In this paper, we propose a new methodology based on the Negative Selection Algorithm that belongs to the field of Computational Intelligence, specifically, Artificial Immune Systems to identify takeover targets. Although considerable research based on customary statistical techniques and some contemporary Computational Intelligence techniques have been devoted to identify takeover targets, most of the existing studies are based upon multiple previous mergers and acquisitions. Contrary to previous research, the novelty of this proposal lies in its ability to suggest takeover targets for novice firms that are at the beginning of their merger and acquisition spree. We first discuss the theoretical perspective and then provide a case study with details for practical implementation, both capitalizing from unique generalization capabilities of artificial immune systems algorithms.

This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".

Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which operate on such data should be sensitive to the privacy risks in publishing their outputs. Differential privacy is a framework for developing tradeoffs between privacy and the utility of these outputs. In this paper we investigate the theory and empirical performance of differentially private approximations to PCA and propose a new method which explicitly optimizes the utility of the output. We show that the sample complexity of the proposed method differs from the existing procedure in the scaling with the data dimension, and that our method is nearly optimal in terms of this scaling. We furthermore illustrate our results, showing that on real data there is a large performance gap between the existing method and our method.

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended to a broader class of operators in the Gaussian case, via the Lo\`eve isometry. Several covariance-driven pathwise invariances are illustrated, including fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process regression.

Consensus clustering emerges as a promising solution to find cluster structures from data. As an efficient approach for consensus clustering, the K-means based method has garnered attention in the literature, but the existing research is still preliminary and fragmented. In this paper, we provide a systematic study on the framework of K-means-based Consensus Clustering (KCC). We first formulate the general definition of KCC, and then reveal a necessary and sufficient condition for utility functions that work for KCC, on both complete and incomplete basic partitionings. Experimental results on various real-world data sets demonstrate that KCC is highly efficient and is comparable to the state-of-the-art methods in terms of clustering quality. In addition, KCC shows high robustness to incomplete basic partitionings with substantial missing values.

Cepstral features have been widely used in audio applications. Domain knowledge has played an important role in designing different types of cepstral features proposed in the literature. In this paper, we present a novel approach for learning optimized cepstral features directly from audio data to better discriminate between different categories of signals in classification tasks. We employ multi-layer feedforward neural networks to model the cepstral feature extraction process. The network weights are initialized to replicate a reference cepstral feature like the mel frequency cepstral coefficient. We then propose a embedded approach that integrates feature learning with the training of a support vector machine (SVM) classifier. A single optimization problem is formulated where the feature and classifier variables are optimized simultaneously so as to refine the initial features and minimize the classification risk. Experimental results have demonstrated the effectiveness of the proposed feature learning approach, outperforming competing methods by a large margin on benchmark data.

Bag-of-Words approach has played an important role in recent works for image classification. In consideration of efficiency, most methods use k-means clustering to generate the codebook. The obtained codebooks often lose the cluster size and shape information with distortion errors and low discriminative power. Though some efforts have been made to optimize codebook in sparse coding, they usually incur higher computational cost. Moreover, they ignore the correlations between codes in the following coding stage, that leads to low discriminative power of the final representation. In this paper, we propose a bilevel visual words coding approach in consideration of representation ability, discriminative power and efficiency. In the bilevel codebook generation stage, k-means and an efficient spectral clustering are respectively run in each level by taking both class information and the shapes of each visual word cluster into account. To obtain discriminative representation in the coding stage, we design a certain localized coding rule with bilevel codebook to select local bases. To further achieve an efficient coding referring to this rule, an online method is proposed to efficiently learn a projection of local descriptor to the visual words in the codebook. After projection, coding can be efficiently completed by a low dimensional localized soft-assignment. Experimental results show that our proposed bilevel visual words coding approach outperforms the state-of-the-art approaches for image classification.

Facing a large number of clustering solutions, cluster ensemble method provides an effective approach to aggregating them into a better one. In this paper, we propose a novel cluster ensemble method from probabilistic perspective. It assumes that each clustering solution is generated from a latent cluster model, under the control of two probabilistic parameters. Thus, the cluster ensemble problem is reformulated into an optimization problem of maximum likelihood. An EM-style algorithm is designed to solve this problem. It can determine the number of clusters automatically. Experimenal results have shown that the proposed algorithm outperforms the state-of-the-art methods including EAC-AL, CSPA, HGPA, and MCLA. Furthermore, it has been shown that our algorithm is stable in the predicted numbers of clusters.

Matrix factorization (MF) is a popular collaborative filtering approach for recommender systems due to its simplicity and effectiveness. Existing MF methods either assume that all latent features are uncorrelated or assume that all are correlated. To address the important issue of what structure should be imposed on the features, we investigate the covariance matrix of the latent features learned from real data. Based on the findings, we propose an MF model with a sparse covariance prior which favors a sparse yet non-diagonal covariance matrix. Not only can this reflect the semantics more faithfully, but imposing sparsity can also have a side effect of preventing overfitting. Starting from a probabilistic generative model with a sparse covariance prior, we formulate the model inference problem as a maximum a posteriori (MAP) estimation problem. The optimization procedure makes use of stochastic gradient descent and majorization-minimization. For empirical validation, we conduct experiments using the MovieLens and Netflix datasets to compare the proposed method with two strong baselines which use different priors. Experimental results show that our sparse covariance prior can lead to performance improvement.

The Nyström method is a well known sampling based low-rank matrix approximation approach. It is usually considered to be originated from the numerical treatment of integral equations and eigendecomposition of matrices. In this paper, we present a novel point of view for the Nyström approximation. We show that theoretically the Nyström method can be regraded as a set of point-wise ordinary least square linear regressions of the kernel matrix, sharing the same design matrix. With the new interpretation, we are able to analyze the approximation quality based on the fulfillment of the homoscedasticity assumption and explain the success and deficiency of various sampling methods. We also empirically show that positively skewed explanatory variable distributions can lead to heteroscedasticity. Based on this discovery, we propose to use non-symmetric explanatory functions to improve the quality of the Nyström approximation with almost no extra computational cost. Experiments show that positively skewed datasets widely exist, and our method exhibits good improvements on these datasets.