Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.

Machine learning approaches to multi-label document classification have to date largely relied on discriminative modeling techniques such as support vector machines. A drawback of these approaches is that performance rapidly drops off as the total number of labels and the number of labels per document increase. This problem is amplified when the label frequencies exhibit the type of highly skewed distributions that are often observed in real-world datasets. In this paper we investigate a class of generative statistical topic models for multi-label documents that associate individual word tokens with different labels. We investigate the advantages of this approach relative to discriminative models, particularly with respect to classification problems involving large numbers of relatively rare labels. We compare the performance of generative and discriminative approaches on document labeling tasks ranging from datasets with several thousand labels to datasets with tens of labels. The experimental results indicate that probabilistic generative models can achieve competitive multi-label classification performance compared to discriminative methods, and have advantages for datasets with many labels and skewed label frequencies.

In this paper, we propose the MIML (Multi-Instance Multi-Label learning) framework where an example is described by multiple instances and associated with multiple class labels. Compared to traditional learning frameworks, the MIML framework is more convenient and natural for representing complicated objects which have multiple semantic meanings. To learn from MIML examples, we propose the MimlBoost and MimlSvm algorithms based on a simple degeneration strategy, and experiments show that solving problems involving complicated objects with multiple semantic meanings in the MIML framework can lead to good performance. Considering that the degeneration process may lose information, we propose the D-MimlSvm algorithm which tackles MIML problems directly in a regularization framework. Moreover, we show that even when we do not have access to the real objects and thus cannot capture more information from real objects by using the MIML representation, MIML is still useful. We propose the InsDif and SubCod algorithms. InsDif works by transforming single-instances into the MIML representation for learning, while SubCod works by transforming single-label examples into the MIML representation for learning. Experiments show that in some tasks they are able to achieve better performance than learning the single-instances or single-label examples directly.

End-user interactive machine learning is a promising tool for enhancing human productivity and capabilities with large unstructured data sets. Recent work has shown that we can create end-user interactive machine learning systems for specific applications. However, we still lack a generalized understanding of how to design effective end-user interaction with interactive machine learning systems. This work presents three explorations in designing for effective end-user interaction with machine learning in CueFlik, a system developed to support Web image search. These explorations demonstrate that interactions designed to balance the needs of end-users and machine learning algorithms can significantly improve the effectiveness of end-user interactive machine learning.

Partially supervised text classification has received great research attention since it only uses positive and unlabeled examples as training data. This problem can be solved by automatically labeling some negative (and more positive) examples from unlabeled examples before training a text classifier. But it is difficult to guarantee both high quality and quantity of the new labeled examples. In this paper, a multi-level example based learning method for partially supervised text classification is proposed, which can make full use of all unlabeled examples. A heuristic method is proposed to assign possible labels to unlabeled examples and partition them into multiple levels according to their labeling confidence. A text classifier is trained on these multi-level examples using weighted support vector machines. Experiments show that the multi-level example based learning method is effective for partially supervised text classification, and outperforms the existing popular methods such as Biased-SVM, ROC-SVM, S-EM and WL.

Multi-Instance Learning (MIL) deals with problems where each training example is a bag, and each bag contains a set of instances. Multi-instance representation is useful in many real world applications, because it is able to capture more structural information than traditional flat single-instance representation. However, it also brings new challenges. Specifically, the distance between data objects in MIL is a set-to-set distance, which is harder to estimate than vector distances used in single-instance data. Moreover, because in MIL labels are assigned to bags instead of instances, although a bag belongs to a class, some, or even most, of its instances may not be truly related to the class. In order to address these difficulties, in this paper we propose a novel Instance Specific Distance (ISD) method for MIL, which computes the Class-to-Bag (C2B) distance by further considering the relevances of training instances with respect to their labeled classes. Taking into account the outliers caused by the weak label association in MIL, we learn ISD by solving an l0+-norm minimization problem. An efficient algorithm to solve the optimization problem is presented, together with the rigorous proof of its convergence. The promising results on five benchmark multi-instance data sets and two real world multi-instance applications validate the effectiveness of the proposed method.

LogAnswer is a question answering (QA) system for the German language, aimed at providing concise and correct answers to arbitrary questions. For this purpose LogAnswer is designed as an embedded artificial intelligence system which integrates methods from several fields of AI, namely natural language processing, machine learning, knowledge representation and automated theorem proving. We intend to employ LogAnswer as a virtual user within Internet-based QA forums, where it must be able to identify the questions that it cannot answer correctly, a task that normally receives little attention in QA research compared to the actual answer derivation. The paper presents a machine learning solution to the wrong answer avoidance (WAA) problem, applying a meta classifier to the output of simple term-based classifiers and a rich set of other WAA features. Experiments with a large set of real-world questions from a QA forum show that the proposed method significantly improves the WAA characteristics of our system.

Multi-label learning deals with the problem where each training example is represented by a single instance while associated with a set of class labels. For an unseen example, existing approaches choose to determine the membership of each possible class label to it based on identical feature set, i.e. the very instance representation of the unseen example is employed in the discrimination processes of all labels. However, this commonly-used strategy might be suboptimal as different class labels usually carry specific characteristics of their own, and it could be beneficial to exploit different feature sets for the discrimination of different labels. Based on the above reflection, we propose a new strategy to multi-label learning by leveraging label-specific features, where a simple yet effective algorithm named LIFT is presented. Briefly, LIFT constructs features specific to each label by conducting clustering analysis on its positive and negative instances, and then performs training and testing by querying the clustering results. Extensive experiments across sixteen diversified data sets clearly validate the superiority of LIFT against other well-established multi-label learning algorithms.

In many real-world applications of the time series classification problem, not only could the negative training instances be missing, the number of positive instances available for learning may also be rather limited. This has motivated the development of new classification algorithms that can learn from a small set P of labeled seed positive instances augmented with a set U of unlabeled instances (i.e. PU learning algorithms). However, existing PU learning algorithms for time series classification have less than satisfactory performance as they are unable to identify the class boundary between positive and negative instances accurately. In this paper, we propose a novel PU learning algorithm LCLC (Learning from Common Local Clusters) for time series classification. LCLC is designed to effectively identify the ground truths’ positive and negative boundaries, resulting in more accurate classifiers than those constructed using existing methods. We have applied LCLC to classify time series data from different application domains; the experimental results demonstrate that LCLC outperforms existing methods significantly.

Entity linking maps name mentions in the documents to entries in a knowledge base through resolving the name variations and ambiguities. In this paper, we propose three advancements for entity linking. Firstly, expanding acronyms can effectively reduce the ambiguity of the acronym mentions. However, only rule-based approaches relying heavily on the presence of text markers have been used for entity linking. In this paper, we propose a supervised learning algorithm to expand more complicated acronyms encountered, which leads to 15.1% accuracy improvement over state-of-the-art acronym expansion methods. Secondly, as entity linking annotation is expensive and labor intensive, to automate the annotation process without compromise of accuracy, we propose an instance selection strategy to effectively utilize the automatically generated annotation. In our selection strategy, an informative and diverse set of instances are selected for effective disambiguation. Lastly, topic modeling is used to model the semantic topics of the articles. These advancements give statistical significant improvement to entity linking individually. Collectively they lead the highest performance on KBP-2010 task.