SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

Improving learning by connecting chemistry curriculum to students' experiences

The purpose of the study was to design, implement, and assess the effects of a teaching unit about fuel sources and chemical energy on students’ learning. The unit was designed to incorporate students’ experiences in a way that was aligned with the Michigan High School Content Expectations. The study was completed with all of the students taking General Chemistry in a rural Michigan high school in the 2010-11 school year. There were 138 participants total. The participants were mostly Caucasian and the majority were in the 11th grade. Of these, 77 constituted the experimental group and were taught the unit. The additional 61 participants in the control group were given the posttest only. Data was derived from the results of pre/post tests, final assessment projects, and the researcher’s observations. A pretest that contained questions about the fuel sources was administered at the beginning of the unit. An identical posttest was administered at the completion of the unit. A final assessment project required students to choose the best fuel source for the area, and support their opinion with facts and data from their research or the learning activities and labs performed in class. The results of the study revealed that the teaching unit did produce significant learning gains in the experimental group. The results also indicated that the teaching unit added value to the current General Chemistry curriculum by expanding what students were learning. The instructional goals of the unit were aligned with the Michigan High School Content Expectations. The results also revealed that the students were able to learn to support their thinking and decisions with explanations based on the data and labs. These are essential science literacy skills. The study supported the view that connecting the required curriculum with students’ experiences and interests was effective, and that students can learn important science literacy skills, such as providing support for arguments and communicating scientific explanations, when given adequate teacher support.