still an open problem. Moreover, previously proposed algorithms cannot handle updates efficiently, thus, severely limiting their capability of handling dynamic graphs. In this paper, we present a fast converging algorithm that guarantees high and controlled precision. We improve the convergence rate of traditional Power Iteration method by adopting successive over-relaxation, and initial guess revision, a vector reuse strategy. The proposed method vastly improves on the traditional Power Iteration in terms of convergence rate and computation time, while retaining its simplicity and strictness. Since it can reuse the previously computed vectors for refreshing PPR vectors, its update performance is also greatly enhanced. Also, since the algorithm halts as soon as it reaches a given error threshold, we can flexibly control the trade-off between accuracy and time, a feature lacking in both sampling-based approximation methods and fully exact methods. Experiments show that the proposed algorithm is at least 20 times faster than the Power Iteration and outperforms other state-of-the-art algorithms.그래프 내에서 개인화된 페이지랭크 (P ersonalized P age R ank, PPR 를 계산하는 것은 검색 , 추천 , 지식발견 등 여러 분야에서 광범위하게 활용되는 중요한 작업 이다 . 개인화된 페이지랭크를 계산하는 것은 고비용의 과정이 필요하므로 , 개인화된 페이지랭크를 계산하는 효율적이고 혁신적인 방법들이 다수 개발되어왔다 . 그러나 수백만 이상의 노드를 가진 대용량 그래프에 대한 효율적인 계산은 여전히 해결되지 않은 문제이다 . 그에 더하여 , 기존 제시된 알고리듬들은 그래프 갱신을 효율적으로 다루지 못하여 동적으로 변화하는 그래프를 다루는 데에 한계점이 크다 . 본 연구에서는 높은 정밀도를 보장하고 정밀도를 통제 가능한 , 빠르게 수렴하는 개인화된 페이지랭크 계산 알고리듬을 제시한다 . 전통적인 거듭제곱법 (Power 에 축차가속완화법 (Successive Over Relaxation) 과 초기 추측 값 보정법 (Initial Guess 을 활용한 벡터 재사용 전략을 적용하여 수렴 속도를 개선하였다 . 제시된 방법은 기존 거듭제곱법의 장점인 단순성과 엄밀성을 유지 하면서 도 수렴율과 계산속도를 크게 개선 한다 . 또한 개인화된 페이지랭크 벡터의 갱신을 위하여 이전에 계산 되어 저장된 벡터를 재사용하 여 , 갱신 에 드는 시간이 크게 단축된다 . 본 방법은 주어진 오차 한계에 도달하는 즉시 결과값을 산출하므로 정확도와 계산시간을 유연하게 조절할 수 있으며 이는 표본 기반 추정방법이나 정확한 값을 산출하는 역행렬 기반 방법 이 가지지 못한 특성이다 . 실험 결과 , 본 방법은 거듭제곱법에 비하여 20 배 이상 빠르게 수렴한다는 것이 확인되었으며 , 기 제시된 최고 성능 의 알고리 듬 보다 우수한 성능을 보이는 것 또한 확인되었다1 Introduction 1 2 Preliminaries: Personalized PageRank 4 2.1 Random Walk, PageRank, and Personalized PageRank. 5 2.1.1 Basics on Random Walk 5 2.1.2 PageRank. 6 2.1.3 Personalized PageRank 8 2.2 Characteristics of Personalized PageRank. 9 2.3 Applications of Personalized PageRank. 12 2.4 Previous Work on Personalized PageRank Computation. 17 2.4.1 Basic Algorithms 17 2.4.2 Enhanced Power Iteration 18 2.4.3 Bookmark Coloring Algorithm. 20 2.4.4 Dynamic Programming 21 2.4.5 Monte-Carlo Sampling. 22 2.4.6 Enhanced Direct Solving 24 2.5 Summary 26 3 Personalized PageRank Computation with Initial Guess Revision 30 3.1 Initial Guess Revision and Relaxation 30 3.2 Finding Optimal Weight of Successive Over Relaxation for PPR. 34 3.3 Initial Guess Construction Algorithm for Personalized PageRank. 36 4 Fully Personalized PageRank Algorithm with Initial Guess Revision 42 4.1 FPPR with IGR. 42 4.2 Optimization. 49 4.3 Experiments. 52 5 Personalized PageRank Query Processing with Initial Guess Revision 56 5.1 PPR Query Processing with IGR 56 5.2 Optimization. 64 5.3 Experiments. 67 6 Conclusion 74 Bibliography 77 Appendix 88 Abstract (In Korean) 90Docto

