Prem Raj Adhikari

Patterns from multiresolution 0-1 data

Biological systems are complex systems and often the biological data is available in different resolutions. Computational algorithms are often designed to work with only specific resolution of data. Hence, upsampling or downsampling is necessary before the data can be fed to the algorithm. Moreover, high-resolution data incorporates significant amount of noise thus producing explosion of redundant patterns such as maximal frequent itemset, closed frequent itemset and non-derivable itemset in the data which can be solved by downsampling the data if the information loss is insignificant during sampling. Furthermore, comparing the results of an algorithm on data in different resolution can produce interesting results which aids in determining suitable resolution of data. In addition, experiments in different resolutions can be helpful in determining the appropriate resolution for computational methods. In this paper, three methods of downsampling are proposed, implemented and experiments are performed on different resolutions and the suitability of the proposed methods are validated and the results compared. Mixture models are trained on the data and the results are analyzed and it was seen that the proposed methods produce plausible results showing that the significant patterns in the data are retained in lower resolution. The proposed methods can be extensively used in integration of databases.

Explaining mixture models through semantic pattern mining and banded matrix visualization

This paper presents an approach to semi-automated data analysis, supported by tools for pattern construction, exploration and explanation. The proposed three-part methodology for multiresolution 0–1 data analysis consists of data clustering with mixture models, extraction of rules from clusters, as well as data and rule visualization using banded matrices. The results of the three-part process: clusters, rules from clusters, and banded structure of the data matrix are finally merged in a unified visual banded matrix display. The incorporation of multiresolution data is enabled by the supporting ontology, describing the relationships between the different resolutions, which is used as background knowledge in the semantic pattern mining process of descriptive rule induction. The presented experimental use case highlights the usefulness of the proposed methodology for analyzing complex DNA copy number amplification data, studied in previous research, for which we provide new insights in terms of induced semantic patterns and cluster/pattern visualization. The methodology is successfully evaluated on four other publicly available data sets, which further demonstrates the utility of the proposed approach.

Fast progressive training of mixture models for model selection

Finite mixture models (FMM) are flexible models with varying uses such as density estimation, clustering, classification, modeling heterogeneity, model averaging, and handling missing data. Expectation maximization (EM) algorithm can learn the maximum likelihood estimates for the model parameters. One of the prerequisites for using the EM algorithm is the a priori knowledge of the number of mixture components in the mixture model. However, the number of mixing components is often unknown. Therefore, determining the number of mixture components has been a central problem in mixture modelling. Thus, mixture modelling is often a two-stage process of determining the number of mixture components and then estimating the parameters of the mixture model. This paper proposes a fast training of a series of mixture models using progressive merging of mixture components to facilitate model selection algorithm to make appropriate choice of the model. The paper also proposes a data driven, fast approximation of the Kullback–Leibler (KL) divergence as a criterion to measure the similarity of the mixture components. We use the proposed methodology in mixture modelling of a synthetic dataset, a publicly available zoo dataset, and two chromosomal aberration datasets showing that model selection is efficient and effective.

Preservation of statistically significant patterns in multiresolution 0-1 data

Measurements in biology are made with high throughput and high resolution techniques often resulting in data in multiple resolutions. Currently, available standard algorithms can only handle data in one resolution. Generative models such as mixture models are often used to model such data. However, significance of the patterns generated by generative models has so far received inadequate attention. This paper analyses the statistical significance of the patterns preserved in sampling between different resolutions and when sampling from a generative model. Furthermore, we study the effect of noise on the likelihood with respect to the changing resolutions and sample size. Finite mixture of multivariate Bernoulli distribution is used to model amplification patterns in cancer in multiple resolutions. Statistically significant itemsets are identified in original data and data sampled from the generative models using randomization and their relationships are studied. The results showed that statistically significant itemsets are effectively preserved by mixture models. The preservation is more accurate in coarse resolution compared to the finer resolution. Furthermore, the effect of noise on data on higher resolution and with smaller number of sample size is higher than the data in lower resolution and with higher number of sample size.

