# proposal Fall 2010

## Project 1 : Classifying New Data Points Using An Outlier Approach

### By: Yongpeng Sun

Intuition:

In LDA, we assign a new data point to the class having the least distance to the center. At the same time however, it is desirable to assign a new data point to a class so that it is less of an outlier in that class as compared to every other class. To this end, compared to every other class, a new data point should be closer to the center of its assigned class and at the same time also, after suitable weighting has been done, be closer to the directions of variation of its assigned class.

Suppose there are two classes 0 and 1 both having $\,d$ dimensions, and a new data point is given. To assign the new data point to a class, we can proceed using the following steps:

Step 1: For each class, find its center and its $\,d$ directions of variation.

Step 2: For the new data point, with regard to each of the two classes, sum up the point's distance to the center and the point's distance to each of the $\,d$ directions of variation weighted (multiplied) by the ratio of the amount of variation in that direction to the total variation in that class.

Step 3: Assign the new point to the class having the smaller of these two sums.

These 3 steps can be easily generalized to the case where the number of classes is more than 2 because, to assign a new data point to a class, we only need to know, with regard to each class, the sum as described above.

I would like to evaluate the effectiveness of my idea / algorithm as compared to LDA and QDA and other classifiers using data sets in the UCI database ( http://archive.ics.uci.edu/ml/ ).

## Project 2: Apply Hadoop Map-Reduce to a Classification Method

By: Maia Hariri, Trevor Sabourin, and Johann Setiawan

Develop map-reduce processes that can properly classify large distributed data sets.

Potential projects:

1. Use Hadoop Map-Reduce to implement the Support Vector Machine (Kernel) classification algorithm.
2. Use Hadoop Map-Reduce to implement the LDA classification algorithm on a novel problem (e.g. forensic identification of handwriting.)

## Project 3 : Hierarchical Locally Linear Classification

By: Pouria Fewzee

Extension of an intrinsic two-class classifier to a multi-class may be challenging, as the common approaches either remain some vague areas in the feature space, or are computationally inefficient. One may found linear classifier and support vector machines two well-known instances of intrinsic two-class classifiers, and the k-1 and k(k-1)/2-hyperplanes as two most common approaches for extension of their capabilities to multi-class tasks. The k-1 bothers from leaving vague areas in the feature space and even the k(k-1)/2 does not have this problem, it is not computationally efficient. Hierarchical classification is proposed as a solution. This not only improves the efficiency of the classifier, but also the suggested tree could provide the specialists with new outlooks in the field.

To build a general purpose classifier which adapts to different patterns, as much as demanded, is another purpose of this project. To realize this goal, locally linear classification is proposed. Performing the locality in classifier design is accomplished by means of utilizing a combination of fuzzy computation tools along with binary decision trees.

## Project 4 : Cluster Ensembles for High Dimensional Clustering

By: Chun Bai, Lisha Yu

Clustering for unsupervised data exploration and analysis has been investigated for decades in machine learning. Its performance is directly influenced by the dimensionality. Data with high dimensionality pose two fundamental challenges for clustering algorithms. First, the data tend to be sparse in a high dimensional space. Second, there often exist noisy features that may mislead clustering algorithm.

The paper studies cluster ensembles for high dimensional data clustering. Three different approaches to constructing cluster ensembles are examined:

1. Random projection based approach
2. Combining PCA and random subsampling
3. Combing random projection with PCA

Moreover, four different consensus function for combing the clustering of the ensemble are examined:

1. Consensus Functions Using Graph Partitioning
-Instance-Based Graph Formulation (IBGF)
-Cluster-Based Graph Formulation (CBGF)
-Hybrid Bipartite Graph Formulation (HBGF)
2. Consensus Function Using Centroid-based Clustering (KMCF)

Using the datasets from UCI, It shows that ensembles generated by random projection perform better than those by PCA and further that this can be attributed to the capability of random projection to produce diverse base clustering. It has also shown that a recent consensus function based on bipartite graph partitioning achieves the best performance.

## Project 5 : Texture Classification Using Compressive Sensing

By: Mohammad Rostami Analysis of textures has many potential applications such as: remote sensing, biomedical image analysis and surface inspection. One of the major tasks in this area is texture classification. A major problem in texture analysis is that the natural textures are not often uniform, due to variations in scale, orientation, or other visual appearances which makes it harder to work with textures as compared to natural images. We can generally model natural images as deterministic signals while statistical models are more successful for texture synthesis.

   Though, many successful methods have been proposed for texture classifications [1], which have solved the fore mentioned problems considerably, but there is still need to develop better algorithms. Similar to other classification problems we will have a dimension reduction step. This step is necessary to make the feature vector invariant to the above mentioned variations. Many methods have been proposed in the literature to achieve this task. Most commonly, some kind of transform is used to map the signal to lower dimension space e.g.: wavelets, FDA, and statistical methods. Recently, Compressive sensing (CS) has also been used for this very purpose [2].


Compressive sensing is a technique for finding sparse solutions to underdetermined linear systems [3]. Consider a linear system with more unknowns than equations.

\mathbf{X} = \beta^{D}\mathbf{Y}               (1)


It is obvious that this problem does not have a unique solution but it can be shown if we assume sparsity as the prior knowledge about the solution, we can end up calculating a unique answer. This means that we can specify a sparse signal uniquely in lower dimensions. This demonstrates that CS has the potential to be used as dimension reduction. In contrast to classic CS where it is required to solve (1), here, instead we would like to design in order to transform our data to lower dimension space with the possibility of retrieving it uniquely. The main problem is that textures are not sparse signals so before doing this step we need to find a method to transform textures to sparse signals. After this step we can use existing methods for classification purpose.

In this project I plan to carry out an extensive overview of existing texture classification methods, compressive sensing and the connection between two. I would survey current methods that use CS as a tool for classification and compare them in various aspects. Besides, I will also implement a novel idea to perform classification task similar to the proposed method in [2]. Principally, I hope to achieve better results by taking advantage of texture signal properties.


[1] T. Ojala, M. Pietikainen, T. Maenpaa: “Multi resolution gray-scale and rotation Invariant texture classification with local binary patterns” IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (2002)971–987 [2] L. Lui, P. Fieguth “Texture classification using compressed sensing.” 2010 Canadian Conference on Computer and Robot Vision (CRV) [3] D. Donoho. “Compressed sensing,” IEEE Transactions on Information Theory, vol.52, pp.1289-1306, 2006.