Criminal data analysis based on low rank sparse representation

FINDING effective clustering methods for a high dimensional dataset is challenging due to the curse of dimensionality. These challenges can usually make the most of basic common algorithms fail in highdimensional spaces from tackling problems such as large number of groups, and overlapping. Most domains uses some parameters to describe the appearance, geometry and dynamics of a scene. This has motivated the implementation of several techniques of a high-dimensional data for finding a low-dimensional space. Many proposed methods fail to overcome the challenges, especially when the data input is high-dimensional, and the clusters have a complex. REGULARLY in high dimensional data, lots of the data dimensions are not related and might hide the existing clusters in noisy data. High-dimensional data often reside on some low dimensional subspaces. The problem of subspace clustering algorithms is to uncover the type of relationship of an objects from one dimension that are related in different subsets of another dimensions. The state-of-the-art methods for subspace segmentation which included the Low Rank Representation (LRR) and Sparse Representation (SR). The former seeks the global lowest-rank representation but restrictively assumes the independence among subspaces, whereas the latter seeks the clustering of disjoint or overlapped subspaces through locality measure, which, however, causes failure in the case of large noise. THIS thesis aims are to identify the key problems and obstacles that have challenged the researchers in recent years in clustering high dimensional data, then to implement an effective subspace clustering methods for solving high dimensional crimes domains for both real events and synthetic data which has complex data structure with 168 different offence crimes. As well as to overcome the disadvantages of existed subspace algorithms techniques. To this end, a Low-Rank Sparse Representation (LRSR) theory, the future will refer to as Criminal Data Analysis Based on LRSR will be examined, then to be used to recover and segment embedding subspaces. The results of these methods will be discussed and compared with what already have been examined on previous approaches such as K-mean and PCA segmented based on K-means. The previous approaches have helped us to chose the right subspace clustering methods. The Proposed method based on subspace segmentation method named Low Rank subspace Sparse Representation (LRSR) which not only recovers the low-rank subspaces but also gets a relatively sparse segmentation with respect to disjoint subspaces or even overlapping subspaces. BOTH UCI Machine Learning Repository, and crime database are the best to find and compare the best subspace clustering algorithm that fit for high dimensional space data. We used many Open-Source Machine Learning Frameworks and Tools for both employ our machine learning tasks and methods including preparing, transforming, clustering and visualizing the high-dimensional crime dataset, we precisely have used the most modern and powerful Machine Learning Frameworks data science that known as SciKit-Learn for library for the Python programming language, as well as we have used R, and Matlab in previous experiment

Unsupervised Learning from Shollow to Deep

Machine learning plays a pivotal role in most state-of-the-art systems in many application research domains. With the rising of deep learning, massive labeled data become the solution of feature learning, which enables the model to learn automatically. Unfortunately, the trained deep learning model is hard to adapt to other datasets without fine-tuning, and the applicability of machine learning methods is limited by the amount of available labeled data. Therefore, the aim of this thesis is to alleviate the limitations of supervised learning by exploring algorithms to learn good internal representations, and invariant feature hierarchies from unlabelled data. Firstly, we extend the traditional dictionary learning and sparse coding algorithms onto hierarchical image representations in a principled way. To achieve dictionary atoms capture additional information from extended receptive fields and attain improved descriptive capacity, we present a two-pass multi-resolution cascade framework for dictionary learning and sparse coding. This cascade method allows collaborative reconstructions at different resolutions using only the same dimensional dictionary atoms. The jointly learned dictionary comprises atoms that adapt to the information available at the coarsest layer, where the support of atoms reaches a maximum range, and the residual images, where the supplementary details refine progressively a reconstruction objective. Our method generates flexible and accurate representations using only a small number of coefficients, and is efficient in computation. In the following work, we propose to incorporate the traditional self-expressiveness property into deep learning to explore better representation for subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the ``self-expressiveness'' property that has proven effective in traditional subspace clustering. Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard back-propagation procedure. Being nonlinear, our neural-network based method is able to cluster data points having complex (often nonlinear) structures. However, Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. We propose two methods to tackle this problem. One method is based on $k$-Subspace Clustering, where we introduce a method that simultaneously learns an embedding space along subspaces within it to minimize a notion of reconstruction error, thus addressing the problem of subspace clustering in an end-to-end learning paradigm. This in turn frees us from the need of having an affinity matrix to perform clustering. The other way starts from using a feed forward network to replace the spectral clustering and learn the affinities of each data from "self-expressive" layer. We introduce the Neural Collaborative Subspace Clustering, where it benefits from a classifier which determines whether a pair of points lies on the same subspace under supervision of "self-expressive" layer. Essential to our model is the construction of two affinity matrices, one from the classifier and the other from a notion of subspace self-expressiveness, to supervise training in a collaborative scheme. In summary, we make constributions on how to perform the unsupervised learning in several tasks in this thesis. It starts from traditional sparse coding and dictionary learning perspective in low-level vision. Then, we exploit how to incorporate unsupervised learning in convolutional neural networks without label information and make subspace clustering to large scale dataset. Furthermore, we also extend the clustering on dense prediction task (saliency detection)

Graph based gene/protein prediction and clustering over uncertain medical databases.

