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Abstract-When performing visualization and classification, people often confront the problem of dimensionality reduction. Isomap is one of the most promising nonlinear dimensionality reduction techniques. However, when Isomap is applied to real-world data, it shows some limitations, such as being sensitive to the noise. In this paper, an improved version of Isomap, namely S-Isomap, is proposed. S-Isomap utilizes class information to guide the procedure of nonlinear dimensionality reduction. Such a kind of procedure is called supervised nonlinear dimensionality reduction. In S-Isomap, the neighborhood graph of the input data is constructed according to a certain kind of dissimilarity between data points, which is specially designed to integrate the class information. The dissimilarity has several good properties which help to discover the true neighborhood of the data, and thus makes S-Isomap a robust technique for both visualization and classification, especially for real-world problems. In the visualization experiments, S-Isomap is compared with Isomap, LLE and WeightedIso. The results show that S-Isomap performs the best. In the classification experiments, S-Isomap is used as a preprocess of classification and compared with Isomap, WeightedIso, as well as some other well-established classification methods including K nearest neighbor classifier, BP neural network, J4.8 decision tree and SVM. The results reveal that S-Isomap excels Isomap and WeightedIso in classification and is highly competitive with those well-known classification methods.

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In many real-world applications, such as image retrieval, it would be natural to measure the distances from one instance to others using instance specific distance which captures the distinctions from the perspective of the concerned instance. However, there is no complete framework for learning instance specific distances since existing methods are incapable of learning such distances for test instance and unlabeled data. In this paper, we propose the Isd method to address this issue. The key of Isd is metric propagation, that is, propagating and adapting metrics of individual labeled examples to individual unlabeled instances. We formulate the problem into a convex optimization framework and derive efficient solutions. Experiments show that Isd can effectively learn instance specific distances for labeled as well as unlabeled instances. The metric propagation scheme can also be used in other scenarios.

Complex objects are usually with multiple labels, and can be represented by multiple modal representations, e.g., the complex articles contain text and image information as well as multiple annotations. Previous methods assume that the homogeneous multi-modal data are consistent, while in real applications, the raw data are disordered, e.g., the article constitutes with variable number of inconsistent text and image instances. Therefore, Multi-modal Multi-instance Multi-label (M3) learning provides a framework for handling such task and has exhibited excellent performance. However, M3 learning is facing two main challenges: 1) how to effectively utilize label correlation; 2) how to take advantage of multi-modal learning to process unlabeled instances. To solve these problems, we first propose a novel Multi-modal Multi-instance Multi-label Deep Network (M3DN), which considers M3 learning in an end-to-end multi-modal deep network and utilizes consistency principle among different modal bag-level predictions. Based on the M3DN, we learn the latent ground label metric with the optimal transport. Moreover, we introduce the extrinsic unlabeled multi-modal multi-instance data, and propose the M3DNS, which considers the instance-level auto-encoder for single modality and modified bag-level optimal transport to strengthen the consistency among modalities. Thereby M3DNS can better predict label and exploit label correlation simultaneously. Experiments on benchmark datasets and real world WKG Game-Hub dataset validate the effectiveness of the proposed methods.