A New Approach for Mining Order-Preserving Submatrices Based on All Common Subsequences

Order-preserving submatrices (OPSMs) have been applied in many fields, such as DNA microarray data analysis, automatic recommendation systems, and target marketing systems, as an important unsupervised learning model. Unfortunately, most existing methods are heuristic algorithms which are unable to reveal OPSMs entirely in NP-complete problem. In particular, deep OPSMs, corresponding to long patterns with few supporting sequences, incur explosive computational costs and are completely pruned by most popular methods. In this paper, we propose an exact method to discover all OPSMs based on frequent sequential pattern mining. First, an existing algorithm was adjusted to disclose all common subsequence (ACS) between every two row sequences, and therefore all deep OPSMs will not be missed. Then, an improved data structure for prefix tree was used to store and traverse ACS, and Apriori principle was employed to efficiently mine the frequent sequential pattern. Finally, experiments were implemented on gene and synthetic datasets. Results demonstrated the effectiveness and efficiency of this method

SUBIC: A Supervised Bi-Clustering Approach for Precision Medicine

Traditional medicine typically applies one-size-fits-all treatment for the entire patient population whereas precision medicine develops tailored treatment schemes for different patient subgroups. The fact that some factors may be more significant for a specific patient subgroup motivates clinicians and medical researchers to develop new approaches to subgroup detection and analysis, which is an effective strategy to personalize treatment. In this study, we propose a novel patient subgroup detection method, called Supervised Biclustring (SUBIC) using convex optimization and apply our approach to detect patient subgroups and prioritize risk factors for hypertension (HTN) in a vulnerable demographic subgroup (African-American). Our approach not only finds patient subgroups with guidance of a clinically relevant target variable but also identifies and prioritizes risk factors by pursuing sparsity of the input variables and encouraging similarity among the input variables and between the input and target variable

Infinite Latent Feature Selection: A Probabilistic Latent Graph-Based Ranking Approach

Feature selection is playing an increasingly significant role with respect to many computer vision applications spanning from object recognition to visual object tracking. However, most of the recent solutions in feature selection are not robust across different and heterogeneous set of data. In this paper, we address this issue proposing a robust probabilistic latent graph-based feature selection algorithm that performs the ranking step while considering all the possible subsets of features, as paths on a graph, bypassing the combinatorial problem analytically. An appealing characteristic of the approach is that it aims to discover an abstraction behind low-level sensory data, that is, relevancy. Relevancy is modelled as a latent variable in a PLSA-inspired generative process that allows the investigation of the importance of a feature when injected into an arbitrary set of cues. The proposed method has been tested on ten diverse benchmarks, and compared against eleven state of the art feature selection methods. Results show that the proposed approach attains the highest performance levels across many different scenarios and difficulties, thereby confirming its strong robustness while setting a new state of the art in feature selection domain.Comment: Accepted at the IEEE International Conference on Computer Vision (ICCV), 2017, Venice. Preprint cop

Few-Shot Image Recognition by Predicting Parameters from Activations

In this paper, we are interested in the few-shot learning problem. In particular, we focus on a challenging scenario where the number of categories is large and the number of examples per novel category is very limited, e.g. 1, 2, or 3. Motivated by the close relationship between the parameters and the activations in a neural network associated with the same category, we propose a novel method that can adapt a pre-trained neural network to novel categories by directly predicting the parameters from the activations. Zero training is required in adaptation to novel categories, and fast inference is realized by a single forward pass. We evaluate our method by doing few-shot image recognition on the ImageNet dataset, which achieves the state-of-the-art classification accuracy on novel categories by a significant margin while keeping comparable performance on the large-scale categories. We also test our method on the MiniImageNet dataset and it strongly outperforms the previous state-of-the-art methods

