Improving performance of classification on severity of ill effects (SEV) index on fish using K-Means clustering algorithm with various distance metrics

The sudden release of large volumes of sediment may create serious problems downstream, such as channel aggradations and flooding, interference with water supply and cooling water intakes, as well as adverse impacts on fisheries and the environment (Khakzad & Elfimov 2015a, 2015b).

MacDonald & Newcombe (1993) grouped effects of suspended sediment on fish into three categories: lethal, sublethal and behavioral. These categories include the following:

• – Lethal effects kill individual fish, alter populations and decrease the capacity of fish to reproduce. They include sublethal and behavioral effects that give rise to reductions in population size.

• – Sublethal effects include tissue injury or changes in the physiology of an organism. The effect is chronic and may lead to an eventual decline in population size.

• – Behavioral effects are effects that result in any change in activity normally associated with a species in an undisturbed environment. These changes may result in immediate death, or changes in population size or death over time.

Newcombe & Jensen (1997) developed a risk index and presented six regression equations for management decisions that relate biological response to duration of exposure and suspended sediment concentration. The equations all have the form: where, z is severity of ill effect, x is duration of exposure (h), y is concentration of suspended sediment (mg SS/L), a is the intercept, and b and c are slope coefficients. However, the study provided primary available estimates of the onset of sublethal and lethal effects, they applied regression models as a method to estimate SEV and have difficulties in showing the important factors affecting SEV (Khakzad & Elfimov 2015a, 2015b). In addition, it is likely that the assumptions that are made in a regression model may be violated if data for diseases or disorders are used in the model, because linear regression models need assumptions to be made, including assumptions about the linearity, normality, and homoscedasticity of the data, among others (Byeon 2014).

As mentioned before, the prediction of significant ill effect for fish that is essentially an uncertain and random process is not easy to accomplish by using deterministic equations. Therefore, it is ideally suited to the K-Means clustering algorithm with various distance metrics since they are primarily aimed at the recognition of a random pattern in a given set of input values. K-Means clustering is helpful in predicting the value of the output of a system from its corresponding random inputs as the application of K-Means clustering does not require knowledge of the underlying physical process as a precondition.

K-Means is a prototype-based, simple partitional clustering algorithm that attempts to find K non-overlapping clusters. These clusters are represented by their centroids (a cluster centroid is typically the mean of the points in that cluster) (Wu 2012). The clustering process of K-Means is as follows. First, K initial centroids are selected, where K is specified by the user and indicates the desired number of clusters. Every point in the data is then assigned to the closest centroid, and each collection of points assigned to a centroid forms a cluster. The centroid of each cluster is then updated based on the points assigned to that cluster. This process is repeated until no point changes clusters.

Considering that there are numerous clustering algorithms proposed in the literature, it may be queried why this paper is focused on the K-Means clustering. Let us understand this from the following two perspectives. First, K-Means has some distinct advantages compared with other clustering algorithms. That is, K-Means is very simple and robust, highly efficient, and can be used for a wide variety of data types. Indeed, it has been ranked the second among the top 10 data mining algorithms (Wu et al. 2008), and has become the defacto benchmark method for newly proposed methods. Moreover, K-Means as an optimization problem still has some theoretical challenges.

The present study develops and presents a new expert system to improving performance of classification by SEV as an indicator of ill effect for fish using K-Means clustering algorithm and results compared with previous models.

In this study, we provide information (data from 303 tests) about aquatic ecosystem quality over a wide range of sediment concentrations, durations of exposure species, life stage and severity of ill effect for fishes (Table 1). Supporting data extracted from the review included taxonomic group, species of fish, natural history, life history phase, and sediment particle size range.

We scored qualitative response data along a semiquantitative ranking scale (Table 1). Superimposed on a 15-point scale (0–14) were four major classes of effect: (1) nil effect, (2) behavioral effects, (3) sub lethal effects (a category that also includes effects such as short-term reduction in feeding success), and (4) lethal effects (direct mortality, or its paralethal surrogates reduced growth, reduced ash density, habitat damage such as reduced porosity of spawning gravel, delayed hatching, and reduction in population size). When these various effects could be compared directly, pollution episodes associated with sub lethal or lethal effects also degraded habitat and reduced population size, which is why these seemingly disparate ill effects are grouped together in the hierarchy. For events between the extremes of nil effect and 100% mortality, we assumed for modeling purposes that the SEV scale represents proportional differences in true effects (Table 2). In this study, we define dose as concentration of suspended sediment (SS) times duration of exposure; dose has the units mg SS.h.L⁻¹. The single decision tree (SDT), which is the basis of data presentation in this study, encompasses all combinations of sediment concentration (1–500,000 mg SS/L) and exposure.

