Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, \ldots). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes ($n< 10^4$). This computational issue is addressed by first describing a new efficient and exact algorithm for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It allows dealing with medium size signals (up to $n \approx 10^5$). Second, a faster but approximation algorithm is described. It is based on a low-rank approximation to the Gram matrix. It is linear in time and space. This approximation algorithm can be applied to large-scale signals ($n \geq 10^6$). These exact and approximation algorithms have been implemented in \texttt{R} and \texttt{C} for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies. An R package implementing the approach will be made available on github.

Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the fact that there are exponentially many variable combinations to potentially consider, and there are infinitely many if we consider weighted combinations, even for linear combinations. Hence, an obvious question is whether we can automate the search for interesting patterns and visualizations. In this paper, we consider the setting where a user wants to learn as efficiently as possible about real-valued attributes. For example, to understand the distribution of crime rates in different geographic areas in terms of other (numerical, ordinal and/or categorical) variables that describe the areas. We introduce a method to find subgroups in the data that are maximally informative (in the formal Information Theoretic sense) with respect to a single or set of real-valued target attributes. The subgroup descriptions are in terms of a succinct set of arbitrarily-typed other attributes. The approach is based on the Subjective Interestingness framework FORSIED to enable the use of prior knowledge when finding most informative non-redundant patterns, and hence the method also supports iterative data mining.

Evaluating human brain potentials during watching different images can be used for memory evaluation, information retrieving, guilty-innocent identification and examining the brain response. In this study, the effects of watching images, with different levels of familiarity, on subjects' Electroencephalogram (EEG) have been studied. Three different groups of images with three familiarity levels of "unfamiliar", "familiar" and "very familiar" have been considered for this study. EEG signals of 21 subjects (14 men) were recorded. After signal acquisition, pre-processing, including noise and artifact removal, were performed on epochs of data. Features, including spatial-statistical, wavelet, frequency and harmonic parameters, and also correlation between recording channels, were extracted from the data. Then, we evaluated the efficiency of the extracted features by using p-value and also an orthogonal feature selection method (combination of Gram-Schmitt method and Fisher discriminant ratio) for feature dimensional reduction. As the final step of feature selection, we used 'add-r take-away l' method for choosing the most discriminative features. For data classification, including all two-class and three-class cases, we applied Support Vector Machine (SVM) on the extracted features. The correct classification rates (CCR) for "unfamiliar-familiar", "unfamiliar-very familiar" and "familiar-very familiar" cases were 85.6%, 92.6%, and 70.6%, respectively. The best results of classifications were obtained in pre-frontal and frontal regions of brain. Also, wavelet, frequency and harmonic features were among the most discriminative features. Finally, in three-class case, the best CCR was 86.8%.

Understanding tie strength in social networks, and the factors that influence it, have received much attention in a myriad of disciplines for decades. Several models incorporating indicators of tie strength have been proposed and used to quantify relationships in social networks, and a standard set of structural network metrics have been applied to predominantly online social media sites to predict tie strength. Here, we introduce the concept of the "social bow tie" framework, a small subgraph of the network that consists of a collection of nodes and ties that surround a tie of interest, forming a topological structure that resembles a bow tie. We also define several intuitive and interpretable metrics that quantify properties of the bow tie. We use random forests and regression models to predict categorical and continuous measures of tie strength from different properties of the bow tie, including nodal attributes. We also investigate what aspects of the bow tie are most predictive of tie strength in two distinct social networks: a collection of 75 rural villages in India and a nationwide call network of European mobile phone users. Our results indicate several of the bow tie metrics are highly predictive of tie strength, and we find the more the social circles of two individuals overlap, the stronger their tie, consistent with previous findings. However, we also find that the more tightly-knit their non-overlapping social circles, the weaker the tie. This new finding complements our current understanding of what drives the strength of ties in social networks.

Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyis entropy estimator, called information potential (IP), is a popular MEE cost in information theoretic learning (ITL). The computational complexity of IP is however quadratic in terms of sample number due to double summation. This creates computational bottlenecks especially for large-scale datasets. To address this problem, in this work we propose an efficient quantization approach to reduce the computational burden of IP, which decreases the complexity from O(N*N) to O (MN) with M << N. The new learning criterion is called the quantized MEE (QMEE). Some basic properties of QMEE are presented. Illustrative examples are provided to verify the excellent performance of QMEE.

Machine learning has been used for years to offer image recognition, spam detection, natural speech comprehension, product recommendations, and medical diagnoses. Today, machine learning algorithms can help us enhance cybersecurity, ensure public safety, and improve medical outcomes. Machine learning systems can also make customer service better and automobiles safer. When I started experimenting with machine learning, I wanted to come up with an application that would solve a real-world problem but would not be too complicated to implement. I also wanted to practice working with regression algorithms.

K-nearest neighbors(KNN for short) is one of the simplest Machine Learning algorithm. KNN is a supervised learning algorithm which can be used for both classification and regression. This is slightly different from the algorithms that we have seen so far. Let me explain this algorithm with an example of classification problem. First step in KNN is to plot training data in a feature space.

Welcome to the second stepping stone of Supervised Machine Learning. Again, this chapter is divided into two parts. Part 2 (here) we take on small coding exercise challenge. If you haven't read the Naive Bayes, I would suggest you to read it thorough here. Don't worry, we shall learn in laymen terms.

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency, and subjective human factors. We developed a novel data-driven geological feature detection approach based on pre-stack seismic measurements. Our detection method employs an efficient and accurate machine-learning detection approach to extract useful subsurface geologic features automatically. Specifically, our method is based on kernel ridge regression model. The conventional kernel ridge regression can be computationally prohibited because of the large volume of seismic measurements. We employ a data reduction technique in combination with the conventional kernel ridge regression method to improve the computational efficiency and reduce memory usage. In particular, we utilize a randomized numerical linear algebra technique, named Nystr\"om method, to effectively reduce the dimensionality of the feature space without compromising the information content required for accurate detection. We provide thorough computational cost analysis to show efficiency of our new geological feature detection methods. We further validate the performance of our new subsurface geologic feature detection method using synthetic surface seismic data for 2D acoustic and elastic velocity models. Our numerical examples demonstrate that our new detection method significantly improves the computational efficiency while maintaining comparable accuracy. Interestingly, we show that our method yields a speed-up ratio on the order of $\sim10^2$ to $\sim 10^3$ in a multi-core computational environment.

Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and manifold learning techniques to capture linear, nonlinear, local, and global features in the original dataset. Dimensionality reduction ensembles are tested first on simulation data and then on two real medical datasets using random forest classifiers; results suggest the efficacy of this approach, with accuracies approaching that of the full dataset. Limitations include computational cost of some algorithms with strong performance, which may be ameliorated through distributed computing and the development of more efficient versions of these algorithms.