New approaches for clustering high dimensional data

Clustering is one of the most effective methods for analyzing datasets that contain a large number of objects with numerous attributes. Clustering seeks to identify groups, or clusters, of similar objects. In low dimensional space, the similarity between objects is often evaluated by summing the difference across all of their attributes. High dimensional data, however, may contain irrelevant attributes which mask the existence of clusters. The discovery of groups of objects that are highly similar within some subsets of relevant attributes becomes an important but challenging task. My thesis focuses on various models and algorithms for this task. We first present a flexible clustering model, namely OP-Cluster (Order Preserving Cluster). Under this model, two objects are similar on a subset of attributes if the values of these two objects induce the same relative ordering of these attributes. OPClustering algorithm has demonstrated to be useful to identify co-regulated genes in gene expression data. We also propose a semi-supervised approach to discover biologically meaningful OP-Clusters by incorporating existing gene function classifications into the clustering process. This semi-supervised algorithm yields only OP-clusters that are significantly enriched by genes from specific functional categories. Real datasets are often noisy. We propose a noise-tolerant clustering algorithm for mining frequently occuring itemsets. This algorithm is called approximate frequent itemsets (AFI). Both the theoretical and experimental results demonstrate that our AFI mining algorithm has higher recoverability of real clusters than any other existing itemset mining approaches. Pair-wise dissimilarities are often derived from original data to reduce the complexities of high dimensional data. Traditional clustering algorithms taking pair-wise dissimilarities as input often generate disjoint clusters from pair-wise dissimilarities. It is well known that the classification model represented by disjoint clusters is inconsistent with many real classifications, such gene function classifications. We develop a Poclustering algorithm, which generates overlapping clusters from pair-wise dissimilarities. We prove that by allowing overlapping clusters, Poclustering fully preserves the information of any dissimilarity matrices while traditional partitioning algorithms may cause significant information loss

Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.Comment: 18 page

Density-Aware Linear Algebra in a Column-Oriented In-Memory Database System

Linear algebra operations appear in nearly every application in advanced analytics, machine learning, and of various science domains. Until today, many data analysts and scientists tend to use statistics software packages or hand-crafted solutions for their analysis. In the era of data deluge, however, the external statistics packages and custom analysis programs that often run on single-workstations are incapable to keep up with the vast increase in data volume and size. In particular, there is an increasing demand of scientists for large scale data manipulation, orchestration, and advanced data management capabilities. These are among the key features of a mature relational database management system (DBMS). With the rise of main memory database systems, it now has become feasible to also consider applications that built up on linear algebra. This thesis presents a deep integration of linear algebra functionality into an in-memory column-oriented database system. In particular, this work shows that it has become feasible to execute linear algebra queries on large data sets directly in a DBMS-integrated engine (LAPEG), without the need of transferring data and being restricted by hard disc latencies. From various application examples that are cited in this work, we deduce a number of requirements that are relevant for a database system that includes linear algebra functionality. Beside the deep integration of matrices and numerical algorithms, these include optimization of expressions, transparent matrix handling, scalability and data-parallelism, and data manipulation capabilities. These requirements are addressed by our linear algebra engine. In particular, the core contributions of this thesis are: firstly, we show that the columnar storage layer of an in-memory DBMS yields an easy adoption of efficient sparse matrix data types and algorithms. Furthermore, we show that the execution of linear algebra expressions significantly benefits from different techniques that are inspired from database technology. In a novel way, we implemented several of these optimization strategies in LAPEG’s optimizer (SpMachO), which uses an advanced density estimation method (SpProdest) to predict the matrix density of intermediate results. Moreover, we present an adaptive matrix data type AT Matrix to obviate the need of scientists for selecting appropriate matrix representations. The tiled substructure of AT Matrix is exploited by our matrix multiplication to saturate the different sockets of a multicore main-memory platform, reaching up to a speed-up of 6x compared to alternative approaches. Finally, a major part of this thesis is devoted to the topic of data manipulation; where we propose a matrix manipulation API and present different mutable matrix types to enable fast insertions and deletes. We finally conclude that our linear algebra engine is well-suited to process dynamic, large matrix workloads in an optimized way. In particular, the DBMS-integrated LAPEG is filling the linear algebra gap, and makes columnar in-memory DBMS attractive as efficient, scalable ad-hoc analysis platform for scientists