Jianlin Feng

Condensed cube: an effective approach to reducing data cube size

Pre-computed data cube facilitates OLAP (on-line analytical processing). It is well-known that data cube computation is an expensive operation. While most algorithms have been devoted to optimizing memory management and reducing computation costs, less work has addressed a fundamental issue: the size of a data cube is huge when a large base relation with a large number of attributes is involved. In this paper, we propose a new concept, called a condensed data cube. The condensed cube is of much smaller size than a complete non-condensed cube. More importantly, it is a fully pre-computed cube without compression, and, hence, it requires neither decompression nor further aggregation when answering queries. Several algorithms for computing a condensed cube are proposed. Results of experiments on the effectiveness of condensed data cube are presented, using both synthetic and real-world data. The results indicate that the proposed condensed cube can reduce both the cube size and therefore its computation time.

Knowledge Graph and Text Jointly Embedding

We examine the embedding approach to reason new relational facts from a largescale knowledge graph and a text corpus. We propose a novel method of jointly embedding entities and words into the same continuous vector space. The embedding process attempts to preserve the relations between entities in the knowledge graph and the concurrences of words in the text corpus. Entity names and Wikipedia anchors are utilized to align the embeddings of entities and words in the same space. Large scale experiments on Freebase and a Wikipedia/NY Times corpus show that jointly embedding brings promising improvement in the accuracy of predicting facts, compared to separately embedding knowledge graphs and text. Particularly, jointly embedding enables the prediction of facts containing entities out of the knowledge graph, which cannot be handled by previous embedding methods. At the same time, concerning the quality of the word embeddings, experiments on the analogical reasoning task show that jointly embedding is comparable to or slightly better than word2vec (Skip-Gram).

Mining Bucket Order-Preserving SubMatrices in Gene Expression Data

The Order-Preserving SubMatrices (OPSMs) are employed to discover significant biological associations between genes and experiment conditions. Herein, we propose a new relaxed OPSM model by considering the linearity relaxation, which is called the Bucket OPSM (BOPSM) model. An efficient method called ApriBopsm is developed to exhaustively mine such BOPSM patterns. We further generalize the BOPSM model by incorporating the similarity relaxation strategy. We develop a generalized BOPSM model called GeBOPSM and adopt a pattern growing method called SeedGrowth to mine GeBOPSM patterns. Informally, the SeedGrowth algorithm adopts two different growing strategies on rows and columns in order to expand a seed BOPSM into a maximal GeBOPSM pattern. We conduct a series of experiments using both synthetic and biological datasets to study the effectiveness of our proposed relaxed models and the efficiency of the relevant mining methods. The BOPSM model is shown to be able to capture the characteristics of noisy OPSM patterns, and is superior to the strict counterparts. ApriBopsm is also significantly more efficient than OPC-Tree, which is the state-of-the-art OPSM mining method. Compared to all the current relaxed OPSM models, the GeBOPSM model achieves the best performance in terms of the number of mined quality patterns.

Discovering significant relaxed order-preserving submatrices

Mining order-preserving submatrix (OPSM) patterns has received much attention from researchers, since in many scientific applications, such as those involving gene expression data, it is natural to express the data in a matrix and also important to find the order-preserving submatrix patterns. However, most current work assumes the noise-free OPSM model and thus is not practical in many real situations when sample contamination exists. In this paper, we propose a relaxed OPSM model called ROPSM. The ROPSM model supports mining more reasonable noise-corrupted OPSM patterns than another well-known model called AOPC (approximate order-preserving cluster). While OPSM mining is known to be an NP-hard problem, mining ROPSM patterns is even a harder problem. We propose a novel method called ROPSM-Growth to mine ROPSM patterns. Specifically, two pattern growing strategies, such as column-centric strategy and row-centric strategy, are presented, which are effective to grow the seed OPSMs into significant ROPSMs. An effective median-rank based method is also developed to discover the underlying true order of conditions involved in an ROPSM pattern. Our experiments on a biological dataset show that the ROPSM model better captures the characteristics of noise in gene expression data matrix compared to the AOPC model. Importantly, we find that our approach is able to detect more quality biologically significant patterns with comparable efficiency with the counterparts of AOPC. Specifically, at least 26.6% (75 out of 282) of the patterns mined by our approach are strongly associated with more than 10 gene categories (high biological significance), which is 3 times better than that obtained from using the AOPC approach.