Semi-supervised machine learning techniques for classification of evolving data in pattern recognition

The amount of data recorded and processed over recent years has increased exponentially. To create intelligent systems that can learn from this data, we need to be able to identify patterns hidden in the data itself, learn these pattern and predict future results based on our current observations. If we think about this system in the context of time, the data itself evolves and so does the nature of the classification problem. As more data become available, different classification algorithms are suitable for a particular setting. At the beginning of the learning cycle when we have a limited amount of data, online learning algorithms are more suitable. When truly large amounts of data become available, we need algorithms that can handle large amounts of data that might be only partially labeled as a result of the bottleneck in the learning pipeline from human labeling of the data. An excellent example of evolving data is gesture recognition, and it is present throughout our work. We need a gesture recognition system to work fast and with very few examples at the beginning. Over time, we are able to collect more data and the system can improve. As the system evolves, the user expects it to work better and not to have to become involved when the classifier is unsure about decisions. This latter situation produces additional unlabeled data. Another example of an application is medical classification, where experts’ time is a rare resource and the amount of received and labeled data disproportionately increases over time. Although the process of data evolution is continuous, we identify three main discrete areas of contribution in different scenarios. When the system is very new and not enough data are available, online learning is used to learn after every single example and to capture the knowledge very fast. With increasing amounts of data, offline learning techniques are applicable. Once the amount of data is overwhelming and the teacher cannot provide labels for all the data, we have another setup that combines labeled and unlabeled data. These three setups define our areas of contribution; and our techniques contribute in each of them with applications to pattern recognition scenarios, such as gesture recognition and sketch recognition. An online learning setup significantly restricts the range of techniques that can be used. In our case, the selected baseline technique is the Evolving TS-Fuzzy Model. The semi-supervised aspect we use is a relation between rules created by this model. Specifically, we propose a transductive similarity model that utilizes the relationship between generated rules based on their decisions about a query sample during the inference time. The activation of each of these rules is adjusted according to the transductive similarity, and the new decision is obtained using the adjusted activation. We also propose several new variations to the transductive similarity itself. Once the amount of data increases, we are not limited to the online learning setup, and we can take advantage of the offline learning scenario, which normally performs better than the online one because of the independence of sample ordering and global optimization with respect to all samples. We use generative methods to obtain data outside of the training set. Specifically, we aim to improve the previously mentioned TS Fuzzy Model by incorporating semi-supervised learning in the offline learning setup without unlabeled data. We use the Universum learning approach and have developed a method called UFuzzy. This method relies on artificially generated examples with high uncertainty (Universum set), and it adjusts the cost function of the algorithm to force the decision boundary to be close to the Universum data. We were able to prove the hypothesis behind the design of the UFuzzy classifier that Universum learning can improve the TS Fuzzy Model and have achieved improved performance on more than two dozen datasets and applications. With increasing amounts of data, we use the last scenario, in which the data comprises both labeled data and additional non-labeled data. This setting is one of the most common ones for semi-supervised learning problems. In this part of our work, we aim to improve the widely popular tecjniques of self-training (and its successor help-training) that are both meta-frameworks over regular classifier methods but require probabilistic representation of output, which can be hard to obtain in the case of discriminative classifiers. Therefore, we develop a new algorithm that uses the modified active learning technique Query-by-Committee (QbC) to sample data with high certainty from the unlabeled set and subsequently embed them into the original training set. Our new method allows us to achieve increased performance over both a range of datasets and a range of classifiers. These three works are connected by gradually relaxing the constraints on the learning setting in which we operate. Although our main motivation behind the development was to increase performance in various real-world tasks (gesture recognition, sketch recognition), we formulated our work as general methods in such a way that they can be used outside a specific application setup, the only restriction being that the underlying data evolve over time. Each of these methods can successfully exist on its own. The best setting in which they can be used is a learning problem where the data evolve over time and it is possible to discretize the evolutionary process. Overall, this work represents a significant contribution to the area of both semi-supervised learning and pattern recognition. It presents new state-of-the-art techniques that overperform baseline solutions, and it opens up new possibilities for future research

