16 research outputs found
Scalable and Robust Community Detection with Randomized Sketching
This paper explores and analyzes the unsupervised clustering of large
partially observed graphs. We propose a scalable and provable randomized
framework for clustering graphs generated from the stochastic block model. The
clustering is first applied to a sub-matrix of the graph's adjacency matrix
associated with a reduced graph sketch constructed using random sampling. Then,
the clusters of the full graph are inferred based on the clusters extracted
from the sketch using a correlation-based retrieval step. Uniform random node
sampling is shown to improve the computational complexity over clustering of
the full graph when the cluster sizes are balanced. A new random degree-based
node sampling algorithm is presented which significantly improves upon the
performance of the clustering algorithm even when clusters are unbalanced. This
algorithm improves the phase transitions for matrix-decomposition-based
clustering with regard to computational complexity and minimum cluster size,
which are shown to be nearly dimension-free in the low inter-cluster
connectivity regime. A third sampling technique is shown to improve balance by
randomly sampling nodes based on spatial distribution. We provide analysis and
numerical results using a convex clustering algorithm based on matrix
completion
Framework for Contextual Outlier Identification using Multivariate Analysis approach and Unsupervised Learning
Majority of the existing commercial application for video surveillance system only captures the event frames where the accuracy level of captures is too poor. We reviewed the existing system to find that at present there is no such research technique that offers contextual-based scene identification of outliers. Therefore, we presented a framework that uses unsupervised learning approach to perform precise identification of outliers for a given video frames concerning the contextual information of the scene. The proposed system uses matrix decomposition method using multivariate analysis to maintain an equilibrium better faster response time and higher accuracy of the abnormal event/object detection as an outlier. Using an analytical methodology, the proposed system blocking operation followed by sparsity to perform detection. The study outcome shows that proposed system offers an increasing level of accuracy in contrast to the existing system with faster response time
Robust PCA by Manifold Optimization
Robust PCA is a widely used statistical procedure to recover a underlying
low-rank matrix with grossly corrupted observations. This work considers the
problem of robust PCA as a nonconvex optimization problem on the manifold of
low-rank matrices, and proposes two algorithms (for two versions of
retractions) based on manifold optimization. It is shown that, with a proper
designed initialization, the proposed algorithms are guaranteed to converge to
the underlying low-rank matrix linearly. Compared with a previous work based on
the Burer-Monterio decomposition of low-rank matrices, the proposed algorithms
reduce the dependence on the conditional number of the underlying low-rank
matrix theoretically. Simulations and real data examples confirm the
competitive performance of our method
Randomized Robust Subspace Recovery for High Dimensional Data Matrices
This paper explores and analyzes two randomized designs for robust Principal
Component Analysis (PCA) employing low-dimensional data sketching. In one
design, a data sketch is constructed using random column sampling followed by
low dimensional embedding, while in the other, sketching is based on random
column and row sampling. Both designs are shown to bring about substantial
savings in complexity and memory requirements for robust subspace learning over
conventional approaches that use the full scale data. A characterization of the
sample and computational complexity of both designs is derived in the context
of two distinct outlier models, namely, sparse and independent outlier models.
The proposed randomized approach can provably recover the correct subspace with
computational and sample complexity that are almost independent of the size of
the data. The results of the mathematical analysis are confirmed through
numerical simulations using both synthetic and real data
Provable Self-Representation Based Outlier Detection in a Union of Subspaces
Many computer vision tasks involve processing large amounts of data
contaminated by outliers, which need to be detected and rejected. While outlier
detection methods based on robust statistics have existed for decades, only
recently have methods based on sparse and low-rank representation been
developed along with guarantees of correct outlier detection when the inliers
lie in one or more low-dimensional subspaces. This paper proposes a new outlier
detection method that combines tools from sparse representation with random
walks on a graph. By exploiting the property that data points can be expressed
as sparse linear combinations of each other, we obtain an asymmetric affinity
matrix among data points, which we use to construct a weighted directed graph.
By defining a suitable Markov Chain from this graph, we establish a connection
between inliers/outliers and essential/inessential states of the Markov chain,
which allows us to detect outliers by using random walks. We provide a
theoretical analysis that justifies the correctness of our method under
geometric and connectivity assumptions. Experimental results on image databases
demonstrate its superiority with respect to state-of-the-art sparse and
low-rank outlier detection methods.Comment: 16 pages. CVPR 2017 spotlight oral presentatio
Detection of Thin Boundaries between Different Types of Anomalies in Outlier Detection using Enhanced Neural Networks
Outlier detection has received special attention in various fields, mainly
for those dealing with machine learning and artificial intelligence. As strong
outliers, anomalies are divided into the point, contextual and collective
outliers. The most important challenges in outlier detection include the thin
boundary between the remote points and natural area, the tendency of new data
and noise to mimic the real data, unlabelled datasets and different definitions
for outliers in different applications. Considering the stated challenges, we
defined new types of anomalies called Collective Normal Anomaly and Collective
Point Anomaly in order to improve a much better detection of the thin boundary
between different types of anomalies. Basic domain-independent methods are
introduced to detect these defined anomalies in both unsupervised and
supervised datasets. The Multi-Layer Perceptron Neural Network is enhanced
using the Genetic Algorithm to detect newly defined anomalies with higher
precision so as to ensure a test error less than that calculated for the
conventional Multi-Layer Perceptron Neural Network. Experimental results on
benchmark datasets indicated reduced error of anomaly detection process in
comparison to baselines
High Dimensional Low Rank plus Sparse Matrix Decomposition
This paper is concerned with the problem of low rank plus sparse matrix
decomposition for big data. Conventional algorithms for matrix decomposition
use the entire data to extract the low-rank and sparse components, and are
based on optimization problems with complexity that scales with the dimension
of the data, which limits their scalability. Furthermore, existing randomized
approaches mostly rely on uniform random sampling, which is quite inefficient
for many real world data matrices that exhibit additional structures (e.g.
clustering). In this paper, a scalable subspace-pursuit approach that
transforms the decomposition problem to a subspace learning problem is
proposed. The decomposition is carried out using a small data sketch formed
from sampled columns/rows. Even when the data is sampled uniformly at random,
it is shown that the sufficient number of sampled columns/rows is roughly
O(r\mu), where \mu is the coherency parameter and r the rank of the low rank
component. In addition, adaptive sampling algorithms are proposed to address
the problem of column/row sampling from structured data. We provide an analysis
of the proposed method with adaptive sampling and show that adaptive sampling
makes the required number of sampled columns/rows invariant to the distribution
of the data. The proposed approach is amenable to online implementation and an
online scheme is proposed.Comment: IEEE Transactions on Signal Processin