Linear Discriminant Analysis (LDA) has been a popular method for extracting features which preserve class separability. The projection vectors are commonly obtained by maximizing the between class covariance and simultaneously minimizing the within class covariance. In practice, when there is no sufficient training samples, the covariance matrix of each class may not be accurately estimated. In this paper, we propose a novel method, called Semi- supervised Discriminant Analysis (SDA), which makes use of both labeled and unlabeled samples. The labeled data points are used to maximize the separability between different classes and the unlabeled data points are used to estimate the intrinsic geometric structure of the data. Specifically, we aim to learn a discriminant function which is as smooth as possible on the data manifold. Experimental results on single training image face recognition and relevance feedback image retrieval demonstrate the effectiveness of our algorithm.

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Semi-supervised Discriminant Analysis

In past decade, more and more data are collected from multiple sources or represented by multiple views, where different views describe distinct perspectives of the data. Although each view could be individually used for finding patterns by clustering, the clustering performance could be more accurate by exploring the rich information among multiple views. Several multi-view clustering methods have been proposed to unsupervised integrate different views of data. However, they are graph based approaches, e.g. based on spectral clustering, such that they cannot handle the large-scale data. How to combine these heterogeneous features for unsupervised large-scale data clustering has become a challenging problem. In this paper, we propose a new robust large-scale multi-view clustering method to integrate heterogeneous representations of largescale data. We evaluate the proposed new methods by six benchmark data sets and compared the performance with several commonly used clustering approaches as well as the baseline multi-view clustering methods. In all experimental results, our proposed methods consistently achieve superiors clustering performances.

Multi-view K-means clustering on big data

For many computer vision applications, the data sets distribute on certain low-dimensional subspaces. Subspace clustering is to find such underlying subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. The proposed method performs clustering on the subspace representation of each view simultaneously. Meanwhile, we propose to use a common cluster structure to guarantee the consistence among different views. In addition, an efficient algorithm is proposed to solve the problem. Experiments on four benchmark data sets have been performed to validate our proposed method. The promising results demonstrate the effectiveness of our method.

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Multi-view Subspace Clustering

We consider the problem of clustering Web image search results. Generally, the image search results returned by an image search engine contain multiple topics. Organizing the results into different semantic clusters facilitates users' browsing. In this paper, we propose a hierarchical clustering method using visual, textual and link analysis. By using a vision-based page segmentation algorithm, a web page is partitioned into blocks, and the textual and link information of an image can be accurately extracted from the block containing that image. By using block-level link analysis techniques, an image graph can be constructed. We then apply spectral techniques to find a Euclidean embedding of the images which respects the graph structure. Thus for each image, we have three kinds of representations, i.e. visual feature based representation, textual feature based representation and graph based representation. Using spectral clustering techniques, we can cluster the search results into different semantic clusters. An image search example illustrates the potential of these techniques.

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Hierarchical clustering of WWW image search results using visual, textual and link information

For quantitative analysis of histopathological images, such as the lymphoma grading systems, quantification of features is usually carried out on single cells before categorizing them by classification algorithms. To this end, we propose an integrated framework consisting of a novel supervised cell-image segmentation algorithm and a new touching-cell splitting method. For the segmentation part, we segment the cell regions from the other areas by classifying the image pixels into either cell or extra-cellular category. Instead of using pixel color intensities, the color-texture extracted at the local neighborhood of each pixel is utilized as the input to our classification algorithm. The color-texture at each pixel is extracted by local Fourier transform (LFT) from a new color space, the most discriminant color space (MDC). The MDC color space is optimized to be a linear combination of the original RGB color space so that the extracted LFT texture features in the MDC color space can achieve most discrimination in terms of classification (segmentation) performance. To speed up the texture feature extraction process, we develop an efficient LFT extraction algorithm based on image shifting and image integral. For the splitting part, given a connected component of the segmentation map, we initially differentiate whether it is a touching-cell clump or a single nontouching cell. The differentiation is mainly based on the distance between the most likely radial-symmetry center and the geometrical center of the connected component. The boundaries of touching-cell clumps are smoothed out by Fourier shape descriptor before carrying out an iterative, concave-point and radial-symmetry based splitting algorithm. To test the validity, effectiveness and efficiency of the framework, it is applied to follicular lymphoma pathological images, which exhibit complex background and extracellular texture with nonuniform illumination condition. For comparison purposes, the results of the proposed segmentation algorithm are evaluated against the outputs of superpixel, graph-cut, mean-shift, and two state-of-the-art pathological image segmentation methods using ground-truth that was established by manual segmentation of cells in the original images. Our segmentation algorithm achieves better results than the other compared methods. The results of splitting are evaluated in terms of under-splitting, over-splitting, and encroachment errors. By summing up the three types of errors, we achieve a total error rate of 5.25% per image.

Partitioning Histopathological Images: An Integrated Framework for Supervised Color-Texture Segmentation and Cell Splitting

We adopt a local Fourier transform as a texture representation scheme and derive eight characteristic maps for describing different aspects of cooccurrence relations of image pixels in each channel of the (SVcosH, SVsinH, V) color space. Then we calculate the first and second moments of these maps as a representation of the natural color image pixel distribution, resulting in a 48-dimensional feature vector. The novel low-level feature is named color texture moments (CTM), which can also be regarded as a certain extension to color moments in eight aspects through eight orthogonal templates. Experiments show that this new feature can achieve good retrieval performance for CBIR.

Mingjing Li

Papers

Color texture moments for content-based image retrieval