Mining order-preserving submatrices from probabilistic matrices

Order-preserving submatrices (OPSMs) capture consensus trends over columns shared by rows in a data matrix. Mining OPSM patterns discovers important and interesting local correlations in many real applications, such as those involving biological data or sensor data. The prevalence of uncertain data in various applications, however, poses new challenges for OPSM mining, since data uncertainty must be incorporated into OPSM modeling and the algorithmic aspects. In this article, we define new probabilistic matrix representations to model uncertain data with continuous distributions. A novel probabilistic order-preserving submatrix (POPSM) model is formalized in order to capture similar local correlations in probabilistic matrices. The POPSM model adopts a new probabilistic support measure that evaluates the extent to which a row belongs to a POPSM pattern. Due to the intrinsic high computational complexity of the POPSM mining problem, we utilize the anti-monotonic property of the probabilistic support measure and propose an efficient Apriori-based mining framework called ProbApri to mine POPSM patterns. The framework consists of two mining methods, UniApri and NormApri, which are developed for mining POPSM patterns, respectively, from two representative types of probabilistic matrices, the UniDist matrix (assuming uniform data distributions) and the NormDist matrix (assuming normal data distributions). We show that the NormApri method is practical enough for mining POPSM patterns from probabilistic matrices that model more general data distributions. We demonstrate the superiority of our approach by two applications. First, we use two biological datasets to illustrate that the POPSM model better captures the characteristics of the expression levels of biologically correlated genes and greatly promotes the discovery of patterns with high biological significance. Our result is significantly better than the counterpart OPSMRM (OPSM with repeated measurement) model which adopts a set-valued matrix representation to capture data uncertainty. Second, we run the experiments on an RFID trace dataset and show that our POPSM model is effective and efficient in capturing the common visiting subroutes among users.

Identifying Differentially Expressed Genes via Weighted Rank Aggregation

Identifying differentially expressed genes is an important problem in gene expression analysis, since these genes, exhibiting sufficiently different expression levels under distinct experiment conditions, could be critical for tracing the progression of a disease. In a micro array study, genes are usually sorted in terms of their differentiation abilities with the more differentially expressed genes being ranked higher in the list. As more micro array studies are conducted, rank aggregation becomes an important means to combine such ranked gene lists in order to discover more reliable differentially expressed genes. In this paper, we study a novel weighted gene rank aggregation problem whose complexity is at least NP-hard. To tackle the problem, we develop a new Markov-chain based rank aggregation method called Weighted MC (WMC). The WMC algorithm makes use of rank-based weight information to generate the transition matrix. Extensive experiments on the real biological datasets show that our approach is more efficient in aggregating long gene lists. Importantly, the WMC method is much more robust for identifying biologically significant genes compared with the state-of-the-art methods.

Query-aware locality-sensitive hashing scheme for \(l_p\) norm

The problem of c-Approximate Nearest Neighbor (c-ANN) search in high-dimensional space is fundamentally important in many applications, such as image database and data mining. Locality-Sensitive Hashing (LSH) and its variants are the well-known indexing schemes to tackle the c-ANN search problem. Traditionally, LSH functions are constructed in a query-oblivious manner, in the sense that buckets are partitioned before any query arrives. However, objects closer to a query may be partitioned into different buckets, which is undesirable. Due to the use of query-oblivious bucket partition, the state-of-the-art LSH schemes for external memory, namely C2LSH and LSB-Forest, only work with approximation ratio of integer

Accurate and Fast Asymmetric Locality-Sensitive Hashing Scheme for Maximum Inner Product Search

c \ge 2