Attributes Measured For Members Of A Herd ✓ Solved

The Following Attributes Are Measured For Members Of A Herd Of Asia

The following attributes are measured for members of a herd of Asian elephants: weight, height, tusk length, trunk length, and ear area. Based on these measurements, what sort of similarity measure from Section 2.4 (measure of similarity and dissimilarity) would you use to compare or group these elephants? Justify your answer and explain any special circumstances.

Consider the training examples shown in Table 3.5 (please find the table from the attached screenshot) for a binary classification problem. (a) Compute the Gini index for the overall collection of training examples. (b) Compute the Gini index for the Customer ID attribute. (c) Compute the Gini index for the Gender attribute. (d) Compute the Gini index for the Car Type attribute using multiway split.

Consider the data set shown in Table 4.9 (please find the table in the attached screenshot). (a) Estimate the conditional probabilities for P(A|+), P(B|+), P(C|+), P(A|-), P(B|-), and P(C|-). (b) Use the estimate of conditional probabilities given in the previous question to predict the class label for a test sample (A = 0, B = 1, C = 0) using the naive Bayes approach. (c) Estimate the conditional probabilities using the m-estimate approach, with p = 1/2 and m = 4.

Sample Paper For Above instruction

Comparing and Clustering Asian Elephants Using Similarity Measures

In the realm of machine learning and data analysis, selecting an appropriate similarity or dissimilarity measure is crucial when comparing or clustering objects based on their attributes. For biological data such as measurements of Asian elephants—encompassing weight, height, tusk length, trunk length, and ear area—choosing a suitable similarity measure requires careful consideration of the nature of the data. This paper discusses the appropriate similarity measure for such multivariate, continuous data, along with justifications and special circumstances influencing this choice.

Choosing the Appropriate Similarity Measure

For the set of attributes measured in Asian elephants, the primary goal is to evaluate how similar or dissimilar individual elephants are based on their measurements. The attributes are continuous variables, and they likely vary in scale—weight in kilograms, height in meters, tusk length in centimeters, etc. Typically, measures of similarity for such data include Euclidean distance, Manhattan distance, and other metric-based measures outlined in Section 2.4 of our course materials.

Euclidean Distance as the Preferred Measure

Given the continuous and scaled nature of the attributes, Euclidean distance is a natural choice for measuring similarity. It computes the straight-line distance between two points in multi-dimensional space:

Distance = √∑ (xi - yi)^2

This measure captures the overall difference across all attributes and is widely used in clustering algorithms such as k-means, hierarchical clustering, and others. Its geometric interpretation aligns intuitively with the notion of similarity—smaller Euclidean distances indicate greater similarity.

Standardization and Scaling Considerations

Before applying Euclidean distance, it is essential to address the differences in scales across attributes. For example, ear area might be in square centimeters, while tusk length might be in centimeters. If these are not normalized, attributes with larger ranges will disproportionately influence the similarity measure. To mitigate this, standardization techniques—such as z-score normalization—are applied to rescale attributes to have zero mean and unit variance, ensuring each attribute contributes equally to the distance calculation.

Special Circumstances and Exceptions

Despite the suitability of Euclidean distance, certain scenarios may necessitate alternative measures:

  • Presence of Categorical Attributes: If other attributes are categorical rather than continuous, measures such as Hamming or Jaccard distances would be more appropriate.
  • Outliers: Extreme values can heavily influence Euclidean distances. In such cases, robust measures like Manhattan distance or utilizing trimmed or robust normalization may be preferred.
  • Domain Knowledge: If certain attributes are deemed more biologically significant, a weighted Euclidean distance can be employed, assigning specific weights to attributes based on their importance.

Conclusion

In conclusion, for comparing elephants based on continuous measurements such as weight, height, tusk length, trunk length, and ear area, the Euclidean distance, coupled with proper data normalization, offers a suitable similarity measure. It aligns well with the geometric intuition of multivariate data and is computationally efficient. Adjustments and alternative measures should be considered based on data peculiarities such as outliers, attribute types, and domain-specific importance.

References

  • Han, J., Kamber, M., & Pei, J. (2012). Data Mining Concepts and Techniques. Morgan Kaufmann.
  • Duda, R. O., Hart, P. E., & Stork, D. G. (2001). Pattern Classification. Wiley-Interscience.
  • Mitchell, T. M. (1997). Machine Learning. McGraw-Hill.
  • Cover, T., & Thomas, J. (2006). Elements of Information Theory. Wiley-Interscience.
  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.
  • Han, J., & Kamber, M. (2006). Data Mining: Concepts and Techniques. Morgan Kaufmann.
  • Everitt, B. S., Landau, S., Leese, M., & Stahl, D. (2011). Cluster Analysis. Wiley.
  • Jain, A. K., Murty, M. N., & Flynn, P. J. (1999). Data Clustering: A Review. ACM Computing Surveys.
  • Sneath, P. H. A., & Sokal, R. R. (1973). Numerical Taxonomy. Freeman.
  • Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics.

Related Assignments