This contribution is from David Corliss. David teaches a class on this subject, giving a (very brief) description of 23 regression methods in just an hour, with an example and the package and procedures used for each case. Here you can check the webcast done for Central Michigan University. The slide deck can be found here. Below is the presentation transcript.

Ensemble Clustering (EC) has gained a great deal of attention throughout the fields of data mining and machine learning, since it emerged as an effective and robust clustering framework. Typically, EC methods try to fuse multiple basic partitions (BPs) into a consensus one, of which each BP is obtained by performing traditional clustering method on the same dataset. One promising direction for ensemble clustering is to derive pairwise similarity from BPs, and then transform it as a graph partition problem. However, these graph based methods may suffer from an information loss when computing the similarity between data points, because they only utilize the categorical data provided by multiple BPs, yet neglect rich information from raw features. This problem can badly undermine the underlying cluster structure in the original feature space, and thus degrade the clustering performance. In light of this, we propose a novel Simultaneous Clustering and Ensemble (SCE) framework to alleviate such detrimental effect, which employs the similarity matrix from raw features to enhance the co-association matrix summarized by multiple BPs. Two neat closed-form solutions given by eigenvalue decomposition are provided for SCE. Experiments conducted on 16 real-world datasets demonstrate the effectiveness of the proposed SCE over the traditional clustering and state-of-the-art ensemble clustering methods. Moreover, several impact factors that may affect our method are also explored extensively.

The dynamic Boltzmann machine (DyBM) has been proposed as a stochastic generative model of multi-dimensional time series, with an exact, learning rule that maximizes the log-likelihood of a given time series. The DyBM, however, is defined only for binary valued data, without any nonlinear hidden units. Here, in our first contribution, we extend the DyBM to deal with real valued data. We present a formulation called Gaussian DyBM, that can be seen as an extension of a vector autoregressive (VAR) model. This uses, in addition to standard (explanatory) variables, components that captures long term dependencies in the time series. In our second contribution, we extend the Gaussian DyBM model with a recurrent neural network (RNN) that controls the bias input to the DyBM units. We derive a stochastic gradient update rule such that, the output weights from the RNN can also be trained online along with other DyBM parameters. Furthermore, this acts as nonlinear hidden layer extending the capacity of DyBM and allows it to model nonlinear components in a given time-series. Numerical experiments with synthetic datasets show that the RNN-Gaussian DyBM improves predictive accuracy upon standard VAR by up to 35%. On real multi-dimensional time-series prediction, consisting of high nonlinearity and non-stationarity, we demonstrate that this nonlinear DyBM model achieves significant improvement upon state of the art baseline methods like VAR and long short-term memory (LSTM) networks at a reduced computational cost.

Matrix completion as a common problem in many application domains has received increasing attention in the machine learning community. Previous matrix completion methods have mostly focused on exploiting the matrix low-rank property to recover missing entries. Recently, it has been noticed that side information that describes the matrix items can help to improve the matrix completion performance. In this paper, we propose a novel matrix completion approach that exploits side information within a principled co-embedding framework. This framework integrates a low-rank matrix factorization model and a label embedding based prediction model together to derive a convex co-embedding formulation with nuclear norm regularization. We develop a fast proximal gradient descent algorithm to solve this co-embedding problem. The effectiveness of the proposed approach is demonstrated on two types of real world application problems.

With the advance of acquisition techniques, plentiful higherorder tensor data sets are built up in a great variety of fields such as computer vision, neuroscience, remote sensing and recommender systems. The real-world tensors often contain missing values, which makes tensor completion become a prerequisite to utilize them. Previous studies have shown that imposing a low-rank constraint on tensor completion produces impressive performances. In this paper, we argue that low-rank constraint, albeit useful, is not effective enough to exploit the local smooth and piecewise priors of visual data. We propose integrating total variation into low-rank tensor completion (LRTC) to address the drawback. As LRTC can be formulated by both tensor unfolding and tensor decomposition, we develop correspondingly two methods, namely LRTC-TV-I and LRTC-TVII, and their iterative solvers. Extensive experimental results on color image and medical image inpainting tasks show the effectiveness and superiority of the two methods against state-of-the-art competitors.

A clustering agreement index quantifies the similarity between two given clusterings. It is most commonly used to compare the results obtained from different clustering algorithms against the ground-truth clustering in the benchmark datasets. In this paper, we present a general Clustering Agreement Index (CAI) for comparing disjoint and overlapping clusterings. CAI is generic and introduces a family of clustering agreement indexes. In particular, the two widely used indexes of Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI), are special cases of the CAI. Our index, therefore, provides overlapping extensions for both these commonly used indexes, whereas their original formulations are only defined for disjoint cases. Lastly, unlike previous indexes, CAI is flexible and can be adapted to incorporate the structure of the data, which is important when comparing clusters in networks, a.k.a communities.

Latent tree analysis seeks to model the correlations amonga set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis—a method widely used in social sciences and medicine to identify homogeneous subgroups in a population. It provides new and fruitful perspectives on a number of machine learningareas, including cluster analysis, topic detection, and deep probabilistic modeling. This paper gives an overview of the research on latent tree analysis and various ways it is used inpractice.

As an interesting and emerging topic, zero-shot recognition (ZSR) makes it possible to train a recognition model by specifying the category's attributes when there are no labeled exemplars available. The fundamental idea for ZSR is to transfer knowledge from the abundant labeled data in different but related source classes via the class attributes. Conventional ZSR approaches adopt a two-step strategy in test stage, where the samples are projected into the attribute space in the first step, and then the recognition is carried out based on considering the relationship between samples and classes in the attribute space. Due to this intermediate transformation, information loss is unavoidable, thus degrading the performance of the overall system. Rather than following this two-step strategy, in this paper, we propose a novel one-step approach that is able to perform ZSR in the original feature space by using directly trained classifiers. To tackle the problem that no labeled samples of target classes are available, we propose to assign pseudo labels to samples based on the reliability and diversity, which in turn will be used to train the classifiers. Moreover, we adopt a robust SVM that accounts for the unreliability of pseudo labels. Extensive experiments on four datasets demonstrate consistent performance gains of our approach over the state-of-the-art two-step ZSR approaches.

Neural network language models (NNLMs) have attracted a lot of attention recently. In this paper, we present a training method that can incrementally train the hierarchical softmax function for NNMLs. We split the cost function to model old and update corpora separately, and factorize the objective function for the hierarchical softmax. Then we provide a new stochastic gradient based method to update all the word vectors and parameters, by comparing the old tree generated based on the old corpus and the new tree generated based on the combined (old and update) corpus. Theoretical analysis shows that the mean square error of the parameter vectors can be bounded by a function of the number of changed words related to the parameter node. Experimental results show that incremental training can save a lot of time. The smaller the update corpus is, the faster the update training process is, where an up to 30 times speedup has been achieved. We also use both word similarity/relatedness tasks and dependency parsing task as our benchmarks to evaluate the correctness of the updated word vectors.

Developed so far, multi-document summarization has reached its bottleneck due to the lack of sufficient training data and diverse categories of documents. Text classification just makes up for these deficiencies. In this paper, we propose a novel summarization system called TCSum, which leverages plentiful text classification data to improve the performance of multi-document summarization. TCSum projects documents onto distributed representations which act as a bridge between text classification and summarization. It also utilizes the classification results to produce summaries of different styles. Extensive experiments on DUC generic multi-document summarization datasets show that, TCSum can achieve the state-of-the-art performance without using any hand-crafted features and has the capability to catch the variations of summary styles with respect to different text categories.