Model Based Co-clustering of Mixed Numerical and Binary Data

Data mining and knowledge discovery aim at finding useful information from typically massive collections of data, and then extracting useful knowledge from the information. To date a large number of approaches have been proposed to find useful information and discover useful knowledge; for example, decision trees, Bayesian belief networks, evidence theory, rough set theory, fuzzy set theory, kNN (k-nearest-neighborhood) classifier, neural networks, and support vector machines. However, these approaches are based on a specific data type. In the real world, an intelligent system often encounters mixed data types, incomplete information (missing values), and imprecise information (fuzzy conditions). In the UCI (University of California – Irvine) Machine Learning Repository, it can be seen that there are many real world data sets with missing values and mixed data types. It is a challenge to enable machine learning or data mining approaches to deal with mixed data types (Ching, 1995; Coppock, 2003) because there are difficulties in finding a measure of similarity between objects with mixed data type attributes. The problem with mixed data types is a long-standing issue faced in data mining. The emerging techniques targeted at this issue can be classified into three classes as follows: (1) Symbolic data mining approaches plus different discretizers (e.g., Dougherty et al., 1995; Wu, 1996; Kurgan et al., 2004; Diday, 2004; Darmont et al., 2006; Wu et al., 2007) for transformation from continuous data to symbolic data; (2) Numerical data mining approaches plus transformation from symbolic data to numerical data (e.g.,, Kasabov, 2003; Darmont et al., 2006; Hadzic et al., 2007); (3) Hybrid of symbolic data mining approaches and numerical data mining approaches (e.g.,, Tung, 2002; Kasabov, 2003; Leng et al., 2005; Wu et al., 2006). Since hybrid approaches have the potential to exploit the advantages from both symbolic data mining and numerical data mining approaches, this chapter, after discassing the merits and shortcomings of current approaches, focuses on applying Self-Organizing Computing Network Model to construct a hybrid system to solve the problems of knowledge discovery from databases with a diversity of data types. Future trends for data mining on mixed type data are then discussed. Finally a conclusion is presented.

It is common in applied research to have large numbers of variables measured on a modest number of cases. Even with low rates of missingness of individual variables, such data sets can have a large number of incomplete cases with a mix of data types. Here, we propose a new joint modeling approach to address the high-dimensional incomplete data with a mix of continuous and binary data. Specifically, we propose a multivariate normal model encompassing both continuous variables and latent variables corresponding to binary variables. We apply a parameter-extended Metropolis–Hastings algorithm to generate the covariance matrix of a mixture of continuous and binary variables. We also introduce prior distribution families for unstructured covariance matrices to reduce the dimension of the parameter space. In several simulation settings, the method is compared with available-case analysis, a rounding method, and a sequential regression method.

We introduce the DP-auto-GAN framework for synthetic data generation, which combines the low dimensional representation of autoencoders with the flexibility of Generative Adversarial Networks (GANs). This framework can be used to take in raw sensitive data and privately train a model for generating synthetic data that will satisfy similar statistical properties as the original data. This learned model can generate an arbitrary amount of synthetic data, which can then be freely shared due to the post-processing guarantee of differential privacy. Our framework is applicable to unlabeled mixed-type data, that may include binary, categorical, and real-valued data. We implement this framework on both binary data (MIMIC-III) and mixed-type data (ADULT), and compare its performance with existing private algorithms on metrics in unsupervised settings. We also introduce a new quantitative metric able to detect diversity, or lack thereof, of synthetic data.

The Umpire 2.0 R-package offers a streamlined, user-friendly workflow to simulate complex, heterogeneous, mixed-type data with known subgroup identities, dichotomous outcomes, and time-to-event data, while providing ample opportunities for fine-tuning and flexibility. Here, we describe how we have expanded the core Umpire 1.0 R-package, developed to simulate gene expression data, to generate clinically realistic, mixed-type data for use in evaluating unsupervised and supervised machine learning (ML) methods. As the availability of large-scale clinical data for ML has increased, clinical data has posed unique challenges, including widely variable size, individual biological heterogeneity, data collection and measurement noise, and mixed data types. Developing and validating ML methods for clinical data requires data sets with known ground truth, generated from simulation. Umpire 2.0 addresses challenges to simulating realistic clinical data by providing the user a series of modules to generate survival parameters and subgroups, apply meaningful additive noise, and discretize to single or mixed data types. Umpire 2.0 provides broad functionality across sample sizes, feature spaces, and data types, allowing the user to simulate correlated, heterogeneous, binary, continuous, categorical, or mixed type data from the scale of a small clinical trial to data on thousands of patients drawn from electronic health records. The user may generate elaborate simulations by varying parameters in order to compare algorithms or interrogate operating characteristics of an algorithm in both supervised and unsupervised ML.

