Random Projection in Machine Learning

In many signal classification domains such as image or video processing, the high dimensionality of the input signals makes the use of standard machine learning algorithms time and computation intensive. Random projection is emerging as a flexible and effective means for dimensionality reduction, particularly when the input signal has a sparse representation in some family of basis functions.

This project examines the effect of the dimensionality of the sparse representation and random projection basis on 2-class separability using several popular machine learning algorithms. In particular, the Discrete Cosine Transform (DCT) basis was chosen as the input space, and SVM, Naive Bayes and Multilayer-Perceptron were used for machine learning. Results showed that the correct classification rate using random projection was comparable to classification in the input domain when the dimensionality of random projection vectors was on the order of the dimensionality of the input domain.

Capturing Spatial Context in Images with a Relational Dictionary

Probabilistic generative models such as Probabilistic Latent Semantic Indexing (PLSI), Latent Dirichlet Allocation (LDA), and their variants have been used with some success on the task of object recognition in images. Recent approaches integrate spatial information into the generative process leading to complex hierarchical models. This work takes a simpler approach by encoding the neighborhood of a particular visual word in a relation dictionary. Thus, an image is represented as histogram over this relational dictionary, and standard topic modeling approaches can be applied. We examine three methods of inducing the neighborhood graph and compare them on an image recognition task using the LabelMe benchmark database. Results for the relational dictionary are on-par with a standard non-relational dictionary, but consistently poor, thereby suggesting a flaw in the experimental setup.