Clustering over protein or gene data is now a popular issue in biomedical databases. In general, large sets of gene tags are clustered using high computation techniques over gene or protein distributed data. Most of the traditional clustering techniques are based on subspace, hierarchical and partitioning feature extraction. Various clustering techniques have been proposed in the literature with different cluster measures, but their performance is limited due to spatial noise and uncertainty. In this paper, an improved graph-based clustering technique is proposed for the generation of efficient gene or protein clusters over uncertain and noisy data. The proposed graph-based visualization can effectively identify different types of genes or proteins along with relational attributes. Experimental results show that the proposed graph model more effectively clusters complex gene or protein data when compared with conventional clustering approaches

New Techniques for Clustering Complex Objects

The tremendous amount of data produced nowadays in various application domains such as molecular biology or geography can only be fully exploited by efficient and effective data mining tools. One of the primary data mining tasks is clustering, which is the task of partitioning points of a data set into distinct groups (clusters) such that two points from one cluster are similar to each other whereas two points from distinct clusters are not. Due to modern database technology, e.g.object relational databases, a huge amount of complex objects from scientific, engineering or multimedia applications is stored in database systems. Modelling such complex data often results in very high-dimensional vector data ("feature vectors"). In the context of clustering, this causes a lot of fundamental problems, commonly subsumed under the term "Curse of Dimensionality". As a result, traditional clustering algorithms often fail to generate meaningful results, because in such high-dimensional feature spaces data does not cluster anymore. But usually, there are clusters embedded in lower dimensional subspaces, i.e. meaningful clusters can be found if only a certain subset of features is regarded for clustering. The subset of features may even be different for varying clusters. In this thesis, we present original extensions and enhancements of the density-based clustering notion to cope with high-dimensional data. In particular, we propose an algorithm called SUBCLU (density-connected Subspace Clustering) that extends DBSCAN (Density-Based Spatial Clustering of Applications with Noise) to the problem of subspace clustering. SUBCLU efficiently computes all clusters of arbitrary shape and size that would have been found if DBSCAN were applied to all possible subspaces of the feature space. Two subspace selection techniques called RIS (Ranking Interesting Subspaces) and SURFING (SUbspaces Relevant For clusterING) are proposed. They do not compute the subspace clusters directly, but generate a list of subspaces ranked by their clustering characteristics. A hierarchical clustering algorithm can be applied to these interesting subspaces in order to compute a hierarchical (subspace) clustering. In addition, we propose the algorithm 4C (Computing Correlation Connected Clusters) that extends the concepts of DBSCAN to compute density-based correlation clusters. 4C searches for groups of objects which exhibit an arbitrary but uniform correlation. Often, the traditional approach of modelling data as high-dimensional feature vectors is no longer able to capture the intuitive notion of similarity between complex objects. Thus, objects like chemical compounds, CAD drawings, XML data or color images are often modelled by using more complex representations like graphs or trees. If a metric distance function like the edit distance for graphs and trees is used as similarity measure, traditional clustering approaches like density-based clustering are applicable to those data. However, we face the problem that a single distance calculation can be very expensive. As clustering performs a lot of distance calculations, approaches like filter and refinement and metric indices get important. The second part of this thesis deals with special approaches for clustering in application domains with complex similarity models. We show, how appropriate filters can be used to enhance the performance of query processing and, thus, clustering of hierarchical objects. Furthermore, we describe how the two paradigms of filtering and metric indexing can be combined. As complex objects can often be represented by using different similarity models, a new clustering approach is presented that is able to cluster objects that provide several different complex representations

Sanitized Clustering against Confounding Bias

Real-world datasets inevitably contain biases that arise from different sources or conditions during data collection. Consequently, such inconsistency itself acts as a confounding factor that disturbs the cluster analysis. Existing methods eliminate the biases by projecting data onto the orthogonal complement of the subspace expanded by the confounding factor before clustering. Therein, the interested clustering factor and the confounding factor are coarsely considered in the raw feature space, where the correlation between the data and the confounding factor is ideally assumed to be linear for convenient solutions. These approaches are thus limited in scope as the data in real applications is usually complex and non-linearly correlated with the confounding factor. This paper presents a new clustering framework named Sanitized Clustering Against confounding Bias (SCAB), which removes the confounding factor in the semantic latent space of complex data through a non-linear dependence measure. To be specific, we eliminate the bias information in the latent space by minimizing the mutual information between the confounding factor and the latent representation delivered by Variational Auto-Encoder (VAE). Meanwhile, a clustering module is introduced to cluster over the purified latent representations. Extensive experiments on complex datasets demonstrate that our SCAB achieves a significant gain in clustering performance by removing the confounding bias. The code is available at \url{https://github.com/EvaFlower/SCAB}.Comment: Machine Learning, in pres