Subspace clustering aims to find groups of similar objects (clusters) that exist in lower dimensional subspaces from a high dimensional dataset. It has a wide range of applications, such as analysing high dimensional sensor data or DNA sequences. However, existing algorithms have limitations in finding clusters in non-disjoint subspaces and scaling to large data, which impinge their applicability in areas such as bioinformatics and the Internet of Things. We aim to address such limitations by proposing a subspace clustering algorithm using a bottom-up strategy. Our algorithm first searches for base clusters in low dimensional subspaces. It then forms clusters in higher-dimensional subspaces using these base clusters, which we formulate as a frequent pattern mining problem. This formulation enables efficient search for clusters in higher-dimensional subspaces, which is done using FP-trees. The proposed algorithm is evaluated against traditional bottom-up clustering algorithms and state-of-the-art subspace clustering algorithms. The experimental results show that the proposed algorithm produces clusters with high accuracy, and scales well to large volumes of data. We also demonstrate the algorithm’s performance using real-life ten genomic datasets.
From an algorithmic point of view, clustering algorithms can be classified into bottom-up algorithms and top-down algorithms @cite_9 . As our algorithm follows a bottom-up strategy, we briefly discuss the relevant algorithms of this class to highlight our contributions.
@cite_9
2079361215
Subspace clustering is an extension of traditional clustering that seeks to find clusters in different subspaces within a dataset. Often in high dimensional data, many dimensions are irrelevant and can mask existing clusters in noisy data. Feature selection removes irrelevant and redundant dimensions by analyzing the entire dataset. Subspace clustering algorithms localize the search for relevant dimensions allowing them to find clusters that exist in multiple, possibly overlapping subspaces. There are two major branches of subspace clustering based on their search strategy. Top-down algorithms find an initial clustering in the full set of dimensions and evaluate the subspaces of each cluster, iteratively improving the results. Bottom-up approaches find dense regions in low dimensional spaces and combine them to form clusters. This paper presents a survey of the various subspace clustering algorithms along with a hierarchy organizing the algorithms by their defining characteristics. We then compare the two main approaches to subspace clustering using empirical scalability and accuracy tests and discuss some potential applications where subspace clustering could be particularly useful. This paper presents a simple attribute graph grammar as a generative representation for made-made scenes, such as buildings, hallways, kitchens, and living rooms, and studies an effective top-down bottom-up inference algorithm for parsing images in the process of maximizing a Bayesian posterior probability or equivalently minimizing a description length (MDL). Given an input image, the inference algorithm computes (or constructs) a parse graph, which includes a parse tree for the hierarchical decomposition and a number of spatial constraints. In the inference algorithm, the bottom-up step detects an excessive number of rectangles as weighted candidates, which are sorted in certain order and activate top-down predictions of occluded or missing components through the grammar rules. In the experiment, we show that the grammar and top-down inference can largely improve the performance of bottom-up detection. Everyone knows what bottom-up is, and how it is different from top-down. At least one is tempted to think so, given that both terms are ubiquitously used, but only rarely defined in the psychology and neuroscience literature. In this review, we highlight the problems and limitations of our current understanding of bottom-up and top-down processes, and we propose a reformulation of this distinction in terms of predictive coding. This paper presents a method to quantitatively evaluate information contributions of individual bottom-up and top-down computing processes in object recognition. Our objective is to start a discovery on how to schedule bottom-up and top-down processes. (1) We identify two bottom-up processes and one top-down process in hierarchical models, termed α, β and γ channels respectively ; (2) We formulate the three channels under an unified Bayesian framework; (3) We use a blocking control strategy to isolate the three channels to separately train them and individually measure their information contributions in typical recognition tasks; (4) Based on the evaluated results, we integrate the three channels to detect objects with performance improvements obtained. Our experiments are performed in both low-middle level tasks, such as detecting edges bars and junctions, and high level tasks, such as detecting human faces and cars, together with a group of human study designed to compare computer and human perception.