Kernel Clustering with Sigmoid-based Regularization for Efficient Segmentation of Sequential Data

Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A popular algorithm for optimally solving this problem is dynamic programming (DP), which has quadratic computation and memory requirements. Given that sequences in practice are too long, this algorithm is not a practical approach. Although many heuristic algorithms have been proposed to approximate the optimal segmentation, they have no guarantee on the quality of their solutions. In this paper, we take a differentiable approach to alleviate the aforementioned issues. First, we introduce a novel sigmoid-based regularization to smoothly approximate the combinatorial constraints. Combining it with objective of the balanced kernel clustering, we formulate a differentiable model termed Kernel clustering with sigmoid-based regularization (KCSR), where the gradient-based algorithm can be exploited to obtain the optimal segmentation. Second, we develop a stochastic variant of the proposed model. By using the stochastic gradient descent algorithm, which has much lower time and space complexities, for optimization, the second model can perform segmentation on overlong data sequences. Finally, for simultaneously segmenting multiple data sequences, we slightly modify the sigmoid-based regularization to further introduce an extended variant of the proposed model. Through extensive experiments on various types of data sequences performances of our models are evaluated and compared with those of the existing methods. The experimental results validate advantages of the proposed models. Our Matlab source code is available on github.

Guaranteed inference in topic models

One of the core problems in statistical models is the estimation of a posterior distribution. For topic models, the problem of posterior inference for individual texts is particularly important, especially when dealing with data streams, but is often intractable in the worst case. As a consequence, existing methods for posterior inference are approximate and do not have any guarantee on neither quality nor convergence rate. In this paper, we introduce a provably fast algorithm, namely Online Maximum a Posteriori Estimation (OPE), for posterior inference in topic models. OPE has more attractive properties than existing inference approaches, including theoretical guarantees on quality and fast rate of convergence to a local maximal/stationary point of the inference problem. The discussions about OPE are very general and hence can be easily employed in a wide range of contexts. Finally, we employ OPE to design three methods for learning Latent Dirichlet Allocation from text streams or large corpora. Extensive experiments demonstrate some superior behaviors of OPE and of our new learning methods.