Interactive visual cluster analysis by contrastive dimensionality reduction

We propose a contrastive dimensionality reduction approach (CDR) for interactive visual cluster analysis. Although dimensionality reduction of high-dimensional data is widely used in visual cluster analysis in conjunction with scatterplots, there are several limitations on effective visual cluster analysis. First, it is non-trivial for an embedding to present clear visual cluster separation when keeping neighborhood structures. Second, as cluster analysis is a subjective task, user steering is required. However, it is also non-trivial to enable interactions in dimensionality reduction. To tackle these problems, we introduce contrastive learning into dimensionality reduction for high-quality embedding. We then redefine the gradient of the loss function to the negative pairs to enhance the visual cluster separation of embedding results. Based on the contrastive learning scheme, we employ link-based interactions to steer embeddings. After that, we implement a prototype visual interface that integrates the proposed algorithms and a set of visualizations. Quantitative experiments demonstrate that CDR outperforms existing techniques in terms of preserving correct neighborhood structures and improving visual cluster separation. The ablation experiment demonstrates the effectiveness of gradient redefinition. The user study verifies that CDR outperforms t-SNE and UMAP in the task of cluster identification. We also showcase two use cases on real-world datasets to present the effectiveness of link-based interactions

Analyzing Granger causality in climate data with time series classification methods

Attribution studies in climate science aim for scientifically ascertaining the influence of climatic variations on natural or anthropogenic factors. Many of those studies adopt the concept of Granger causality to infer statistical cause-effect relationships, while utilizing traditional autoregressive models. In this article, we investigate the potential of state-of-the-art time series classification techniques to enhance causal inference in climate science. We conduct a comparative experimental study of different types of algorithms on a large test suite that comprises a unique collection of datasets from the area of climate-vegetation dynamics. The results indicate that specialized time series classification methods are able to improve existing inference procedures. Substantial differences are observed among the methods that were tested

A picture is worth a thousand words : content-based image retrieval techniques

In my dissertation I investigate techniques for improving the state of the art in content-based image retrieval. To place my work into context, I highlight the current trends and challenges in my field by analyzing over 200 recent articles. Next, I propose a novel paradigm called __artificial imagination__, which gives the retrieval system the power to imagine and think along with the user in terms of what she is looking for. I then introduce a new user interface for visualizing and exploring image collections, empowering the user to navigate large collections based on her own needs and preferences, while simultaneously providing her with an accurate sense of what the database has to offer. In the later chapters I present work dealing with millions of images and focus in particular on high-performance techniques that minimize memory and computational use for both near-duplicate image detection and web search. Finally, I show early work on a scene completion-based image retrieval engine, which synthesizes realistic imagery that matches what the user has in mind.LEI Universiteit LeidenNWOImagin

SIS 2017. Statistics and Data Science: new challenges, new generations

The 2017 SIS Conference aims to highlight the crucial role of the Statistics in Data Science. In this new domain of ‘meaning’ extracted from the data, the increasing amount of produced and available data in databases, nowadays, has brought new challenges. That involves different fields of statistics, machine learning, information and computer science, optimization, pattern recognition. These afford together a considerable contribute in the analysis of ‘Big data’, open data, relational and complex data, structured and no-structured. The interest is to collect the contributes which provide from the different domains of Statistics, in the high dimensional data quality validation, sampling extraction, dimensional reduction, pattern selection, data modelling, testing hypotheses and confirming conclusions drawn from the data