Fast Approximate KK-Means via Cluster Closures

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are computed and each data point is re-assigned to its nearest center. The cluster re-assignment step becomes prohibitively expensive when the number of data points and cluster centers are large. In this paper, we propose a novel approximate $k$-means algorithm to greatly reduce the computational complexity in the assignment step. Our approach is motivated by the observation that most active points changing their cluster assignments at each iteration are located on or near cluster boundaries. The idea is to efficiently identify those active points by pre-assembling the data into groups of neighboring points using multiple random spatial partition trees, and to use the neighborhood information to construct a closure for each cluster, in such a way only a small number of cluster candidates need to be considered when assigning a data point to its nearest cluster. Using complexity analysis, image data clustering, and applications to image retrieval, we show that our approach out-performs state-of-the-art approximate $k$-means algorithms in terms of clustering quality and efficiency

Optimized Cartesian KK-Means

Product quantization-based approaches are effective to encode high-dimensional data points for approximate nearest neighbor search. The space is decomposed into a Cartesian product of low-dimensional subspaces, each of which generates a sub codebook. Data points are encoded as compact binary codes using these sub codebooks, and the distance between two data points can be approximated efficiently from their codes by the precomputed lookup tables. Traditionally, to encode a subvector of a data point in a subspace, only one sub codeword in the corresponding sub codebook is selected, which may impose strict restrictions on the search accuracy. In this paper, we propose a novel approach, named Optimized Cartesian $K$-Means (OCKM), to better encode the data points for more accurate approximate nearest neighbor search. In OCKM, multiple sub codewords are used to encode the subvector of a data point in a subspace. Each sub codeword stems from different sub codebooks in each subspace, which are optimally generated with regards to the minimization of the distortion errors. The high-dimensional data point is then encoded as the concatenation of the indices of multiple sub codewords from all the subspaces. This can provide more flexibility and lower distortion errors than traditional methods. Experimental results on the standard real-life datasets demonstrate the superiority over state-of-the-art approaches for approximate nearest neighbor search.Comment: to appear in IEEE TKDE, accepted in Apr. 201

The Combined Signatures of Hypoxia and Cellular Landscape Provides a Prognostic and Therapeutic Biomarker in HBV-Related Hepatocellular Carcinoma

Prognosis and treatment options of HBV-related hepatocellular carcinoma (HBV-HCC) are generally based on tumor burden and liver function. Yet, tumor growth and therapeutic resistance of HBV-HCC are strongly influenced by intratumoral hypoxia and cells infiltrating the tumor microenvironment (TME). We, therefore, studied whether linking parameters associated with hypoxia and TME cells could have a better prediction of prognosis and therapeutic responses. Quantification of 109 hypoxia-related genes and 64 TME cells was performed in 452 HBV-HCC tumors. Prognostic hypoxia and TME cells signatures were determined based on Cox regression and meta-analysis for generating the Hypoxia-TME classifier. Thereafter, the prognosis, tumor, and immune characteristics as well as the benefit of therapies in Hypoxia-TME defined subgroups were analyzed. Patients in the Hypoxialow /TMEhigh subgroup showed a better prognosis and therapeutic responses than any other subgroups, which can be well elucidated based on the differences in terms of immune-related molecules, tumor somatic mutations, and cancer cellular signaling pathways. Notably, our analysis furthermore demonstrated the synergistic influence of hypoxia and TME on tumor metabolism and proliferation. Besides, the classifier allowed a further subdivision of patients with early- and late-HCC stages. In addition, the Hypoxia-TME classifier was validated in another independent HBV-HCC cohort (n=144) and several pan-cancer cohorts. Overall, the Hypoxia-TME classifier showed a pretreatment predictive value for prognosis and therapeutic responses, which might provide new directions for strategizing patients with optimal therapies. This article is protected by copyright. All rights reserved