Data Science
Portfolio
by Sarah Silva

This decision tree was trained on the Titanic dataset using caret::train() with method="rpart" and complexity parameter cp=0.02.

How to read it: Start at the top node — the first split is on Sex (male ≥ 0.5). Going left means the condition is TRUE (male passengers), going right means FALSE (female passengers).

Key splits: Male passengers are further split by Age (<13 = children, more likely to survive) and SibSp (siblings aboard). Female passengers are split by Pclass and Fare — women in 1st/2nd class had >90% survival rates. This tree achieved 84.9% accuracy on the test set.

This error bar plot shows the average rating (± standard error) for each genre combination with more than 1,000 ratings in the MovieLens dataset.

Key finding: Comedy has the lowest average rating (3.27 stars), while Comedy|Romance and Drama|War top the chart near 4.0 stars. The error bars are small, indicating high confidence in these estimates.

This confirms a genre bias effect — knowing the genre combination of a film helps predict how it will be rated. This is an important feature for recommendation system models.

Weekly average movie ratings from 1995 to 2017, with a LOESS smoother (blue line) showing the trend over time.

Key finding: Ratings started higher (~3.7) in the mid-1990s and gradually declined to ~3.5 by 2017, with the LOESS curve showing a mild but consistent downward trend. This suggests a small but real temporal effect on ratings.

This supports including a time component f(d_u,i) in the recommendation system model — where d_u,i represents the date user u rated movie i.

Scatter plot of average rating against ratings per year for films released in 1993 or later, with a GAM smoother.

Key finding: There is a clear positive relationship — movies that are rated more frequently also tend to receive higher average ratings. This is not because being popular makes a film better, but because popular films attract more ratings from viewers who already liked them.

This popularity bias is important for recommendation systems: missing ratings for unpopular films should be filled with a value below the overall average to account for this effect.

Boxplot showing the distribution of total ratings per film, grouped by release year, with a square root transformation on the y-axis.

Key finding: Films from around 1995 have the highest median number of ratings. The distribution rises from the 1970s, peaks around 1993–1996, then declines for more recent films — simply because newer films have had less time to accumulate ratings.

This confirms the recency bias: newer films appear less popular not because they are worse, but because fewer users have had time to watch and rate them.

This heatmap shows the V matrix from the Singular Value Decomposition of a 100-student × 24-subject grade dataset (8 Math, 8 Science, 8 Arts tests).

How to read it: Each column is a right singular vector (principal direction in feature space). The colors represent the magnitude and direction of each feature's contribution — red = positive, blue = negative.

Key finding: The first column is nearly constant across all subjects — meaning PC1 captures overall ability. The second column shows a contrast between Arts vs. Math/Science. The third differentiates Math from Science. Together, 3 components explain 98.8% of variance.

Heatmap of correlations between all 24 subject scores (8 Math, 8 Science, 8 Arts), where red = positive correlation and blue = negative.

Key finding: There are three visible blocks of high correlation — one per subject group. Within each block (e.g., Math 1 through Math 8), correlations are very high. Between Math and Science, correlations are moderate. Between Arts and Math/Science, correlations are weaker.

This structure motivates using SVD/PCA to capture these patterns efficiently — rather than working with all 24 variables individually.

Raw grade matrix visualization: 100 students (rows, top = best) × 24 subjects (columns: 8 Math, 8 Science, 8 Arts). Red = high score (A+), blue = low score (F), white = average (C).

Key finding: The clear gradient from red (top) to blue (bottom) shows that overall student ability drives most of the variation. The three visible column groupings confirm that subject-level effects (Math vs. Science vs. Arts) are real but secondary.

This visual motivates SVD — students who do well tend to do well across all subjects, which is exactly what PC1 (overall ability) captures.

Boxplots of the first 10 principal components, grouped by tumor type: B = Benign, M = Malignant.

Key finding: PC1 is the only component where the IQRs do not overlap between B and M groups — malignant tumors have consistently higher PC1 values. All other PCs (PC2–PC10) show overlapping distributions, meaning they carry much less discriminatory power.

This confirms that PC1 (explaining 44.3% of variance) is the most diagnostically relevant dimension — and explains why KNN achieved 97.4% accuracy on scaled features that emphasize this separation.

Scatter plot of the first two principal components for all 569 BRCA biopsy samples. Pink = Benign (B), Teal = Malignant (M).

Key finding: The two groups are clearly separated along the PC1 axis (horizontal). Malignant tumors (teal) occupy higher PC1 values, while Benign tumors (pink) cluster at lower PC1 values. PC2 provides some additional separation but less dramatically.

This visualization is powerful: it shows that just two numbers per patient (their PC1 and PC2 scores) are enough to distinguish most cancer cases from benign ones — a key insight for dimensionality reduction in medical diagnostics.