#Formation xlstat software#

By best choice, we mean the choice that minimizes SSE.Ĭlick here for a proof of this property (using calculus). Property 1: The best choice for the centroids c 1, …, c k are the n-tuples which are the means of the C 1, …, C k. There is no guarantee that we will find centroids c 1, …, c k that minimize SSE and a lot depends on our initial choices for the centroids in step 2. If we think of the distance squared between any data element in S and its nearest centroid as an error value (between a data element and its prototype) then across the system we are trying to minimize Where m j is the number of data elements in C j. If we don’t require that the centroids belong to the data set S, then we typically define the new centroid c j for cluster C j in step 4 to be the mean of all the elements in that cluster, i.e. If there are k clusters C 1, …, C k with corresponding centroids c 1, …, c k, then for each data element x in S, step 3 of the k-means algorithm consists of finding the value j which minimizes dist 2( x, c j) i.e. Since minimizing the distance is equivalent to minimizing the square of the distance, we will instead look at dist 2( x, y) = ( dist( x, y)) 2. There are a number of ways to define the distance between two n-tuples in the data set S, but we will focus on the Euclidean measure, namely, if x = ( x 1, …, x n) and y = (y 1, …, y n) then the distance between x and y is defined by Step 4: Based on centroids make a new assignment of data elements to the k clusters.Step 3: For each cluster select its centroid.Step 2: Make an initial assignment of the data elements to the k clusters.There are various choices available for each step in the process.Īn alternative version of the algorithm is as follows: Step 5: Go back to step 3, repeating the process until the centroids don’t change (or some other convergence criterion is met).Step 4: For each cluster make a new selection of its centroid.Step 3: Assign each data element to its nearest centroid (in this way k clusters are formed one for each centroid, where each cluster consists of all the data elements assigned to that centroid).Step 2: Make an initial selection of k centroids.Step 1: Choose the number of clusters k.For each cluster C j, one element c j is chosen from that cluster called a centroid.ĭefinition 1: The basic k-means clustering algorithm is defined as follows: Flash profiling is slower and more labor-intensive, making it suitable for exploratory studies with a smaller number of consumers, while CATA questions are faster and less labor-intensive, making it suitable for studies with a larger group of consumers.įlash profile CATA Rv coefficient sensory descriptive.The objective of this algorithm is to partition a data set S consisting of n-tuples of real numbers into k clusters C 1, …, C k in an efficient way. These results demonstrate a high accuracy and reproducibility of sensory information obtained by consumers applying descriptive sensory methods in foods. The RV coefficient was 0.94, indicating a very high similarity between both methods. The results of the flash profile and CATA questions showed the formation of four groups, the first group consisting of samples D and E the second, third and fourth groups, A, B and C, respectively.

#Formation xlstat software#

In addition, the RV coefficient was used to compare the sensory maps generated by both methods, using the R software and XLSTAT-test version.

For data analysis, generalized procruster analysis (GPA) was used for the PF and the Cochran Q test with correspondence analysis for the CATA questions. Participants evaluated five Andean Mint beverages using flash profile (FP) methodology (n=20) and Check-All-That-Apply (CATA) questions (n=105). This study compares two descriptive methods based on consumers' perceptions of the sensory profile of Andean Mint (Muña) herbal teas. Comparison of descriptive sensory methods: flash profile and CATA questions to characterize muña infusions (Minthostachys mollis).