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Data Analytics Super-Summary — Cheat Sheet

Scan time: ~10 minutes. Vital concepts only.

Ch1 — Data & Attribute Types

Stevens' 4 Measurement Scales

Scale Order? Equal Intervals? True Zero? Example Operations
Nominal No No No Gender, Color, ZIP =, !=
Ordinal Yes No No Rankings, Grades A-F =, !=, <, >
Interval Yes Yes No Temperature (C/F) +, -, mean, std
Ratio Yes Yes Yes Weight, Height, Age all ops, ratios OK

Key rule: You can always go DOWN the scale (treat ratio as ordinal) but never UP.

Dataset Types

Type Structure Example
Record/Matrix Rows = objects, Cols = attrs Spreadsheet, CSV
Document Term-frequency vectors Bag-of-words
Transaction Sets of items per record Shopping baskets
Graph Nodes + edges Social networks, Web
Ordered Sequence / time-series Stock prices, sensor logs

Discrete vs Continuous

  • Discrete: countable values (number of children, dice roll)
  • Continuous: measurable on a real line (height, temperature)

Ch2 — Descriptive Statistics (Univariate & Bivariate)

Location Measures

Measure Formula / Definition Notes
Mode Most frequent value Can be multiple; use for nominal
Median Middle value (sorted) Robust to outliers
Mean sum(xi) / n Sensitive to outliers
Q1 25th percentile
Q3 75th percentile
IQR Q3 - Q1 Middle 50% spread

Dispersion Measures

Measure Formula Notes
Range max - min Very sensitive to outliers
IQR Q3 - Q1 Robust
MAD mean( xi - median
Variance sum((xi - mean)^2) / (n-1) Sample variance
Std Dev sqrt(variance) Same units as data

Skewness

Positive skew:  long tail to the RIGHT   =>  mean > median > mode
Symmetric:      bell-shaped              =>  mean = median = mode
Negative skew:  long tail to the LEFT    =>  mean < median < mode

Boxplot

  [min*]  Q1 [====median====] Q3  [max*]
            |<------ IQR ----->|

Whiskers: lower = Q1 - 1.5*IQR,  upper = Q3 + 1.5*IQR
Outliers: points beyond whiskers (plotted individually)

Bivariate Statistics

Measure Formula Range
Covariance sum((xi-xbar)(yi-ybar)) / (n-1) (-inf,+inf)
Pearson r cov(X,Y) / (sx * sy) [-1, +1]
Spearman rho Pearson r computed on RANKS of X and Y [-1, +1]
  • r = +1: perfect positive linear; r = -1: perfect negative; r = 0: no linear correlation
  • Spearman: use when data is ordinal OR relationship is monotone but not linear

Ch3 — Descriptive Statistics (Multivariate)

Summary Matrices

Matrix Size Diagonal Symmetry Content
Location matrix 7 x p N/A No min/Q1/med/mean/mode/Q3/max per column
Covariance matrix p x p variances Symmetric cov(Xi, Xj)
Correlation matrix p x p all 1s Symmetric Pearson r(Xi, Xj)

Key Multivariate Plots

Plot Best for
Scatter matrix All pairwise relationships at once
Parallel coordinates Each object = polyline; spot clusters/outliers
Star/Radar chart One polygon per object; compare profiles
Chernoff faces Encode attributes as facial features; detect groups
Heatmap + dendrogram Similarity structure; combined with clustering

Ch4 — Data Preprocessing

Missing Values

Strategy When to use
Remove row Few missing, dataset large enough
Fill with mean Numeric, symmetric distribution
Fill with median Numeric, skewed distribution
Fill with mode Nominal attribute
Fill with per-class mean When class label is known

Discretization (Numeric -> Bins)

Equal-width:  W = (max - min) / N    (bins have equal range)
Equal-depth:  sort, then N/k objects per bin  (bins have equal count)

Encoding Categorical -> Numeric

Method k categories -> Example (Low/Med/High)
One-hot k binary cols 100 / 010 / 001
Gray code log2(k) bits 00 / 01 / 11
Thermometer k-1 bits 00 / 10 / 11

Normalization

Min-max:  v' = (v - min) / (max - min) * (new_max - new_min) + new_min
          Typical new range: [0, 1]

Z-score:  v' = (v - mu) / sigma
          Result: mean=0, std=1

Always normalize before computing Euclidean distance.

Distance Metrics

Metric Formula Notes
Euclidean sqrt(sum((xi-yi)^2)) Standard; sensitive to scale
Manhattan sum( xi-yi
Minkowski (sum( xi-yi
Hamming count of positions where xi!=yi For strings/bit vectors
Edit/Levenshtein min insertions/deletions/substitutions For strings

Ch5 — Clustering

K-Means

1. Choose K initial centroids (random or K-means++)
2. Assign each object to nearest centroid
3. Recompute centroids as mean of assigned objects
4. Repeat steps 2-3 until assignments don't change
SSE = sum over all objects of dist(object, its_centroid)^2
Elbow method: plot SSE vs K; pick K at the "elbow"

K-means++: next centroid chosen with probability proportional to dist^2 from nearest existing centroid — better initial placement, faster convergence.

