In this paper, we present an agglomerative fuzzy K-means clustering algorithm for numerical data, an extension to the standard fuzzy K-means algorithm by introducing a penalty term to the objective function to make the clustering process not sensitive to the initial cluster centers. The new algorithm can produce more consistent clustering results from different sets of initial clusters centers. Combined with cluster validation techniques, the new algorithm can determine the number of clusters in a data set, which is a well known problem in $k$-means clustering. Experimental results on synthetic data sets (2 to 5 dimensions, 500 to 5000 objects and 3 to 7 clusters), the BIRCH two-dimensional data set of 20000 objects and 100 clusters, and the WINE data set of 178 objects, 17 dimensions and 3 clusters from UCI, have demonstrated the effectiveness of the new algorithm in producing consistent clustering results and determining the correct number of clusters in different data sets, some with overlapping inherent clusters.

The performance of the most clustering algorithms highly relies on the representation of data in the input space or the Hilbert space of kernel methods. This paper is to obtain an appropriate data representation through feature selection or kernel learning within the framework of the Local Learning-Based Clustering (LLC) (Wu and Schölkopf 2006) method, which can outperform the global learning-based ones when dealing with the high-dimensional data lying on manifold. Specifically, we associate a weight to each feature or kernel and incorporate it into the built-in regularization of the LLC algorithm to take into account the relevance of each feature or kernel for the clustering. Accordingly, the weights are estimated iteratively in the clustering process. We show that the resulting weighted regularization with an additional constraint on the weights is equivalent to a known sparse-promoting penalty. Hence, the weights of those irrelevant features or kernels can be shrunk toward zero. Extensive experiments show the efficacy of the proposed methods on the benchmark data sets.

Hashing has recently sparked a great revolution in cross-modal retrieval because of its low storage cost and high query speed. Recent cross-modal hashing methods often learn unified or equal-length hash codes to represent the multi-modal data and make them intuitively comparable. However, such representations could inherently sacrifice their representation scalability because the data from different modalities may not have one-to-one correspondence and could be encoded more efficiently by different hash codes of unequal lengths. To mitigate these problems, this paper exploits a related and relatively unexplored problem: encode the heterogeneous data with varying hash lengths and generalize the cross-modal retrieval in various challenging scenarios. To this end, a generalized and flexible cross-modal hashing framework, termed Matrix Tri-Factorization Hashing (MTFH), is proposed to work seamlessly in various settings including paired or unpaired multi-modal data, and equal or varying hash length encoding scenarios. MTFH exploits an efficient objective function to flexibly learn modality-specific hash codes with different length settings, while synchronously learning two semantic correlation matrices for heterogeneous data comparable. As a result, the derived hash codes are more semantically meaningful for various challenging cross-modal retrieval tasks. Extensive experiments evaluated on public benchmark datasets highlight the superiority of MTFH under various retrieval scenarios and show its competitive performance with the state-of-the-arts.

In recent years, with the development of deep learning (DL), the hyperspectral image (HSI) classification methods based on DL have shown superior performance. Although these DL-based methods have great successes, there is still room to improve their ability to explore spatial-spectral information. In this article, we propose a 3-D octave convolution with the spatial-spectral attention network (3DOC-SSAN) to capture discriminative spatial-spectral features for the classification of HSIs. Especially, we first extend the octave convolution model using 3-D convolution, namely, a 3-D octave convolution model (3D-OCM), in which four 3-D octave convolution blocks are combined to capture spatial-spectral features from HSIs. Not only the spatial information can be mined deeply from the high- and low-frequency aspects but also the spectral information can be taken into account by our 3D-OCM. Second, we introduce two attention models from spatial and spectral dimensions to highlight the important spatial areas and specific spectral bands that consist of significant information for the classification tasks. Finally, in order to integrate spatial and spectral information, we design an information complement model to transmit important information between spatial and spectral attention features. Through the information complement model, the beneficial parts of spatial and spectral attention features for the classification tasks can be fully utilized. Comparing with several existing popular classifiers, our proposed method can achieve competitive performance on four benchmark data sets.