K-Means clustering is used so that clusters of items with the same target category are identified, and predictions for new data items are made by assuming they are of the same type as the nearest cluster center (Kim & Yamashita 2010).

K-Means clustering is similar to two other more modern methods:

• Radial basis function neural networks. An RBF network also identifies the centers of clusters, but RBF networks make predictions by considering the Gaussian-weighted distance to all other cluster centers rather than just the closest one.

• Probabilistic neural networks. Each data point is treated as a separate cluster, and a prediction is made by computed the Gaussian-weighted distance to each point.

Usually, both RBF networks and PNN networks are more accurate than K-Means clustering models. PNN networks are among the most accurate of all methods, but they become impractically slow when there are more than about 10,000 rows in the training data file. K-Means clustering is faster than RBF or PNN networks, and it can handle large training files.

K-Means clustering can be used only for classification (i.e., with a categorical target variable), not for regression. The target variable may have two or more categories. The algorithm in its simplest form is comprised of the following steps:

• 1.

  Place K points into the space represented by the objects that are being clustered. These points represent initial group centroids.

• 2.

  Assign each object to the group that has the closest centroid.

• 3.

  When all objects have been assigned, recalculate the positions of the K centroids.

• 4.

  Repeat Steps 2 and 3 until the centroids no longer move.

This produces a separation of the objects into groups from which the metric to be minimized can be calculated. The K-Means clustering routine was not designed to show the relationship between clusters. Instead, K-Means clusters are constructed so that the average behavior in each group is distinct from any of the other groups. For example, in a time series experiment you could use K-Means clustering to identify unique classes of pedestrian-involved crashes that are determined in a time dependent manner.

In this section of study, the K-Means clustering algorithm was used to evaluate the performance of classification using the SEV index on fish. There are two issues in creating a K-Means clustering model: 1) determine the optimal number of clusters to create; and 2) determine the center of each cluster.

In this paper, we provide an automatic search function that creates models using a varying number of clusters, tests each one and reports which is best. The model performance tests can be performed using cross-validation or holdout sampling. The results for determining the optimal number of clusters based on misclassification(%) shown in Figure 1. As can be seen (Figure 1), the best number of clusters is 47.

Given the number of clusters, the second part of the problem is determining where to place the center of each cluster. Often, points are scattered and don't fall into easily recognizable groupings. Cluster center determination is done in two steps:

A. Determine starting positions for the clusters. This is performed in two steps:

• 1.

  Assign the first center to a random point.

• 2.

  Find the point furthest from any existing center and assign the next center to it. Repeat this until the specified number of cluster centers have been found.

B. Adjust the center positions until they are optimized.

Table 3 and 4 shown the results of the confusing matrix and sensitivity & specificity for each target category for the SEV index. The key concept of the confusion matrix is that it calculates the number of correct and incorrect predictions, which are further summarized with the number of count values and breakdown into each class.

Comparing accuracy for each target category for the SEV index in Table 4 showed that categories 12 and 10 (accuracies for categories 10 and 12 are 78.22% and 75.58%, respectively) have low accuracy with lower recognition rate and forecast accuracy and weaker practical value. A validation measure is therefore required to tell us how good the clustering is. Indeed, cluster validity has become the core task of cluster analysis, for which a great number of validation measures have been proposed and carefully studied in the literature.

Clustering for understanding is to employ cluster analysis to automatically find conceptually meaningful groups of objects that share common characteristics. It plays an important role in helping people to analyze, describe and utilize the valuable information hidden in the groups. Despite the vast amount of research devoted to the SEV index, there is as yet no consistent and conclusive solution to cluster validation, and the best suitable measures to use in practice remain unclear. In this paper, we provide the methodology, which is simple and qualitative, by comparing the predictive clustering algorithm with various distance metrics to improve the performance of classification by the SEV index on fish. We implemented the K-Means clustering algorithm on 303 results regarding aquatic ecosystem quality and 14 categories based on SEV. Results of this study showed that categories 12 and 10 on SEV should be improved, and we have to consider their accuracy in calculations related to analysis of aquatic ecosystem quality. Finally, we can use the K-Means clustering algorithm to make inferences that help us understand the ‘big picture’ of the model and to identify other areas of concern that may warrant further investigation, analysis, problem identification and countermeasure design.