The new student admissions was regularly held every year by all grades of education, including in IPB University. Since 2013, IPB University has a track record of every school that has succeeded in sending their graduates, even until they successfully completed their education at IPB University. It was recorded that there were 5,345 schools that included in the data. It was necessary to making every school in the data into the clusters, so IPB could see which schools were classified as good or not good in terms of sending their graduates to continue their education at IPB based on the characteristics of the clusters. This study using the k-prototypes algorithm because it can be used on the data that consisting of categorical and numerical data (mixed type data). The k-prototypes algorithm could maintain the efficiency of the k-means algorithm in handling large data sizes, but eliminated the limitations of k-means. The results showed that the optimal number of clusters in this study were four clusters. The fourth cluster (421 school members) was the best cluster related to the student admission at IPB University. On the other hand, the third cluster (391 school members) was the worst cluster in this study.

Similarity measures aim at quantifying the extent to which objects resemble each other. Many techniques in data mining, data analysis or information retrieval require a similarity measure, and selecting an appropriate measure for a given problem is a difficult task. In this paper, the diverse forms similarity measures can take are examined, as well as their relationships and respective properties. Their semantic differences are highlighted and numerical tools to quantify these differences are proposed, considering several points of view and including global and local comparisons, order-based and value-based comparisons, and mathematical properties such as derivability. The paper studies similarity measures for two types of data: binary and numerical data, i.e., set data represented by the presence or absence of characteristics and data represented by real vectors.

Cluster analysis seeks to assign objects with similar characteristics into groups called clusters so that objects within a group are similar to each other and dissimilar to objects in other groups. Spectral clustering has been shown to perform well in different scenarios on continuous data: it can detect convex and non-convex clusters, and can detect overlapping clusters. However, the constraint on continuous data can be limiting in real applications where data are often of mixed-type, i.e., data that contains both continuous and categorical features. This paper looks at extending spectral clustering to mixed-type data. The new method replaces the Euclidean-based similarity distance used in conventional spectral clustering with different dissimilarity measures for continuous and categorical variables. A global dissimilarity measure is than computed using a weighted sum, and a Gaussian kernel is used to convert the dissimilarity matrix into a similarity matrix. The new method includes an automatic tuning of the variable weight and kernel parameter. The performance of spectral clustering in different scenarios is compared with that of two state-of-the-art mixed-type data clustering methods, k-prototypes and KAMILA, using several simulated and real data sets.

It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions. The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision‐making problems from multi‐levels and multi‐angles, and the neighbourhood rough set model (NRS) can facilitate the analysis and processing of numerical or mixed type data, and can address the limitation of multigranulation decision‐theoretic rough sets (MG‐DTRS), which is not easy to cope with complex data. Based on the in‐depth study of hybrid‐valued decision systems and MG‐DTRS models, this study analysed neighbourhood MG‐DTRS (NMG‐DTRS) deeply by fusing MG‐DTRS and NRS; a matrix‐based approach for approximation sets of NMG‐DTRS model was proposed on the basis of the matrix representations of concepts; the positive, boundary and negative domains were constructed from the matrix perspective, and the concept of positive decision recognition rate was introduced. Furthermore, the authors explored the related properties of NMG‐DTRS model, and designed and described the corresponding solving algorithms in detail. Finally, some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm, but also showed the relationship between the decision recognition rate and the granularity and threshold.

Categorical structural equation modeling (SEM) methods that fit the model to estimated polychoric correlations have become popular in the social sciences. When population thresholds are high in absolute value, contingency tables in small samples are likely to contain zero frequency cells. Such cells make the estimation of the polychoric correlations more difficult. Some SEM programs use solutions such as adding .5 to the zero frequency cells. However, the adequacy of this solution has never been systematically explored in the literature. In this article, the frequency with which contingency tables with zero cells occur in small samples is explored. Second, it is explored whether or not adding .5 is in any way preferable to leaving the cell value as zero. Binary and 3-category data and a variety of threshold values and correlation values are considered. The findings suggest that the two methods of dealing with zero frequency cells have quite different properties. With binary data, the method of adding .5 is recommended, unless thresholds are opposite-signed and the underlying correlation is suspected to be large. No adjustment is recommended for greater numbers of categories.

