III. Model-Free Analysis

Overview

This chapter describes the major functions in the Clustering pull-down menu. Including:

KCN

How to set the parameters for running Kohonen Clustering Network.

FCM

How to set the parameters for Fuzzy C-Means (Fuzzy Clustering).

Show KCN/FCM

How to display and analyze the KCN or FCM clustering results.

To use clustering analysis, you have to run KCN first, then FCM, and use "show FCM" to evaluate the result. Usually, KCN should be run once only. You may need to repeat running FCM using different cluster number for a few times to obtain optimal results.

1. KCN

1.1 Basic-Level Setting

To run KCN, at minimum, you only need to specify the following 3 or 4 information and then press Run. Useful setting is marked by *.

Output Path

KCN will generate 4 files in this directory: kohonen_map, kohonen_wave, kohonen_count, and kcn_log.txt. The default is the data path.

Cluster Number *

This is usually the key to successful clustering. Larger cluster number could separate more detailed differences but will be slower. The default value, 50, works fine for most cases. If input pixel number is huge, increase this for better clustering.

Background Threshold

To remove un-interested background noise. The more you eliminate from KCN, the better the results would be. You can specify signal intensity level, or use a ratio of the highest intensity, or use mask.

Skip Top & Bottom Slices

This option should be chosen especially after doing image registration (i.e. realignment) since this processing will introduce signal drop-out at both ends of the volume.

1.2 Median-Level Setting

If you are not satisfy with the results, you can apply more preprocessing to the data. Some of them are very useful (marked by *).

Normalization

Normalize the time-series signal intensity of each pixel by its mean, median, or average of some scans.

Range

Processing the whole volume as one or processing each slice separately. The latter one will create a set of clustering result for each slice and a combinatory result. It is useful if there is slice timing issue.

ROI

Restrict analysis in the specified ROI. Useful for refining the analysis. The selected ROI will be applied to all slices.

Std Threshold *

Another strategy to remove un-interested voxels based on the idea that noise or tissues without activities has lower standard deviation (std) in time domain. Methods include: std, or std/mean.

Smoothing *

Spatial smoothing to increase SNR using Gaussian kernel.

Filter *

Temporal filtering or smoothing to increase SNR. Currently, only median filter is available for removing spikes in the time-series.

1.3 Advanced-Level Setting

You can also adjust the parameters of the KCN algorithm. They are seldom changed.

Initialization Method

This is another key parameter that could have significant influence on the result. Improper initialization will lead to poor clustering or even diverge. Useable methods include:

Theoratically, random initialization is better, but emperically random select works well.

Max Iteration

Maximum number of iteration. KCN usually converges within 40 iterations. Exceeding this value may indicate algorithm diverge.

Type of Error

Choose the absolute or relative error tolerance.

Error Tolerance

Error tolerance for convergence.

Learning Rate

Larger number makes finer adjustment but will converge slower. Should be < 1.

2. FCM

2.1 Basic-Level Setting

To run FCM, at minimum, you only need to specify the following 2 information before pressing Run. Useful setting is marked by *.

Output Path

FCM will generate 4 files in this directory: fcm_map, fcm_wave, fcm_count, and fcm_log.txt. The default is the data path.

KCN Path, Filename

The location and the filename of KCN result files. The default is the data path.

Cluster Number *

This is usually the key to successful clustering. Larger cluster number could separate more detailed pattern differences. You would need to try several numbers to find the optimal clustering result. The default value, 10, is a good starting point. (Should be < 128.)

Find Cluster Number: Auto/Specify

Find the optimal cluster number within the specified range using an separation/compactness index proposed by Kwon S.H., Electr. Let. 34:2176-77, 1998.

2.2 Median-Level Setting

Although the default setting for FCM could usually give satisfactory result (you only need to adjust cluster number), you can still fine tune its performance by different preprocessing strategies:

Normalization

Normalize the time-series signal intensity of each pixel. Sometimes, "/median" could produce good result.

Distance *

The type of distance measurement, including:

In some cases, using Correlation-based distance could produce better result.

Smoothing

Spatial smoothing to increase SNR using Gaussian kernel.

2.3 Advanced-Level Setting

You can also tweak the parameters of FCM algorithm. They are seldom changed.

Fuzzy Factor

Fuzzy factor determine the degree of the fuzziness -- the larger the fuzzier. The smaller this number, it becomes closer to hard partitioning. Usually, 1.2 or 1.3 is good. Should be > 1.

Probability

The probability threshold to determine which cluster a pixel delonged to.

Max Iteration

Maximum number of iteration.

Error Tolerance

Absolute erroer tolerance.

3. Show KCN/FCM

After finishing KCN or FCM analysis, you can see what are the identified patterns by choosing "Show KCN Cluster" or "Show FCM Cluster" from the Clustering pull-down menu. This will display a window like below:

You can left-click on the pattern waveform you are interested in for further evaluation, such as seeing where it showed up in the brain. At most 10 patterns can be chosen.

3.1 File

The display property of the waveforms:

3.2 Show

3.3 Sort

3.4 Same Scale

Display the waveforms in the same scale. Otherwise, display them by zoom-in to their max and min values.

3.5 Sub-Clusters

Display the KCN cluster number belonged to each FCM cluster.

3.6 View Sub-Wave

Display the KCN cluster waveforms belonging to the selected FCM cluster. ONLY one FCM cluster can be selected at a time.