Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtained via linear transformation of latent representations that are easy to cluster; but in practice, the transformation from the latent space to the data can be more complicated. In this work, we assume that this transformation is an unknown and possibly nonlinear function. To recover the clustering-friendly' latent representations and to better cluster the data, we propose a joint DR and K-means clustering approach in which DR is accomplished via learning a deep neural network (DNN). The motivation is to keep the advantages of jointly optimizing the two tasks, while exploiting the deep neural network's ability to approximate any nonlinear function. This way, the proposed approach can work well for a broad class of generative models. Towards this end, we carefully design the DNN structure and the associated joint optimization criterion, and propose an effective and scalable algorithm to handle the formulated optimization problem. Experiments using different real datasets are employed to showcase the effectiveness of the proposed approach.
The data model @math in the above line of work may be oversimplified: The data generating process can be much more complex than this linear transform. Therefore, it is well justified to seek powerful non-linear transforms, e.g. DNNs, to model this data generating process, while at the same time make use of the joint DR and clustering idea. Two recent works, @cite_12 and @cite_24 , made such attempts.
@cite_24 @cite_12
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Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtained via linear transformation of latent representations that are easy to cluster; but in practice, the transformation from the latent space to the data can be more complicated. In this work, we assume that this transformation is an unknown and possibly nonlinear function. To recover the clustering-friendly' latent representations and to better cluster the data, we propose a joint DR and K-means clustering approach in which DR is accomplished via learning a deep neural network (DNN). The motivation is to keep the advantages of jointly optimizing the two tasks, while exploiting the deep neural network's ability to approximate any nonlinear function. This way, the proposed approach can work well for a broad class of generative models. Towards this end, we carefully design the DNN structure and the associated joint optimization criterion, and propose an effective and scalable algorithm to handle the formulated optimization problem. Experiments using different real datasets are employed to showcase the effectiveness of the proposed approach. Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtained via linear transformation of latent representations that are easy to cluster; but in practice, the transformation from the latent space to the data can be more complicated. In this work, we assume that this transformation is an unknown and possibly nonlinear function. To recover the 'clustering-friendly' latent representations and to better cluster the data, we propose a joint DR and K-means clustering approach in which DR is accomplished via learning a deep neural network (DNN). The motivation is to keep the advantages of jointly optimizing the two tasks, while exploiting the deep neural network's ability to approximate any nonlinear function. This way, the proposed approach can work well for a broad class of generative models. Towards this end, we carefully design the DNN structure and the associated joint optimization criterion, and propose an effective and scalable algorithm to handle the formulated optimization problem. Experiments using different real datasets are employed to showcase the effectiveness of the proposed approach. Linear or non-linear data transformations are widely used processing techniques in clustering. Usually, they are beneficial to enhancing data representation. However, if data have a complex structure, these techniques would be unsatisfying for clustering. In this paper, based on the auto-encoder network, which can learn a highly non-linear mapping function, we propose a new clustering method. Via simultaneously considering data reconstruction and compactness, our method can obtain stable and effective clustering. Experiments on three databases show that the proposed clustering model achieves excellent performance in terms of both accuracy and normalized mutual information. We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is trivial, yet we maintain the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy. We show that this approach yields good generative models on four image datasets and can be used for inpainting.