A practical approach for hybrid distributed MPC

Integrating Genetic Risk Factors with Age, Presenting White Cell Count and MRD Response As Continuous Variables to Predict Relapse in Paediatric Acute Lymphoblastic Leukemia (ALL)

Data integration methods that analyze multiple sources of data simultaneously can often provide more holistic insights than can separate inquiries of each data source. Motivated by the advantages of data integration in the era of "big data", we investigate feature selection for high-dimensional multi-view data with mixed data types (e.g. continuous, binary, count-valued). This heterogeneity of multi-view data poses numerous challenges for existing feature selection methods. However, after critically examining these issues through empirical and theoretically-guided lenses, we develop a practical solution, the Block Randomized Adaptive Iterative Lasso (B-RAIL), which combines the strengths of the randomized Lasso, adaptive weighting schemes, and stability selection. B-RAIL serves as a versatile data integration method for sparse regression and graph selection, and we demonstrate the effectiveness of B-RAIL through extensive simulations and a case study to infer the ovarian cancer gene regulatory network. In this case study, B-RAIL successfully identifies well-known biomarkers associated with ovarian cancer and hints at novel candidates for future ovarian cancer research.

SUMMARY Consider data arranged into k 2 x 2 contingency tables. The principal result is the derivation of a statistical test for making an inference on whether each of the k contingency tables has the same relative risk. The test is based on a conditional reference set and can be regarded as an extension of the Fisher-Irwin treatment of a single 2 x 2 contingency table. Both exact and asymptotic procedures are presented. The analysis of k 2 x 2 contingency tables is required in several contexts. The two principal ones are (i) the comparison of binary response random variables, i.e. random variables taking on the values zero or one, for two treatments, over a spectrum of different conditions or populations; and (ii) the comparison of the degree of association among two binary random variables over k different populations. Cochran (1954) has investigated this problem with respect to testing if the success probability for each of two treatments is the same for every contingency table. Cochran's recommendation is that the equality of the two success probabilities should be tested using the total number, summed over all tables, of successes for one of the treatments. Cochran considers the asymptotic distribution of the total number of successes, for one of the treatments, conditional on all marginals being fixed in every table. He recommends this technique whenever the difference between the two populations on a logistic or probit scale is nearly constant for each contingency table. The constant logistic difference is equivalent to the relative risk being equal for each table. Mantel & Haenlszel (1959), in an important paper discussing retrospective studies, have also proposed an asymptotic method for analysing several 2 x 2 contingency tables. Their worlk on this problem was evidently done independently of Cochran, for their method is exactly the same as Cochran's except for a modification dealing with the correction factor associated with a finite population. Birch (1964) and Cox (1966) clarified the problem by showing, that under the assumption of constant logistic differences for each table, same relative risk, the conditional distribution of the total number of successes, for one of the treatments, leads to a uniformly most powerful unbiased test. Birch and Cox also derived the exact probability distribution of this conditional random variable under the given model. In this paper, we investigate the more general situation where the difference between the logits in each table is not necessarily constant. Procedures are derived for making an inference with regard to the hypothesis of constant logistic differences. Both the exact and asymptotic distributions are derived for the null and nonnull cases. This problem has been discussed by several investigators. A constant logistic difference corresponds to no interaction between the treatments and the k populations. The case k = 2 corresponds to one in which Bartlett (1935) has derived both an exact and an asymptotic procedure. Norton (1945)

Optimizing flood predictions by integrating LSTM and physical-based models with mixed historical and simulated data

The natural performance of the location model is a potential tool for allocating an object into one of the two observed groups involving mixtures of continuous and binary variables. In constructing location model, continuous variable is used to estimate parameters while binary variable is utilized to create segmentation in each group. Such segmentation is called as multinomial cells. Basically, the multinomial cells will grow exponentially according to the number of the binary variable. These multinomial cells will become empty when there is no object can be assigned into some of them. Then the occurring of empty cells will lead to unreliable parameter estimation. Consequently, the construction of the discriminant rule based on location model is impossible. Therefore, this paper attempts to discuss how the location model based on maximum likelihood estimation can be constructed even dealing with many measured binary variables. In other word, how is location model able to deal with the issue of many empty ...