Hierarchical (Agglomerative)

Start: each object is its own cluster
Repeat: merge the two closest clusters
Stop: when one cluster remains (or desired K reached)
Linkage Distance(A,B) = Behavior
MIN (Single) min dist between any pair Chaining effect; elongated
MAX (Complete) max dist between any pair Compact, roughly equal size
Average mean dist between all pairs Compromise
Ward minimize increase in SSE after merge Usually best; similar to K-means

DBSCAN

Parameters: Eps (radius), MinPts (density threshold)
Core point:   has >= MinPts neighbors within Eps
Border point: within Eps of a core point, but not core itself
Noise point:  neither core nor border
- Handles arbitrary cluster shapes - Automatically finds number of clusters - Robust to outliers (labeled as noise)

Comparing Clustering Methods

Method Need K? Shape Outliers Complexity
K-means Yes Spherical Sensitive O(nKiter)
Hierarchical No* Any Sensitive O(n^2) or O(n^2 log n)
DBSCAN No Arbitrary Robust O(n log n)

Ch6 — Frequent Pattern Mining

Key Definitions

Support(X)       = |transactions containing X| / |total transactions|
Confidence(X->Y) = support(X union Y) / support(X)
Lift(X->Y)       = confidence(X->Y) / support(Y)
Lift value Meaning
> 1 Positive correlation (buy together more than chance)
= 1 Independent
< 1 Negative correlation

Apriori Algorithm

  • Anti-monotone property: if itemset X is infrequent, ALL supersets of X are infrequent
  • Algorithm: generate candidate k-itemsets from frequent (k-1)-itemsets, prune using anti-monotone
  • Weakness: multiple database scans, large candidate sets

FP-Growth Algorithm

  • Build compact FP-tree (prefix tree of transactions)
  • Mine conditional pattern bases — no candidate generation
  • Faster than Apriori, especially for dense/long patterns
  • Requires only 2 database scans

Itemset Types

Type Definition
Frequent support >= min_support
Maximal frequent Frequent and NO frequent superset exists
Closed frequent Frequent and NO superset with SAME support exists

Relationship: Maximal ⊂ Closed ⊂ Frequent

Association Rules Summary

  • Generate rules from frequent itemsets
  • Prune by min_confidence
  • Rank by lift to find most interesting rules

Ch7 — Classification

Decision Trees

Entropy:   H(S) = -sum(pi * log2(pi))     (0 = pure, 1 = max impurity for 2 classes)
Info Gain: IG(S,A) = H(S) - sum(|Sv|/|S| * H(Sv))   for each split value v
GainRatio: IG / SplitInfo    (penalizes attributes with many values)

Gini:      Gini(S) = 1 - sum(pi^2)
Split:     choose attribute/value minimizing weighted Gini of children

k-Nearest Neighbors (k-NN)

1. Normalize all features (min-max or z-score)
2. For test object: compute Euclidean distance to all training objects
3. Find k nearest neighbors
4. Predict: majority class among k neighbors
- Larger k: smoother boundary, less overfitting, but may underfit - k=1: exact fit to training, prone to overfitting - No training phase (lazy learner)

Naive Bayes

P(C|X) proportional to P(C) * product(P(xi|C))

Numeric features: Gaussian NB
  P(x|C) = (1 / (sigma * sqrt(2*pi))) * exp(-0.5 * ((x - mu) / sigma)^2)

Categorical features: frequency table
  P(xi=v|C) = count(xi=v in class C) / count(class C)

Laplace smoothing: add 1 to counts to avoid zero probabilities
  P(xi=v|C) = (count + 1) / (total + k)  where k = number of distinct values

Evaluation Metrics

Confusion Matrix:
              Predicted +    Predicted -
Actual +         TP              FN
Actual -         FP              TN

Accuracy  = (TP + TN) / (TP + TN + FP + FN)
Precision = TP / (TP + FP)      -- "of predicted positive, how many actually positive?"
Recall    = TP / (TP + FN)      -- "of actual positive, how many did we catch?"
F1        = 2 * Precision * Recall / (Precision + Recall)

k-Fold Cross-Validation

1. Split dataset into k equal folds
2. For i = 1 to k:
     train on all folds except fold i
     test on fold i
     record accuracy
3. Final accuracy = average of k accuracies
- Reduces variance of evaluation estimate - k=10 is standard; k=n is leave-one-out (LOO-CV)

"When to Use What" — Decision Guide

Task / Situation Recommended Method Key Parameter(s)
Explore distribution of one variable Histogram, boxplot Bin width
Find outliers Boxplot (IQR rule) 1.5*IQR threshold
Measure linear relationship Pearson r —
Measure monotone (non-linear) relationship Spearman rho —
Visualize all pairwise relationships Scatter matrix —
Compare multivariate profiles Parallel coordinates / radar —
Handle missing numeric values Fill with mean or per-class mean Class label available?
Handle missing nominal values Fill with mode —
Scale before distance-based methods Min-max normalization New range [0,1]
Scale for statistical methods Z-score normalization —
Cluster: known K, spherical clusters K-means K, max_iter
Cluster: unknown K, hierarchical view Hierarchical (Ward linkage) Linkage type
Cluster: arbitrary shapes, with noise DBSCAN Eps, MinPts
Find item co-occurrence rules Apriori or FP-growth min_support, min_confidence
Dense transactions, long patterns FP-growth (faster) min_support
Classify: interpretable model Decision Tree (ID3/C4.5) max_depth, min_samples
Classify: no training time needed k-NN k, distance metric
Classify: fast, works with small data Naive Bayes Laplace smoothing
Evaluate classifier robustly k-Fold Cross-Validation k (usually 10)
Imbalanced classes: measure performance Precision, Recall, F1 (not accuracy) —
Attribute selection for decision tree Information Gain / Gain Ratio Threshold

End of Super-Summary