Fast Progressive Training of Mixture Models for Model Selection

Finite Mixture Models are flexible models with varying uses such as density estimation, clustering, classification, modeling heterogeneity, model averaging, and handling missing data. One of the prerequisites of using mixture models is the a priori knowledge of the number of mixture components so that the Expectation Maximization (EM) algorithm can learn the maximum likelihood parameters of the mixture model. However, the number of mixing components is often unknown and determining the number of mixture components has been a central problem in mixture modelling. Thus, mixture modelling is often a two-stage process of determining the number of mixture components and then estimating the parameters of the mixture model. This paper proposes a fast, search-based model selection algorithm for mixture models using progressive merging of mixture components. The paper also proposes a data driven, fast approximation of the Kullback-Leibler (KL) divergence as a criterion to merge the mixture components. The proposed methodology is used in mixture modelling of two chromosomal aberration datasets showing that model selection is efficient and effective.

Explaining Mixture Models through Semantic Pattern Mining and Banded Matrix Visualization

Semi-automated data analysis is possible for the end user if data analysis processes are supported by easily accessible tools and methodologies for pattern/model construction, explanation, and exploration. The proposed three–part methodology for multiresolution 0–1 data analysis consists of data clustering with mixture models, extraction of rules from clusters, as well as data, cluster, and rule visualization using banded matrices. The results of the three-part process—clusters, rules from clusters, and banded structure of the data matrix—are finally merged in a unified visual banded matrix display. The incorporation of multiresolution data is enabled by the supporting ontology, describing the relationships between the different resolutions, which is used as background knowledge in the semantic pattern mining process of descriptive rule induction. The presented experimental use case highlights the usefulness of the proposed methodology for analyzing complex DNA copy number amplification data, studied in previous research, for which we provide new insights in terms of induced semantic patterns and cluster/pattern visualization.

Gene selection in time-series gene expression data

The dimensionality of biological data is often very high. Feature selection can be used to tackle the problem of high dimensionality. However, majority of the work in feature selection consists of supervised feature selection methods which require class labels. The problem further escalates when the data is time-series gene expression measurements that measure the effect of external stimuli on biological system. In this paper we propose an unsupervised method for gene selection from time-series gene expression data founded on statistical significance testing and swap randomization. We perform experiments with a publicly available mouse gene expression dataset and also a human gene expression dataset describing the exposure to asbestos. The results in both datasets show a considerable decrease in number of genes.

Resolution Transfer in Cancer Classification Based on Amplification Patterns

In the current scientific age, the measurement technology has considerably improved and diversified producing data in different representations. Traditional machine learning and data mining algorithms can handle data only in a single representation in their standard form. In this contribution, we address an important challenge encountered in data analysis: what to do when the data to be analyzed are represented differently with regards to the resolution? Specifically, in classification, how to train a classifier when class labels are available only in one resolution and missing in the other resolutions? The proposed methodology learns a classifier in one data resolution and transfers it to learn the class labels in a different resolution. Furthermore, the methodology intuitively works as a dimensionality reduction method. The methodology is evaluated on a simulated dataset and finally used to classify cancers in a real–world multiresolution chromosomal aberration dataset producing plausible results.

Mixture Models from Multiresolution 0-1 Data

Multiresolution data has received considerable research interest due to the practical usefulness in combining datasets in different resolutions into a single analysis. Most models and methods can only model a single data resolution, that is, vectors of the same dimensionality, at a time. This is also true for mixture models, the model of interest. In this paper, we propose a multiresolution mixture model capable of modeling data in multiple resolutions. Firstly, we define the multiresolution component distributions of mixture models from the domain ontology. We then learn the parameters of the component distributions in the Bayesian network framework. Secondly, we map the multiresolution data in a Bayesian network setting to a vector representation to learn the mixture coefficients and the parameters of the component distributions. We investigate our proposed algorithms on two data sets. A simulated data allows us to have full data observations in all resolutions. However, this is unrealistic in all practical applications. The second data consists of DNA aberrations data in two resolutions. The results with multiresolution models show improvement in modeling performance with regards to the likelihood over single resolution mixture models.